research on football betting

• How To Research For a Football Bet: 5 Things To Look For

Building a successful strategy for football betting can be a real challenge. Even if you do manage to achieve it, this doesn’t mean you will just place bets and collect your winnings. Constant effort is required and there are certain steps in the preparation for each bet that just can’t be ignored.

How to Study Football Betting

The research before each football match is the key to success, as it’s the only way to get a good evaluation of what’s to be expected.

Depending on the markets you choose, there might be plenty of details, but the basis remains the same most of the time.

Let’s cover the aspects of how to analyse football matches for betting. They won’t instantly make you a winner, but it’s a huge step in the right direction.

1. Check the Performance of Both Teams Over a Long Period

This is an obvious step and yet, somehow plenty of people underestimate its importance. The long-term performance of both teams involved is the best way to get a good idea of their average performance. There is a reason the legendary Bill Shankly once said: “form is temporary, class is permanent”. Certain bookies like bet365 will under-price a well known team, just because punters assume they’ll win. Sometimes a side like Man Utd may always struggle away to Sunderland, but the bookies don’t reflect this in their odds – they want to suck people in that just jump on the big named teams.

The exact time frame depends on what you are looking for, but the minimum should be around a couple of months or even a year. This will give you a good start and a platform to build on when you go into more details later.

The important questions here are how does the team perform in terms of goals scored, goals conceded, playing home or away (depending on the game), results against teams similar to the next opponent and many more valid points that should be considered.

2. Check the Short-Term Trends

After you have a good understanding of the bigger picture, it’s time to dig deeper and see what is the current shape of both teams. As we know, confidence is key in football and certain players can look like world beaters one day and like Sunday league amateurs the next. That makes short-term trends extremely important.

Take a look at the last 5-10 games of each team, this should be enough to show you what to expect. Once again, stats such as goals scored, goals conceded, average possession and form of the best players are the things you should be looking for. It’s a good idea to actually read a short match report for each of the games in case you haven’t watched them. You never know if a team was just unlucky with some near misses, wonder goals conceded or referee mistakes.

3. Team News Is Essential

Almost every punter out there knows that you should check the list of suspended, injured and doubtful players. The problem of most people is that they don’t fully evaluate the influence of the absentees. A certain player can be badly missed against certain opposition and easily compensated against another. For example, a team missing its best centre back could struggle against an attacking-minded opponent and do well against a side that prefers to sit back.

WhoScored.com has a great section in their match previews that highlights current injuries and suspensions

Of course, you should also take a look who’s going to replace the missing players. How did their subs perform the last time they played? Are they just bench-warmers or squad players that get enough minutes to be in good shape? Those questions and many more need to be answered.

There is another aspect that is often ignored. The schedule of both teams is essential, as nowadays the number of games played per season demands rotation. This is especially true for the English Premier League due to the lack of a winter break. Check the last couple of games of each team and what’s coming next. It should give you a good idea if the manager will start his strongest line-up or try to rotate a bit.

4. Previous Meetings Between the Two Teams

The next step would be to check how both teams performed against each other in the past. The last couple of games are the most telling, but the historical data shouldn’t be underestimated. Certain fierce rivalries such as the North London Derby between Tottenham and Arsenal, for example, has its own rules and the game often does not depend on form as much.

There is another important thing you might notice – certain teams or even certain players sometimes have a good streak against a specific opposition. Plenty of examples can be seen in the English Premier League where Sunderland is on a great streak against the local rival Newcastle in the past couple of years. The Magpies are also the favorite opponent for Arsenal’s striker Olivier Giroud who is scoring against them on a regular basis.

5. Listen to the Experts

Nowadays, you can find so many opinions on the Internet that could be pretty overwhelming. Most of them would just confuse you and can’t contribute much to your analysis. Still, there are certain experts that could be useful. Whether is successful punters or well-known journalists, there are people who are good at analyzing and predicting football matches.

We don’t recommend you to directly copy someone else’s opinion, but taking your time to read a preview is not a bad idea. Seeing a different perspective could confirm your own expectations or show you an angle you might have missed.

List of Soccer Analysis Websites

After we went through the most important steps you have to take in your preparation, it’s time to list some useful websites that can help you in this regard. Most of them will provide you the necessary data:

SoccerStats.Com

Oddsportal.com.

One of the best free odds comparison services in the business. You will find the best prices for almost any football match out there. It has all the important markets and then some more. On top of that, there are plenty of stats, betting tools, a reliable live score service and even tipsters who provide picks. It’s pretty much the full package.

The OLBG community is probably the biggest when it comes to betting. The platform has many useful features including free tournaments with real prizes, hundreds of successful tipsters and much more. One of the best things is that it’s not limited to football only, so you could check it for other sports as well.

Make your list of things to look for when betting on football

Consider this article as your starter pack for how to bet on football . It’s not enough, but it’s a pretty solid beginning. We strongly encourage you to build on it by finding your own ways for an even better evaluation of the matches you are willing to bet on. Also, there are so many reliable websites and services out there, that you should spend some time checking what can be useful to you.

Mike has over 14 years of experience with online sports betting, having used countless online betting sites. Mike previously provided football betting tips on goals and corners in Facebook groups before starting his own betting website. A huge football fan, Mike has been writing betting guides and football betting advice for years.

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Open Access

Peer-reviewed

Research Article

A statistical theory of optimal decision-making in sports betting

Roles Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Visualization, Writing – original draft, Writing – review & editing

* E-mail: [email protected]

Affiliation Dept of Biomedical Engineering, City College of New York, New York, NY, United States of America

• Jacek P. Dmochowski

• Published: June 28, 2023
• https://doi.org/10.1371/journal.pone.0287601
• Peer Review
• Reader Comments

The recent legalization of sports wagering in many regions of North America has renewed attention on the practice of sports betting. Although considerable effort has been previously devoted to the analysis of sportsbook odds setting and public betting trends, the principles governing optimal wagering have received less focus. Here the key decisions facing the sports bettor are cast in terms of the probability distribution of the outcome variable and the sportsbook’s proposition. Knowledge of the median outcome is shown to be a sufficient condition for optimal prediction in a given match, but additional quantiles are necessary to optimally select the subset of matches to wager on (i.e., those in which one of the outcomes yields a positive expected profit). Upper and lower bounds on wagering accuracy are derived, and the conditions required for statistical estimators to attain the upper bound are provided. To relate the theory to a real-world betting market, an empirical analysis of over 5000 matches from the National Football League is conducted. It is found that the point spreads and totals proposed by sportsbooks capture 86% and 79% of the variability in the median outcome, respectively. The data suggests that, in most cases, a sportsbook bias of only a single point from the true median is sufficient to permit a positive expected profit. Collectively, these findings provide a statistical framework that may be utilized by the betting public to guide decision-making.

Citation: Dmochowski JP (2023) A statistical theory of optimal decision-making in sports betting. PLoS ONE 18(6): e0287601. https://doi.org/10.1371/journal.pone.0287601

Editor: Baogui Xin, Shandong University of Science and Technology, CHINA

Received: December 19, 2022; Accepted: June 8, 2023; Published: June 28, 2023

Copyright: © 2023 Jacek P. Dmochowski. This is an open access article distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Data Availability: Data is available at https://github.com/dmochow/optimal_betting_theory .

Funding: The author received no specific funding for this work.

Competing interests: The authors have declared that no competing interests exist.

Introduction

The practice of sports betting dates back to the times of Ancient Greece and Rome [ 1 ]. With the much more recent legalization of online sports wagering in many regions of North America, the global betting market is projected to reach 140 billion USD by 2028 [ 2 ]. Perhaps owing to its ubiquity and market size, sports betting has historically received considerable interest from the scientific community [ 3 ].

A topic of obvious relevance to the betting public, and one that has also been the subject of multiple studies, is the efficiency of sports betting markets [ 4 ]. While multiple studies have reported evidence for market inefficiencies [ 5 – 11 ], others have reached the opposite conclusion [ 12 , 13 ]. The discrepancy may signify that certain, but not all, sports markets exhibit inefficiencies. Research into sports betting has also revealed insights into the utility of the “wisdom of the crowd” [ 14 – 16 ], the predictive power of market prices [ 17 – 20 ], quantitative rating systems [ 21 , 22 ], and the important finding that sportsbooks exploit public biases to maximize their profits [ 13 , 23 ].

Indeed, the decisions made by sportsbooks to set the offered odds and payouts have been previously analyzed [ 13 , 23 , 24 ]. On the other hand, arguably less is known about optimality on the side of the bettor . The classic paper by Kelly [ 25 ] provides the theory for optimizing betsize (as a function of the likelihood of winning the bet) and can readily be applied to sports wagering. The Kelly bet sizing procedure and two heuristic bet sizing strategies are evaluated in the work of Hvattum and Arntzen [ 26 ]. The work of Snowberg and Wolfers [ 27 ] provides evidence that the public’s exaggerated betting on improbable events may be explained by a model of misperceived probabilities. Wunderlich and Memmert [ 28 ] analyze the counterintuitive relationship between the accuracy of a forecasting model and its subsequent profitability, showing that the two are not generally monotonic. Despite these prior works, idealized statistical answers to the critical questions facing the bettor, namely what games to wager on, and on what side to bet, have not been proposed. Similarly, the theoretical limits on wagering accuracy, and under what statistical conditions they may be attained in practice, are unclear.

To that end, the goal of this paper is to provide a statistical framework by which the astute sports bettor may guide their decisions. Wagering is cast in probabilistic terms by modeling the relevant outcome (e.g. margin of victory) as a random variable. Together with the proposed sportsbook odds, the distribution of this random variable is employed to derive a set of propositions that convey the answers to the key questions posed above. This theoretical treatment is complemented with empirical results from the National Football League that instantiate the derived propositions and shed light onto how closely sportsbook prices deviate from their theoretical optima (i.e., those that do not permit positive returns to the bettor).

Importantly, it is not an objective of this paper to propose or analyze the utility of any specific predictors (“features”) or models. Nevertheless, the paper concludes with an attempt to distill the presented theorems into a set of general guidelines to aid the decision making of the bettor.

Problem formulation: “Point spread” betting

For positive s (home team favored), the home team is said to “cover the spread” if m > s , whereas the visiting team has “beat the spread” otherwise. Conversely, for negative s (visiting team favored), the visiting team covers the spread if m < s , and the home team has beat the spread otherwise. The home (visiting) team is said to win “against the spread” if m − s is positive (negative).

Denote the profit (on a unit bet) when correctly wagering on the home and visiting teams by ϕ h and ϕ v , respectively. Assuming a bet size of b placed on the home team, the conventional payout structure is to award the bettor with b (1 + ϕ h ) when m > s . The entire wager is lost otherwise. The total profit π is thus bϕ h when correctly wagering on the home team (− b otherwise). When placing a bet of b on the visiting team, the bettor receives b (1 + ϕ v ) if m < s and 0 otherwise. Typical values of ϕ h and ϕ v are 100/110 ≈ 0.91, corresponding to a commission of 4.5% charged by the sportsbook.

In practice, the event m = s (termed a “push”) may have a non-zero probability and results in all bets being returned. In keeping with the modeling of m by a continuous random variable, here it is assumed that P ( m = s ) = 0. This significantly simplifies the development below. Note also that for fractional spreads (e.g. s = 3.5), the probability of a push is indeed zero.

Wagering to maximize expected profit.

Consider first the question of which team to wager on to maximize the expected profit. As the profit scales linearly with b , a unit bet size is assumed without loss of generality.

Corollary 1 . Assuming equal payouts for home and visiting teams ( ϕ h = ϕ v ), maximization of expected profit is achieved by wagering on the home team if and only if the spread is less than the median margin of victory .

A subtle but important point is that knowledge of which side to bet on for each match is insufficient for maximizing overall profit. The reason is that even if wagering on the side with higher expected profit, it is possible (and in fact quite common, see empirical results below) that the “optimal” wager carries a negative expectation. Thus, an understanding of when wagering should be avoided altogether is required. This is the subject of the theorem below.

It is instructive to consider the conditions above for typical values of ϕ h and ϕ v . When wagering on the home team with ϕ h = 0.91, positive expectation requires the spread to be no larger than the 0.476 quantile of m . When wagering on the visiting team, the spread must exceed the 0.524 quantile. This means that, if the spread is contained within the 0.476-0.524 quantiles of the margin of victory, wagering should be avoided . Practically, it is thus important to obtain estimates of this interval and its proximity to the median score in units of points .

The result of Theorem 2 is reminiscent of the “area of no profitable bet” scenario described in [ 28 ]. Whereas the latter result is presented in terms of outcome probabilities estimated by the bettor and the sportsbook, Theorem 2 here delineates the conditions under which the sportsbook’s point spread assures a negative expectation on the bettor’s side.

Optimal estimation of the margin of victory.

Theorem 3 . Define an “error” as a wager that is placed on the team that loses against the spread. The probability of error is bounded according to : min{ F m ( s ), 1 − F m ( s )} ≤ p (error) ≤ max{ F m ( s ), 1 − F m ( s )}.

The result of Theorem ( 8 ) provides both the best- and worst-case scenario of a given wager. When F m ( s ) is close to 1/2, both the minimum and maximum error rates are near 50%, and wagering is reduced to an event akin to a coin flip. On the other hand, when the true median is far from the spread (i.e., F m ( s ) deviates from 1/2), the minimum and maximum error rates diverge, increasing the highest achievable accuracy of the wager.

Optimality in “moneyline” wagering

Corollary 4 . Define an “error” as a wager that is placed on the team that loses the match outright. The probability of error in moneyline wagering is bounded according to : min{ F m (0), 1 − F m (0)} ≤ p (error) ≤ max{ F m (0), 1 − F m (0)}.

Notice that optimal decision-making in moneyline wagers requires knowledge of quantiles that may be near 0 (if ϕ v ≫ ϕ h ) or near 1 (if ϕ h ≫ ϕ v ). More subtly, the required quantiles will differ for matches that exhibit different payout ratios. For example, a match with two even sides will require knowledge of central quantiles, while a match with a 4:1 favorite will require knowledge of the 80th and 20th percentiles. The implications of this property on quantitative modeling are described in the Discussion .

The moneyline wagering considered in this section is a two-alternative bet that is popular in North American sports. In European betting markets, the most common type of wager is the three-alternative “Home-Draw-Away” bet where there is no point spread and the task of the bettor is to forecast one of the three potential outcomes: m > 0, m = 0, or m < 0, each of which are endowed with a payout (see, for example, [ 26 , 29 , 30 ]). Clearly the the probability p ( m = 0) will be non-zero in this context. As a result, the methodology here, which models m by a continuous random variable, cannot be straightforwardly applied to the case of the Home-Draw-Away bet. The extension of the present findings to the case of multi-way bets with discrete m is a potential topic of future research.

Optimality in “over-under” betting

The following two results may be proven by replacing m with τ , ϕ h with ϕ o , and ϕ v with ϕ u in the Proofs of Theorems 1 and 2, respectively.

In the special case of ϕ o = ϕ u , one should bet on the over only if and only if the sportsbook total τ falls below the median of t .

Define F t ( τ ) as the CDF of the true point total evaluated at the sportsbook’s proposed total. The following corollary may be proven by following the Proof of Theorem 3.

Corollary 8 . Define an “error” in over-under betting as a wager that is placed on the “over” when t < τ or on the “under” when t > τ. The probability of error is bounded according to : min{ F t ( τ ), 1 − F t ( τ )} ≤ p (error) ≤ max{ F t ( τ ), 1 − F t ( τ )}.

Empirical results from the National Football League

In order to connect the theory to a real-world betting market, empirical analyses utilizing historical data from the National Football League (NFL) were conducted. The margins of victory, point totals, sportsbook point spreads, and sportsbook point totals were obtained for all regular season matches occurring between the 2002 and 2022 seasons ( n = 5412). The mean margin of victory was 2.19 ± 14.68, while the mean point spread was 2.21 ± 5.97. The mean point total was 44.43 ± 14.13, while the mean sportsbook total was 43.80 ± 4.80. The standard deviation of the margin of victory is nearly 7x the mean, indicating a high level of dispersion in the margin of victory, perhaps due to the presence of outliers. Note that the standard deviation of a random variable provides an upper bound on the distance between its mean and median [ 31 ], which is relevant to the problem at hand.

To estimate the distribution of the margin of victory for individual matches, the point spread s was employed as a surrogate for θ . The underlying assumption is that matches with an identical point spread exhibit margins of victory drawn from the same distribution. Observations were stratified into 21 groups ranging from s o = −7 to s o = 10. This procedure was repeated for the analysis of point totals, where observations were stratified into 24 groups ranging from t o = 37 to t o = 49.

How accurately do sportsbooks capture the median outcome?

It is important to gain insight into how accurately the point spreads proposed by sportsbooks capture the median margin of victory. For each stratified sample of matches, the median margin of victory was computed and compared to the sample’s point spread. The distribution of margin of victory for matches with a point spread s o = 6 is shown in Fig 1a , where the sample median of 4.34 (95% confidence interval [2.41,6.33]; median computed with kernel density estimation to overcome the discreteness of the margin of victory; confidence interval computed with the bootstrap) is lower than the sportsbook point spread. However, the sportsbook value is contained within the 95% confidence interval.

• PPT PowerPoint slide
• PNG larger image
• TIFF original image

( a ) The distribution of margin of victory for National Football League matches with a consensus sportsbook point spread of s = 6. The median outcome of 4.26 (dashed orange line, computed with kernel density estimation) fell below the sportsbook point spread (dashed blue line). However, the 95% confidence interval of the sample median (2.27-6.38) contained the sportsbook proposition of 6. ( b ) Same as (a), but now showing the distribution of point total for all matches with a sportsbook point total of 46. Although the sportsbook total exceeded the median outcome by approximately 1.5 points, the confidence interval of the sample median (42.25-46.81) contained the sportsbook’s proposition. ( c ) Combining all stratified samples, the sportsbook’s point spread explained 86% of the variability in the median margin of victory. The confidence intervals of the regression line’s slope and intercept included their respective null hypothesis values of 1 and 0, respectively. ( d ) The sportsbook point total explained 79% of the variability in the median total. Although the data hints at an overestimation of high totals and underestimation of low totals, the confidence intervals of the slope and intercept contained the null hypothesis values.

https://doi.org/10.1371/journal.pone.0287601.g001

Aggregating across stratified samples, the sportsbook point spread explained 86% of the variability in the true median margin of victory ( r 2 = 0.86, n = 21; Fig 1c ). Both the slope (0.93, 95% confidence interval [0.81,1.04]) and intercept (-0.41, 95% confidence interval [-1.03,0.16]) of the ordinary least squares (OLS) line of best fit (dashed blue line) indicate a slight overestimation of the margin of victory by the point spread. This is most apparent for positive spreads (i.e., a home favorite). Nevertheless, the confidence intervals of both the slope and intercept did include the null hypothesis values of 1 and 0, respectively. The data for all sportsbook point spreads with at least 100 matches is provided in Table 1 .

Regular season matches from the National Football League occurring between 2002-2022 were stratified according to their sportsbook point spread. Each set of 3 grouped rows corresponds to a subsample of matches with a common sportsbook point spread. The “level” column indicates whether the row pertains to the 95% confidence interval (0.025 and 0.975 quantiles) or the mean value across bootstrap resamples. The dependent variables include the 0.476, 0.5, and 0.524 quantiles, as well as the expected profit of wagering on the side with higher likelihood of winning the bet for hypothetical point spreads that deviate from the median outcome by 1, 2, and 3 points, respectively.

https://doi.org/10.1371/journal.pone.0287601.t001

The distribution of observed point totals for matches with a sportsbook total of τ = 46 is shown in Fig 1b , where the computed median of 44.45 (95% confidence interval [42.25,46.81]) is suggestive of a slight overestimation of the true total. Combining data from all samples, the sportsbook point total explained 79% of the variability in the median point total ( r 2 = 0.79, n = 24; Fig 1d ).

Interestingly, the data hints at the sportsbook’s proposed point total underestimating the true total for relatively low totals (i.e., black line is below the blue for sportsbook totals below 43), while overestimating the total for those matches expected to exhibit high scoring (i.e., black line is above the blue line for sportsbook totals above 43). Note, however, that the confidence intervals of the regression line (slope: [0.72,1.02], intercept: [-1.14, 12.05]) did contain the null hypothesis values. The data for all sportsbook point total with at least 100 samples is provided in Table 2 .

Matches were stratified into 24 subsamples defined by the value of the sportsbook total. The dependent variables are the 0.476, 0.5, and 0.524 quantiles of the true point total, as well as the expected profit of wagering conditioned on the amount of bias in the sportsbook’s total.

https://doi.org/10.1371/journal.pone.0287601.t002

Do sportsbook estimates deviate from the 0.476-0.524 interval?

In the common case of ϕ = 0.91, a positive expected profit is only feasible if the point spread (or point total) is either below the 0.476 or above the 0.524 quantiles of the outcome’s distribution. It is thus interesting to consider how often this may occur in a large betting market such as the NFL. To that end, the 0.476 and 0.524 quantiles of the margin of victory were estimated in each stratified sample (horizontal bars in Fig 2 ; the point spread is indicated with an orange marker; all quantiles are listed in Table 1 ).

With a standard payout of ϕ = 0.91, achieving a positive expected profit is only feasible if the sportsbook point spread falls outside of the 0.476-0.524 quantiles of the margin of victory. The 0.476 and 0.524 quantiles were thus estimated for each stratified sample of NFL matches. Light (dark) black bars indicate the 95% confidence intervals of the 0.476 (0.524) quantiles. Orange markers indicate the sportsbook point spread, which fell within the quantile confidence intervals for the large majority of stratifications. An exception was s = 5, where the sportsbook appeared to overestimate the margin of victory. For two other stratifications ( s = 3 and s = 10), the 0.524 quantile tended to underestimate the sportsbook spread, with the 95% confidence intervals extending to just above the spread.

https://doi.org/10.1371/journal.pone.0287601.g002

For the majority of samples, the confidence intervals of the 0.476 and 0.524 quantiles contained the sportsbook spread. One exception was the spread s = 5, where the margin of victory fell below the sportsbook value (95% confidence interval of the 0.524 quantile: [0.87,4.85]). The margin of victory for s = 3 (95% confidence interval of the 0.524 quantile: [0.78,3.08]) and s = 10 (95% confidence interval of the 0.524 quantile: [6.42,10.06]) also tended to underestimate the sportsbook spread, with the confidence intervals just containing the sportsbook value.

The analysis was repeated for point totals ( Fig 3 , all quantiles listed in Table 2 ). All but one stratified sample exhibited 0.476 and 0.524 quantiles whose confidence intervals contained the sportsbook total ( t = 47, [41.59, 45.42]). Examination of the sample quantiles suggests that NFL sportsbooks are very adept at proposing point totals that fall within 2.4 percentiles of the median outcome.

The 0.476 and 0.524 quantiles of the true point total were estimated for each stratified sample of NFL matches. For all but one stratification ( t = 47, 95% confidence interval [41.59-45.42], sportsbook overestimates the total), the confidence intervals of the sample quantiles contained the sportsbook proposition. Visual inspection of the data suggests that, in the NFL betting market at least, sportsbooks are very adept at proposing totals that fall within the critical 0.476-0.524 quantiles.

https://doi.org/10.1371/journal.pone.0287601.g003

How large of a discrepancy from the median is required for profit?

In practice, it is desirable to have an understanding of how large of a sportsbook bias, in units of points, is required to permit a positive expected profit. To address this, the value of the empirically measured CDF of the margin of victory was evaluated at offsets of 1, 2, and 3 points from the true median in each direction. The resulting value was then converted into the expected value of profit (see Materials and Methods ). The computation was performed separately within each stratified sample, and the height of each bar in Fig 4 indicates the hypothetical expected profit of a unit bet when wagering on the team with the higher probability of winning against the spread . For the sake of clarity, only the four largest samples ( s ∈ {−3, 2.5, 3, 7}) are shown in the Figure, with data for all samples listed in Table 1 .

In order to estimate the magnitude of the deviation between sportsbook point spread and median margin of victory that is required to permit a positive profit to the bettor, the hypothetical expected profit was computed for point spreads that differ from the true median by 1, 2, and 3 points in each direction. The analysis was performed separately within each stratified sample, and the figure shows the results of the four largest samples. For 3 of the 4 stratifications, a sportsbook bias of only a single point is required to permit a positive expected return (height of the bar indicates the expected profit of a unit bet assuming that the bettor wagers on the side with the higher probability of winning; error bars indicate the 95% confidence intervals as computed with the bootstrap). For a sportsbook spread of s = 3 (dark black bars), the expected profit on a unit bet is 0.021 [0.008-0.035], 0.094 [0.067-0.119], and 0.166 [0.13-0.2] when the sportsbook’s bias is +1, +2, and +3 points, respectively (mean and confidence interval over 500 bootstrap resamples).

https://doi.org/10.1371/journal.pone.0287601.g004

The expected profit is negative (i.e., ( ϕ − 1)/2 = −0.045) when the spread equals the median (center column). Interestingly however, for 3 of the 4 largest stratified samples, a positive profit is achievable with only a single point deviation from the median in either direction (the confidence intervals indicated by error bars do not extend into negative values). Averaged across all n = 21 stratifications, the expected profit of a unit bet is 0.022 ± 0.011, 0.090 ± 0.021, and 0.15 ± 0.030 when the spread exceeds the median by 1, 2, and 3 points, respectively (mean ± standard deviation over n = 21 stratifications, each of which is an average over 1000 bootstrap ensembles). Similarly, the expected return is 0.023 ± 0.013, 0.089 ± 0.026, and 0.15 ± 0.037 when the spread undershoots the median by 1, 2, and 3 points respectively. This indicates that sportsbooks must estimate the median outcome with high precision in order to prevent the possibility of positive returns.

The analysis was repeated on the data of point totals. A deviation from the true median of only 1 point was sufficient to permit a positive expected profit in all four of the largest stratifications ( Fig 5 ; t ∈ {41, 43, 44, 45}; error bars indicate 95% confidence intervals; data for all samples is provided in Table 2 ). When the sportsbook overestimates the median total by 1, 2, and 3 points, the expected profit on a unit bet is 0.014 ± 0.0071, 0.073 ± 0.014, and 0.13 ± 0.020, respectively (mean ± standard deviation over n = 24 samples, each of which is a average over 1000 bootstrap resamples). When the sportsbook underestimates the median, the expected profit on a unit bet is 0.015±0.0071, 0.076± 0.014, and 0.14± 0.020, for deviations of 1, 2, and 3 points, respectively. Note that despite the dependent variable having a larger magnitude (compared to margin of victory), the required sportsbook error to permit positive profit is the same as shown by the analysis of point spreads.

Vertical axis depicts the expected profit of an over-under wager, conditioned on the sportsbook’s posted total deviating from the true margin by a value of 1, 2, or 3 points (horizontal axis). The analysis was performed separately for each unique sportsbook total, and the figure displays the results for the four largest samples. A deviation from the true median of a single point permits a positive expected profit in all four of the depicted groups. For a sportsbook total of t = 44 (green bars), the expected profit on a unit bet is 0.015 [0.004-0.028], 0.075 [0.053-0.10], and 0.13 [0.10-0.17] when the sportsbook’s bias is +1, +2, and +3 points, respectively (mean and confidence interval over 500 bootstrap resamples).

https://doi.org/10.1371/journal.pone.0287601.g005

The theoretical results presented here, despite seemingly straightforward, have eluded explication in the literature. The central message is that optimal wagering on sports requires accurate estimation of the outcome variable’s quantiles. For the two most common types of bets—point spread and point total—estimation of the 0.476, 0.5 (median), and 0.524 quantiles constitutes the primary task of the bettor (assuming a standard commission of 4.5%). For a given match, the bettor must compare the estimated quantiles to the sportsbook’s proposed value, and first decide whether or not to wager ( Theorem 2 ), and if so, on which side ( Theorem 1 ).

The sportsbook’s proposed spread (or point total) effectively delineates the potential outcomes for the bettor ( Theorem 3 ). For a standard commission of 4.5%, the result is that if the sportsbook produces an estimate within 2.4 percentiles of the true median outcome, wagering always yields a negative expected profit— even if consistently wagering on the side with the higher probability of winning the bet . This finding underscores the importance of not wagering on matches in which the sportsbook has accurately captured the median outcome with their proposition. In such matches, the minimum error rate is lower bounded by 47.6%, the maximum error rate is upper bounded by 52.4%, and the excess error rate ( Theorem 4 ) is upper bounded by 4.8%.

The seminal findings of Kuypers [ 13 ] and Levitt [ 23 ], however, imply that sportsbooks may sometimes deliberately propose values that deviate from their estimated median to entice a preponderance of bets on the side that maximizes excess error. For example, by proposing a point spread that exaggerates the median margin of victory of a home favorite, the minimum error rate may become, for example, 45% (when wagering on the road team), and the excess error rate when wagering on the home team is 10%. In this hypothetical scenario, the sportsbook may predict that, due to the public’s bias for home favorites, a majority of the bets will be placed on the home team. The empirical data presented here hint at this phenomenon, and are in alignment with previous reports of market inefficiencies in the NFL betting market [ 5 , 32 – 35 ]. Namely, the sportsbook point spread was found to slightly overestimate the median margin of victory for some subsets of the data ( Fig 2 ). Indeed, the stratifications showing this trend were home favorites, agreeing with the idea that the sportsbooks are exploiting the public’s bias for wagering on the favorite [ 23 ].

The analysis of sportsbook point spreads performed here indicates that only a single point deviation from the true median is sufficient to allow one of the betting options to yield a positive expectation. On the other hand, realization of this potential profit requires that the bettor correctly, and systematically, identify the side with the higher probability of winning against the spread. Forecasting the outcomes of sports matches against the spread has been elusive for both experts and models [ 6 , 36 ]. Due to the abundance of historical data and user-friendly statistical software packages, the employment of quantitative modeling to aid decision-making in sports wagering [ 37 ] is strongly encouraged. The following suggestions are aimed at guiding model-driven efforts to forecast sports outcomes.

The argument against binary classification for sports wagering

The minimum error and minimum excess error rates defined in Theorems 3 and 4, respectively, are analogous to the Bayes’ minimum risk and Bayes’ excess risk in binary classification [ 38 ]. Indeed, one can cast the estimation of margin of victory in sports wagering as a binary classification problem, aiming to predict the event of “the home team winning against the spread”. Here this approach is not advocated. In conventional binary classification, the target variable (or “class label”) is static and assumed to represent some phenomenon (e.g. presence or absence of an object). In the context of sports wagering, however, the event m > s need not be uniform for different matches. For example, the event of a large home favorite winning against the spread may differ qualitatively from that of a small home “underdog” winning against the spread. Moreover, the sportsbook’s proposed point spread is a dynamic quantity. To illustrate the potential difficulty of utilizing classifiers in sports wagering, consider the case of a match with a posted spread of s = 4, where the goal is to predict the sign of m − 4. But now imagine that the the spread moves to s = 3. The resulting binary classification problem is now to predict the sign of m − 3, and it is not straightforward to adapt the previously constructed classifier to this new problem setting. One may be tempted to modify the bias term of the classifier, but it is unclear by how much it should be adjusted, and also whether a threshold adjustment is in fact the optimal approach in this scenario. On the other hand, by posing the problem as a regression, it is trivial to adapt one’s optimal decision: the output of the regression can simply be compared to the new spread.

The case for quantile regression

Conventional ordinary least-squares (OLS) regression yields estimates of the mean of a random variable, conditioned on the predictors. This is achieved by minimizing the mean squared error between the predicted and target variable.

The findings presented here suggest that conventional regression may be a sub-optimal approach to guiding wagering decisions, whose optimality relies on knowledge of the median and other quantiles. The presence of outliers and multi-modal distributions, as may be expected in sports outcomes, increases the deviation between the mean and median of a random variable. In this case, the dependent variable of conventional regression is distinct from the median and thus less relevant to the decision-making of the sports bettor. The significance of this may be exacerbated by the high noise level on the target random variable, and the low ceiling on model accuracy that this imposes.

Therefore, a more suitable approach to quantitative modeling in sports wagering is to employ quantile regression, which estimates a random variable’s quantiles by minimizing the quantile loss function [ 39 ]. Any features that are expected to forecast sports outcomes could be provided as the predictors in a quantile regression to produce estimates that are aligned with the bettor’s objectives: to avoid wagering on matches with negative expectation for both outcomes, and to wager on the side with zero excess error.

Potential challenges in moneyline wagering

Bias-variance in sports wagering

The view that low variance implies “simple” models has recently been challenged in the context of artificial neural networks [ 41 ]. Nevertheless, the desire for low-variance, high-bias modeling in sports wagering does suggest the preference for simpler models. Thus, it is advocated to employ a limited set of predictors and a limited capacity of the model architecture. This is expected to translate to improved generalization to future data.

Sport-specific considerations

The three types of wagers considered in this work—point spread, moneyline, and over-under—are the most popular bet types in North American sports. The empirical analysis employed data from the National Football League (NFL). One unique aspect of American football is its scoring system, in which the points accumulated by each team increase primarily in increments of 3 or 7 points. The structure of the scoring imposes constraints on the distribution of the margin of victory m . For example, in American Football, the distribution of the margin of victory is expected to exhibit local maxima near values such as: ±3, ±7, ±10. In the case of games in the National Basketball Association (NBA), the most common margins of victory tend to occur in the 5-10 interval, reflecting the overall higher point totals in basketball and its most common point increments (2 and 3). As a result, the shape and quantiles of the distribution of m may vary qualitatively between the NBA and NFL.

As a final illustrative example of the importance of the quantiles of m , consider the hypothetical scenario of two American football teams playing a match whose parameters θ have been exactly matched three times previously. In those past matches, the outcomes were m = 3, m = 7, and m = 35. In this fictitious example, the median is 7 but the mean is 15. Now imagine that the point spread for the next match has been set to s = 10 (home team favored to win the match by 10 points). Assuming that one has committed to wagering on the match, the optimal decision is to bet on the visiting team, despite that fact that the home team has won the previous matches by an average of 15 points.

Materials and methods

All analysis was performed with custom Python code compiled into a Jupyter Notebook (available at https://github.com/dmochow/optimal_betting_theory ). The figures and tables in this manuscript may be reproduced by executing the notebook.

Empirical data

Historical data from the National Football League (NFL) was obtained from bettingdata.com , who has courteously permitted the data to be shared on the repository listed above. All regular season matches from 2002 to 2022 were included in the analysis ( n = 5412). The data set includes point spreads and point totals (with associated payouts) from a variety of sportsbooks, as well as a “consensus” value. The latter was utilized for all analysis.

Data stratification

In order to estimate quantiles of the distributions of margin of victory and point totals from heterogeneous data (i.e., matches with disparate relative strengths of the home and visiting teams), the sportsbook point spread and sportsbook point total were used as a surrogate for the parameter vector defining the identity of each individual match ( θ in the text). This permitted the estimation of the 0.476, 0.5, and 0.524 quantiles over subsets of congruent matches.

Only spreads or totals with at least 100 matches in the dataset were included, such that estimation of the median would be sufficiently reliable. To that end, data was stratified into 21 samples for the analysis of margin of victory: {-7, -6, -3.5, -3, -2.5, -2, -1, 1, 2, 2.5, 3, 3.5, 4, 4.5, 5, 5.5, 6, 6.5, 7, 7.5, 10) and 24 samples for the analysis of point totals (37, 37.5, 38, 39, 39.5, 40, 40.5, 41, 41.5, 42, 42.5, 43, 43.5, 44, 44.5, 45, 45.5, 46, 46.5, 47, 47.5, 48, 48.5, 49 }. This resulted in the employment of n = 3843 matches in the analysis of point spreads and n = 4300 matches in the analysis of point totals.

Note that the stratification process did not account for varying payouts, for example −110 versus −105 in the American odds system, as this would greatly increase the number of stratified samples while decreasing the number of matches in each sample. It is likely that the resulting error is negligible, however, due to the likelihood of the payout discrepancy being fairly balanced across the home and visiting teams.

Median estimation

In order to overcome the discrete nature of the margins of victory and point totals, kernel density estimation was employed to produce continuous quantile estimates. The KernelDensity function from the scikit-learn software library was employed with a Gaussian kernel and a bandwidth parameter of 2. For the margin of victory, the density was estimated over 4000 points ranging from -40 to 40. For the analysis of point totals, the density was estimated over 4000 points ranging from 10 to 90. The regression analysis relating median outcome to sportsbook estimates ( Fig 1 ) was performed with ordinary least squares (OLS).

Confidence interval estimation

In order to generate variability estimates for the 0.476, 0.5, and 0.524 quantiles of the margin of victory and point total, the bootstrap [ 42 ] technique was employed. 1000 resamples of the same size as the original sample were generated in each case. The confidence intervals were then constructed as the interval between the 2.5 and 97.5 percentiles of the relevant quantity. Bootstrap resampling was also employed to derive confidence intervals on the regression parameters relating the median outcomes to sportsbook spreads or totals ( Fig 1 ), as well as the confidence intervals on the expected profit of wagering conditioned on a fixed sportsbook bias (Figs 4 and 5 ).

Expected profit estimation

To model the idealized case of always placing the wager on the side with the higher probability of winning against the spread, the reported expected profit was taken as the maximum of the two expected values in ( 15 ). The analogous procedure was conducted for the analysis of point totals.

Acknowledgments

The author would like to thank Ed Miller and Mark Broadie for fruitful discussions during the preparation of the manuscript. The author would also like to acknowledge the effort of the reviewers, in particular Fabian Wunderlich, for providing many helpful comments and critiques throughout peer review.

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The Art and Science of Football Betting: A Comprehensive Guide

Understanding Football Betting

Strategies for successful football betting, responsible betting practices.

Football, the beautiful game, is not only a source of entertainment and passion but also a realm of opportunity for those who wish to engage in football betting. Betting on football matches has grown into a global industry, offering excitement, camaraderie, and, for some, a chance to turn their knowledge into profits. This article will take you on a journey through the intricate world of football betting, exploring its different aspects, strategies, and responsible practices.

Football betting, often referred to as sports betting, involves wagering on the outcome of football matches. While the concept may seem straightforward, there is a lot more to it than meets the eye. Here are some essential elements to understand. If you're looking for a reliable platform to kickstart your football betting journey, consider exploring onlinekladionice.com , where you'll find a wide range of betting markets and valuable insights to enhance your betting experience. This platform offers a seamless interface, competitive odds, and a community of passionate bettors who share tips and strategies, making it an excellent choice for both novice and experienced punters.

Betting Markets : Football betting offers a diverse range of markets, including match result (1X2), over/under goals, Asian handicaps, and countless others. Each market provides a different way to bet on the game.

Odds : Odds represent the bookmakers' assessment of a team's likelihood of winning or a particular event occurring. Understanding how odds work is crucial for making informed bets.

Bookmakers : Bookmakers are companies that provide platforms for individuals to place bets. Popular bookmakers include Bet365, William Hill, and Betfair.

Successful football betting requires a combination of knowledge, research, and discipline. Here are some strategies to help you make more informed decisions:

Research : In-depth research is the backbone of successful football betting. Analyze team statistics, form, injury reports, and historical performance to make informed predictions.

Bankroll Management : Set a budget for your betting activities and stick to it. Responsible bankroll management ensures you don't overspend and helps you avoid chasing losses.

Value Betting : Look for bets where the odds offered by bookmakers are higher than your assessment of the team's real probability of winning. This approach is known as value betting.

Specialize : Focus on specific leagues, teams, or betting markets. Becoming an expert in a niche area can give you an edge over the bookmakers.

Avoid Emotional Betting : Emotional betting can lead to impulsive decisions. Bet with your head, not your heart.

Stay Informed : Keep up with the latest news and developments in the world of football. Injuries, suspensions, and managerial changes can have a significant impact on match outcomes.

Football betting can be a fun and potentially profitable hobby when done responsibly. Here are some practices to keep in mind:

Set Limits : Establish daily, weekly, or monthly betting limits to prevent excessive gambling.

Avoid Chasing Losses : If you experience a losing streak, resist the urge to bet more to recover losses. Accept that losses are a part of betting.

Use Reputable Bookmakers : Choose well-established bookmakers with a strong reputation for fair play and transparent practices.

Self-Exclusion : Most bookmakers offer self-exclusion options for individuals who feel they are losing control. Utilize these features if necessary.

Seek Help : If you believe your gambling is becoming a problem, seek assistance from support organizations or professionals who specialize in gambling addiction.

Football betting can be a thrilling and potentially profitable pastime for those who approach it with knowledge, discipline, and responsibility. Understanding the various betting markets, employing strategies, and adhering to responsible betting practices are crucial for an enjoyable and sustainable experience. For those seeking exciting adventures in the world of football betting, it's important to remember that while it can add an extra layer of excitement to the game, it should be viewed as entertainment, not as a guaranteed way to make money. Always bet responsibly and within your means to ensure your betting adventures remain enjoyable and sustainable.

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• Published: 17 December 2021

In-play forecasting in football using event and positional data

• Maximilian Klemp 1   na1 ,
• Fabian Wunderlich 1   na1 &
• Daniel Memmert 1  

Scientific Reports volume  11 , Article number:  24139 ( 2021 ) Cite this article

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Two highly relevant aspects of football, namely forecasting of results and performance analysis by means of performance indicators, are combined in the present study by analysing the value of in-play information in terms of event and positional data in forecasting the further course of football matches. Event and positional data from 50 matches, including more than 300 million datapoints were used to extract a total of 18 performance indicators. Moreover, goals from more than 30,000 additional matches have been analysed. Results suggest that surprisingly goals do not possess any relevant informative value on the further course of a match, if controlling for pre-game market expectation by means of betting odds. Performance indicators based on event and positional data have been shown to possess more informative value than goals, but still are not sufficient to reveal significant predictive value in-play. The present results are relevant to match analysts and bookmakers who should not overestimate the value of in-play information when explaining match performance or compiling in-play betting odds. Moreover, the framework presented in the present study has methodological implications for performance analysis in football, as it suggests that researchers should increasingly segment matches by scoreline and control carefully for general team strength.

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Introduction

Forecasting of results 1 , 2 and performance analysis using event and positional data 3 , 4 are two highly relevant and highly topical strands of research with regard to data-driven analysis in the game of football. However, until now, event and positional data have surprisingly not been used in the context of in-play forecasting models in football. The present paper presents a framework for a joint evaluation of both aspects, as well as empirical evidence on the usability of in-play information for forecasting purposes.

Event data and positional data from football matches aim at capturing all events and movements on the pitch and are comprehensively studied in sports science 5 , 6 . Event data provides a detailed and ordered sequence of all the player’s actions during the match, such as passes, shots, or tackles 7 . Although efforts to automatically detect events from video 8 or positional data 9 are undertaken, the most reliable and most widely used approach remains to be manual annotation by expert video analysts, supported by human and computer-based quality control 10 , 11 , 12 . Each event is described by the time and location where the action took place on the field as well as the event type. Depending on the data provider, additional information such as a subtype or the outcome of the event is given. By aggregating event data to count-based metrics, the technical performance of players or teams in a match can be assessed and related to indicators of success. Recent contributions followed this approach to establish player evaluation frameworks 10 , 11 , 13 , 14 . In match analysis research, metrics derived from event data have been utilized to explain teams’ success in a match 3 , 15 throughout a season 16 , 17 , 18 , and to examine playing styles 19 .

Positional data, sometimes also referred to as tracking data, reflects information on the x/y-coordinates of all players and the ball at each observed point in time (usually 25 frames per second). In football, positional data in training is mostly gathered by Global Positioning Systems or Local Positioning Systems. In contrast, match positional data is tracked by recording video data with multiple cameras from several positions and applying computer vision algorithms and triangulation to get the players’ and ball’s positions 20 . Positional data has been used to examine players’ activity profiles with respect to playing positions 21 or success over a season 22 , reporting the distance covered or efforts undertaken. Besides these physical parameters, tactical analyses by means of positional data have scrutinized the teams’ positioning on the field and, following from that, tried to quantify the space controlled by players and teams 23 . Here, a particular area is considered under the control of a player if that player can reach any point in that area before anyone else. These efforts resulted in the proposal of the pitch control parameter 24 , which has since been the subject of further research 25 . While event data is relatively widely available and notable amounts of data have been published 10 , 11 , tracking data is less available and, therefore, recent research using tracking data has mostly considered only small sample sizes 14 .

Another aspect of event and positional data, that is relevant to bookmakers and match analysts, but has not been tackled so far, is the value of such data in forecasting further success. The literature on forecasting in football (for an overview, see 1 , 2 is driven by the idea of developing and testing models with the intention to estimate the outcomes of matches in advance. Mathematically, this includes efforts to find models that accurately reflect the inherent processes in football matches, such as Poisson models, (Koopman, et al. 26 ; Maher 27 ), regression models 28 , 29 , birth process models 30 or, more recently, increasingly machine learning methods 31 .

The interest in research on football forecasting, however, is also driven by economic considerations, such as understanding the mechanisms of the sports betting market 32 , 23 , 34 or financially profiting from it by identifying profitable betting strategies 26 , 35 . The sports betting market “has been the subject of considerable structural change caused by the growth of Internet betting alternatives to traditional bookmakers” 33 , which, according to the authors, implied an increasing competitive pressure resulting in more accurate bookmaker forecasts. A more recent significant change in the betting market is the increased importance of in-play betting, which refers to bets placed during a football match in progress. However, the forecasting literature does not seem to have kept pace with this development, as the question of effective in-play forecasting in football has not been sufficiently addressed. To the best of our knowledge, the work of Zou et al. 36 as well as the work of Robberechts et al. 37 are the only articles focussing precisely on this topic so far. While both studies adopted a Bayesian approach to predict the further course of a match based on in-play information, they do not report, how valuable in-play information is for forecasting the outcome of the match, compared to a baseline of pre-game expectation.

The deduction of in-play forecasting models from existing pre-play models is relatively straight forward, as the existing models and given pre-game information can simply be transferred to an adjusted remaining match time. However, the crucial question of genuine in-play forecasting is whether information from the previous course of the match is valuable to improve upon forecasts based on pre-game information. Zou et al. 36 claim promising results in this regard, while other statistical investigations of football matches suggest that in-play effects on goal scoring (i.e. deviations from constant scoring rates), if existent, can be considered very small 38 , 39 . While the previously mentioned analyses relied solely on the information of goals during matches, data-richer in-match information based on event and positional data has the potential to possess a higher value in in-play forecasting.

The present paper thus contributes to an improved understanding of the extent to which event and positional data can be valuable in in-play forecasting of football matches. Specifically, it shall be examined, whether previously used models can be meaningfully improved by introducing indicators extracted from these data as predictors. While event and position data have been shown to possess value in describing teams’ performance on the one hand and in-play information has been used to forecast the further course of a match on the other, to the best of our knowledge, this is the first paper to focus on combining both these strands of research in football analysis.

The data used for the present analysis consists of two separate datasets. This approach was chosen because the number of matches for which position and event data are available is limited, while more fundamental information is accessible for a much higher number of matches. In this way, it was possible to establish a reliable baseline of the predictive value of widely available indicators, before testing the added value of position and event data against this baseline. The first dataset includes matches from 10 seasons (07/08–16/17) in 10 of the strongest European football leagues (first divisions of England, Spain, Germany, Italy, France, Portugal, Belgium, Turkey, Netherlands and Greece). For each match, the number of goals scored by each team in each half as well as average betting odds for the outcomes home, draw, away, over 2.5 goals and under 2.5 goals are available. This results in a total dataset of 31,912 matches and is split into five seasons of in-sample data (15,844 matches) and five seasons of out-of-sample data (16,068 matches) for analysis. Data have been obtained from https://football-data.co.uk .

The second dataset consists of position data and event data from 50 matches from the German Bundesliga in the season 2014/2015. The matches used stemmed from 31 distinct matchdays in the season, and 11 different teams played in these matches. For these 50 matches, positional data had been gathered through a semiautomatic optical tracking system (VISTRACK, by Impire Corp., Germany) at a sampling rate of 25 Hz. The measurement error of this system in tracking players’ positions (expressed as root mean squared error) was shown to be less than one meter for different activities 40 . Event data was gathered by manual video tagging of matches, followed by automated and manual post-processing 41 . The inter-operator reliability of this method was shown to be very good for the number of team events detected (with kappa values of 0.86 to 0.94) and individual events (Intra-class correlation of 0.96 to 0.99) 41 . The final event dataset consisted of 77,671 events (on average 1,553 ± 95 events per match), while the position dataset in total spanned 7,004,231 rows and 46 columns (x- and y-coordinates of 22 players and the ball; on average 140,085 ± 2406 rows per match) which results in a total of more than 300 million data points. These numbers indicate the high volume and complexity of the data used, which on the one hand, result in a high amount of information, on the other hand, in considerable challenges in the aggregation to indicators on the match level. Following the volume and complexity of the data produced during a football match, handling these can be termed an endeavour in Big Data analysis.

The study was approved by the local ethics committee at the German Sport University Cologne (DSHS 093/2017) and fully complies with the guidelines stated in the Declaration of Helsinki.

Performance indicators

Technical indicators.

Several, count-based indicators of technical performance were extracted from event data per team per half. Following previous work 3 , 16 , 17 , 42 , the numbers of shots, passes, short passes, long passes, crosses, throw-ins and clearances were gathered.

Physical indicators

From positional data, different indicators of physical performance were calculated. For both teams and both halves, we collected total running distance 21 , running distance covered while the team is in possession of the ball and running distance covered while the team is not in possession of the ball 22 . Unlike previous papers, we normalized the distance covered in and out of possession by dividing it through the time spent in and out of possession for both teams, respectively, in order to avoid a confounding effect of overall ball possession rates. We also calculated high-speed running distance (distance covered at speeds higher than 14.4 \(\frac{km}{h}\) ) based on commonly used velocity thresholds 21 .

Tactical indicators

Furthermore, indicators of tactical performance were extracted from positional data utilising pitch control models and ball metrics. We calculated the area of the pitch controlled by both teams during the two halves. The area controlled per player was computed following the methods described by Kim 24 and, to account for different pitch sizes, calculated the relative space on the pitch controlled by both teams. We computed space control on the whole pitch as well as space control in the defensive third, midfield third and attacking third for both teams, respectively 43 . Additionally, ball possession rates per team were extracted 3 and, for the first time, we also extracted the distance travelled by the ball during both teams’ possession (normalized by the teams’ time in possession).

An overview of all performance indicators and their abbreviations can be found in Table 1 .

Statistical framework

General idea of in-play forecasting.

The idea of in-play forecasting is to use information getting available over the course of a match to forecast the further course of this particular match. In the present study, the value of information becoming available during the first half to forecast the outcome of the second half of the match is tested. To design a statistical framework that honestly tests for in-play forecasting, some points need to be considered. First, the subject of forecasting is not the final outcome of a match, but only the isolated outcome of the second half. If the halftime score is 3–0, the home team naturally has a highly improved probability of winning the match, and the halftime result will help improve the forecast for the outcome drastically. However, this is just a direct consequence of the current scoreline and not what we consider to be in-play forecasting. If the information of the halftime score of 3–0 implies that the home team also has a high probability of winning the second half, this would be valuable information for in-play forecasting. Second, the model needs to control for pre-game expectation as even before the match, the isolated outcome of the second half can be modelled and forecasted. We only consider the first half to have actual value for in-play forecasting if the first half adds additional value to the current pre-game expectation for the second half.

Forecasting accuracy

The first dataset covering a large sample size is used to test the ability of pre-game information (betting odds) and the most basic in-play information (goals in the first half) to forecast the outcome of the second half in terms of home win, draw and away win. Framing the outcome of the match with respect to these categories is a common procedure in forecasting 29 , 31 , 35 since the betting market is structured likewise and the home advantage is already taken into account in this way. Five different models are compared, including two simple benchmark models as well as three ordered logistic regression models. The model UNI uses a uniform forecast of 33.33% for the three possible outcomes for each match, while the model FRQ uses the observed frequency of the three outcomes in the in-sample data as the forecast for each match in the out-of-sample data. Moreover, three different ordered logistic regression models are fitted in-sample using the second half result as the dependent variable. The model PROB uses the probability of a home win and the probability of an away win as obtained from the betting odds as the independent variables (see Wunderlich and Memmert 44 for the calculation used to obtain probabilities from betting odds). The model GOAL uses the goal difference at the end of the first half (i.e. the halftime result) as the independent variable, and the model BOTH uses both the probabilities and the goal difference. These three fitted ordered logistic regression models are then used to forecast the outcomes in the out-of-sample dataset. For more information on UNI and FRQ as benchmark models as well as on using ordered logistic regression for forecasting outcomes in football, we refer to Hvattum and Arntzen 29 .

In summary, the five models represent different levels and types of information, namely no information at all (UNI), only football-specific, but no match specific information (FRQ), only in-play information from the first half (GOAL), only pre-game information (PROB) or both pre-game and in-play information (BOTH). The forecasting accuracy of all five models is measured utilising the widely used rank probability score 45 , and the accuracy of various models is compared by performing a paired t-test for each pair of these models.

Correlation analysis

On the one hand, event and positional data contain an incredible wealth of data points per match, as has already been outlined before. On the other hand, the number of available matches with positional data is limited, in particular, if compared to the almost unlimited availability of pure match results in terms of goals. This small sample size is a challenge, which is even intensified by the fact that very different match outcomes in terms of goals (i.e. 5–1 and 1–0) are assigned to the same category of a home win, and as such, the outcome in terms of home win, draw and away win is even more prone to randomness. For this reason, the above method cannot simply be applied to the complete set of performance indicators. Moreover, we would like to get a better understanding of the interaction of the performance indicators with overall team strength and the course of the match, as well as the ability of these indicators to explain and forecast success. Therefore, a correlation analysis including four different correlation coefficients is performed for each performance indicator.

We denote \({p}_{H}\) and \({p}_{A}\) as the probability for the home and the away team to win the match as obtained from the betting odds. Based on the fact that betting odds have an excellent predictive value in football 29 , 31 , 33 , 46 , these probabilities can be utilised as a highly accurate measure of relative team strength 47 . The performance indicators are denoted as \({i}_{H}^{x}\) for the home team and \({i}_{A}^{x}\) for the away team, where \(x=1\) represents the first half and \(x=2\) represents the second half. Analogously, the number of goals scored by each team are denoted as \({g}_{H}^{x}\) and \({g}_{A}^{x}\) .

As a minimum requirement to assume predictive power in a performance indicator, it should in some way be related to immediate success or expected success (i.e. team strength), which is tested by two measures.

Strength dependence

Strength dependence is defined as:

which means that the correlation between the strength difference and the difference in the respective performance indicator with respect to the first half is calculated. Thus, a high positive correlation coefficient means that there is a strong connection between the strength of a team (i.e. the expected success) and the respective performance indicator.

Explanatory power

Explanatory power is defined as:

which means that the correlation between the respective performance indicator and the number of goals, both with respect to the first half is calculated. By doing this, the relationship between a performance indicator and the success of a team in the same half (i.e. the immediate success) can be tested. This approach is a standard approach in performance analysis in football to measure the importance of performance indicators 48 , however, it can be highly confounded by the course of a match, which means that it remains unclear whether the performance indicator explains success or is just the consequence of the current scoreline and the teams' resulting tactical approaches.

In addition, two measures of predictive performance are introduced, as a relation to team strength or success does not necessarily imply predictive value. Therefore, the connection between performance measures in the first half and success in the second half is analysed.

Predictive power

Predictive power is defined as:

which is similar to the explanatory power, but uses the outcome of the second half, which has two advantages. First, it is possible that a positive performance in the first half is connected to success in the first half, but not to the performance and success in the second half. Second, when comparing across different halves, we circumvent the problem mentioned above that the outcome of the first half is highly associated with the scoreline throughout the first half.

Predictive overperformance

Predictive power already comes close to the idea of in-play forecasting; however, it still does not control for pre-game information on the team strengths. If we assume that stronger teams are more successful across the whole match and show a higher performance concerning a particular performance indicator across the entire match, this would imply a positive value for the predictive performance. In order to test for the real value of the first half information in terms of in-play forecasting, the approach needs to control for the pre-game expectation. This is done by calculating an expectation for goals and performance indicators based on the pre-game winning probabilities.

The expected values of the performance indicator for the first half are denoted as \(E\_{i}_{H}^{1}\) for the home team and \(E\_{i}_{A}^{1}\) for the away team and analogously for the expected goals \(E\_{g}_{H}^{2}\) and \(E\_{g}_{A}^{2}\) in the second half. To estimate these numbers, we use these four expectations as dependent variables in regression models and use the probability of a home win, the probability of an away win and the probability of over 2.5 goals as independent variables. Count variables (SHOT, PASS, SPASS, LPASS, CROSS, THROW, CLEAR, FOUL) are modelled by Poisson regressions, while other variables are modelled by linear regressions (RD, RD_IP, RD_OOP, RD_HS, BD). For those variables representing a percentage (BP, SC, SC_DEF, SC_MID, SC_ATT), only \(E\_{i}_{H}^{1}\) needs to be calculated while the expectation of the away team is consequently \({E\_}_{{i}_{A}^{1}}=1-E\_{i}_{H}^{1}\) . Please note that in slight variation to this formula, the expectation of SC_DEF for one team is calculated as the counterpart to the expectation of SC_ATT for the other team and vice versa. The regression for goals is not fitted based on the dataset of 50 matches but on the larger in-sample dataset of 15,844 matches.

The predictive overperformance is then defined as:

which means that the overperformance with regard to the performance indicator in the first half is correlated to the overperformance in terms of goals in the second half. In case of a highly positive correlation, this measure is evidence that a high performance with regard to the performance indicator has predictive value for the second half, even if controlling for team strength.

Descriptive statistics

Descriptive statistics for all performance indicators, including mean, standard deviation, minimum and maximum for home and away teams, are summarized in Table 2 .

Table 3 illustrates results for the accuracy of five models in forecasting the outcomes of the second half.

As expectable, UNI has the worst predictive accuracy and is significantly outperformed by FRQ showing the second-worst result. Both naïve benchmark models are significantly outperformed by the three logistic regression models. Surprisingly, based on the first half goals, GOAL only mildly improves the forecasting accuracy of the benchmark model FRQ and is massively outperformed by PROB based on betting odds. This means that the betting odds reflecting the pre-game expectation possess a far higher predictive value than the goals reflecting basic in-play information. The model BOTH even fails to significantly outperform PROB, which means that when controlling for pre-game information, the in-game information in terms of goals seems not valuable for in-play forecasting at all. This is evidence that either in-play forecasting is hardly possible in general or that goals are too noisy and random-affected to gain sufficient value. The performance indicators will help to answer whether in-play forecasting becomes possible through the use of more sophisticated measures.

To provide a basis for comparison for the analysis of performance indicators, the correlation analysis was also performed for the number of goals. The strength dependence is 0.34, which is evidence for the obvious fact that stronger teams score more goals. Simultaneously, it demonstrates the relatively high randomness in goals that prevents an even more explicit connection. The explanatory power of goals is 1.00 being a direct consequence of the definition. The predictive power is 0.10, while the predictive overperformance is − 0.03, which is in line with the above results. It suggests some weak predictive power, which, however, almost completely disappears if controlling for team strength.

Table 4 reports the four correlation coefficients for each of the 18 performance indicators. Additionally, Fig.  1 illustrates the predictive value of the different performance indicators by showing how the correlation coefficients change when using the different measures of association examined.

Correlation coefficients in the four measures of association for all performance indicators examined. Top panel shows technical performance indicators, middle panel shows tactical performance indicators and bottom panel shows physical performance indicators. Dashed horizontal line indicates a correlation coefficient of 0. Please refer to Method for a detailed description of the measures and performance indicators.

A variety of performance indicators are found to have a significant relationship to team strength. This refers to shots, passes, short passes as well as the ball distance and the four indicators of space control. The highest non-significant correlations are found for ball possession, crosses, clearances as well as running distance, out-of-possession running distance, and high-speed running distance. While most of the performance indicators are positively correlated, some exceptions show negative values. One example is running distance, which means that weaker teams generally need to run more than stronger teams. This is in line with previous research showing that more successful teams are covering less distance 49 . At first glance, it might come as a surprise that some performance indicators have an even higher correlation than the goals that—by definition—should be the clearest indicator of success. However, this can be easily explained by the fact that these performance indicators occur more frequently than goals 50 , 51 and thus are less susceptible to randomness.

Results with regard to the explanatory power underline the problem of using this approach. Significant positive relationships are now found for long passes and clearances and significant negative relationships for throw-ins and high-speed running distance. For several performance indicators the direction or magnitude of effects seem to be in conflict with the strength dependence, which is very likely to be a reason of the confounding influence of the current scoreline. For example, clearances as an action taken in defence and under high pressure are rather performed by weak teams. At the same time, clearances are negatively correlated to the immediate success in that half, which can be assumed to be driven by more defensive tactics of teams currently leading.

With regard to the predictive power and predictive overperformance, promising results are found for passes, short passes, ball possession and ball distance. While passes and short passes are significant with regard to the predictive power at a 10% level, all variables fail to reach significance with regard to the predictive overperformance. However, if compared to goals, those performance indicators have higher correlations and seem to be more promising for in-play forecasting purposes.

The present study has presented a framework to distinguish more clearly between strength, performance and success in football. This framework is useful to analyse the predictive value of in-play information, but also revealed several insights related to performance analysis in football. The major result in this regard is the remarkable differences between strength dependence, explanatory power and predictive power for the majority of variables. Two different aspects can be considered responsible for this result and, at the same time, illustrate the highly misleading character of the common use of explanatory power in performance analysis.

First, performance indicators might rather reflect the general team strength than the specific performance in the respective match. This is corroborated by the finding that no performance indicator revealed a statistically significant relationship with regard to predictive overperformance (the correlation between a team’s performance in the first half and goals scored in the second half controlled for a priori expectation of team strength). At the same time, the team strength (known before the match) shows statistically significant correlations with many variables related to the teams’ performance. In conclusion , the result that the teams’ in-play performance is suitable for both explaining and predicting goal-scoring success, can be attributed in large part to the teams’ overall strength. This team strength, which is already known before the start of the match, affects both the teams’ performance and their success in scoring goals. Therefore, it might act as a strongly confounding variable on the relationship between performance and success.

Second, performance indicators that should serve as an explanation for the result might, in fact, rather be a consequence of the current result (i.e., the scoreline). The scoreline is known to have a substantial impact on technical 52 , 53 and physical performance 54 and consequently a correlation between performance and success within a half or a match can either be explained by performance affecting the success or by scoreline (i.e. past success) affecting performance. To solve this issue, performance analysis should attempt to break down a match into smaller segments to control for the effect of the scoreline on both performance and success.

In summary, both team strength and scoreline appear to be important contextual factors affecting independent and dependent variables within a match analysis framework. Accordingly, performance analysts in football should take care to carefully control for the effect of both variables. As a prerequisite for this, matches should ideally be segmented into sequences of respectively equal scorelines prior to statistical analyses.

With regard to forecasting, the present study has presented the theoretical idea of in-play forecasting including an empirical analysis based on a variety of performance indicators. Theoretically, we have argued that in-play forecasting models need to control carefully for pre-game expectation, in order to genuinely quantify the predictive value of in-play information. The presented approach makes use of pre-game betting odds, which are known to possess an exceptionally high predictive value 29 , 33 , 46 . The analysis of goals revealed that betting odds before the match are far more accurate in forecasting the second half of football matches than the outcome of the first half. More strikingly, goals in the first half did not add any significant value to a forecasting model for the second half, once controlling for pre-game betting odds. To ensure that the forecasting accuracy results are not affected by the choice of statistical methods, we checked their robustness against the accuracy measure and inference test choice. No relevant changes to the results and conclusions occurred when applying ignorance scores instead of rank probability scores 55 or bootstrapping methods 56 instead of t-tests. In summary, the results suggest that goals do not enable conclusions to be drawn about the further course of a match and as such, are not sufficient information for in-play forecasting.

To gain insights into the question of whether the process of football matches is inherently unsuitable for in-play forecasting or goals are just a too noisy source of information, several technical, physical and tactical performance indicators based on event and positional data were analysed. This idea is consistent with a line of research in performance analysis in football aiming to find more suitable performance indicators than goals 4 , 14 . Results revealed some promising performance indicators, in particular passes, short passes, ball possession and ball distance. Still none of these parameters revealed significant predictive overperformance, which is further evidence for the difficulty of in-play forecasting, but at the same time can be considered a consequence of the limited number of matches with event and positional data. While 50 matches are already a large set of data with regard to positional data literature, including analyses with less than ten 57 , 58 or even only one match 59 , it is by no means comparable to the large datasets of more than ten thousand matches evaluable in football forecasting related to goals 1 , 29 , 46 . For this reason, the present study will not be able to give conclusive answers neither to in-play forecasting nor to the use of event and positional data in forecasting. However, to the best of our knowledge, the analysis of such detailed performance indicators in football forecasting has never been done before. Further studies with a higher number of matches will be a fruitful domain of research to gain more insights into the value of performance indicators. Moreover, larger datasets will make it reasonably possible to use machine learning methods, for example, to combine all the different performance indicators into a single one. We would also encourage researchers to tackle whether such performance indicators are useful in traditional (i.e., non-in-play) forecasting tasks using indicators from previous matches to forecast future matches.

Finally, we acknowledge that our representation of event data ignores the sequential nature of match events. It should be noted that match events can not only be viewed as separate, discrete events but also as sequences of different actions, where each of them is affected by the preceding one and affecting the following one, thereby forming a continuous process. This representation could be the base for the examination of further indicators describing teams’ tactical performance and their relationship with match outcome.

The present study has focused on the use of in-play information to forecast the further course of a football match. We presented evidence that pre-game information is far more valuable in forecasting football matches then in-play information in terms of goals. While performance indicators based on event and positional data have been shown to possess more informative value than goals, even these indicators were not sufficient to reveal significant predictive value in-play. This is surprising and valuable news to match analysts who should not overestimate the value of in-play information in explaining match performance and bookmakers who should not overestimate the effect of in-play information on the accurate calculation of in-play betting odds. In defining strength dependence, explanatory power, predictive power and predictive overperformance, we presented a valuable framework for in-play forecasting and performance analysis in football. We would like to encourage researchers to adopt our framework for analyses with larger sample sizes. This will not only allow more robust conclusions about the relationships between variables but could also enable the use of more sophisticated machine learning methods for in-play forecasting 31 as well as for the computation of in-depth performance indicators to quantify player or team performance 10 , 11 , 14 . Moreover, as a consequence of this study, we would strongly encourage the idea of segmenting matches by scoreline when using event or positional data for forecasting or performance analysis in football.

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Acknowledgements

We would like to thank Joris Wittkugel and Philipp Walther for their support in analysing the data and reporting the results. All Figures shown in the manuscript were created by the authors.

Open Access funding enabled and organized by Projekt DEAL. This research was supported by Internal Research Funding of the German Sport University Cologne (L-11-10011-212-131000).

Author information

These authors contributed equally: Maximilian Klemp and Fabian Wunderlich.

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Institute of Training and Computer Science in Sport, German Sport University Cologne, Am Sportpark Müngersdorf 6, 50933, Cologne, Germany

Maximilian Klemp, Fabian Wunderlich & Daniel Memmert

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M.K., F.W. and D.M. designed the study. M.K. carried out the preprocessing of raw data and computations of performance indicators. F.W. conceived the statistical framework and performed the calculations of inferential statistics. M.K. and F.W. wrote the manuscript. D.M. provided critical revision of the article.

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Klemp, M., Wunderlich, F. & Memmert, D. In-play forecasting in football using event and positional data. Sci Rep 11 , 24139 (2021). https://doi.org/10.1038/s41598-021-03157-3

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How to Research for a Football Bet: 5 Things to Look for

Jonny Vito / January 2, 2024

Creating a winning football betting strategy might be difficult. Even if you do succeed, it does not mean you will simply receive your earnings. It is critically important to do things right in order to get profits out of your online games betting . But how does that work in practice?

Monetize Your Football Bets

You will hardly be able to monetize your bets without proper research and preparation. And there are several details to keep on your radar depending on the markets chosen. Let’s be more specific and go over the research process.

#1 — Examine the Long-Term Performance of Both Teams

This is a straightforward step; yet many people underestimate its significance. The long-term performance of both teams is the best approach to determine their average performance. Certain bookmakers may under-price a well-known team simply because punters believe they would win. Sometimes a team like Manchester United struggles away to Sunderland, but the bookmakers don’t reflect this in their odds because they want to pull people in who only bet on the big names.

The specific time range depends on what you’re searching for, but it should be at least a couple of months, if not a year. This will provide you an excellent foundation to build on when you delve into further detail later. The crucial questions here are how the team performs in terms of goals scored, goals allowed, playing at home or away (depending on the game), results against teams comparable to the next opponent, etc.

#2 — Examine the Short-Term Trends

After you’ve grasped the overall picture, it’s time to go deeper and determine the current condition of both teams. As we all know, confidence is everything in sports, and some players might appear to be world beaters. That’s why short-term patterns are particularly essential.

Take a look at each team’s recent 5-10 games; this should be enough for you to understand what to expect. Again, metrics such as goals scored, goals surrendered, average possession, and form of the greatest players should be considered. It’s a good idea to read a short match report for each of the games if you haven’t already; it is the best way to bet on football .

#3 — Read Team News

Almost every punter understands that you should look at the list of suspended, injured, and questionable players. A team that is without its top center back, for example, may struggle against an offensive opponent yet do well against a club that tends to sit back.

Of course, you should consider who will fill in for the injured players. How did their substitutes fare the previous time they appeared? Are they simply benchwarmers or squad players who receive enough minutes to stay in shape? These and other questions must be addressed.

Another point is frequently overlooked. The schedules of both clubs are critical as the number of games played per season presently necessitates rotation. So check out each team’s previous few games and what’s coming ahead. It should tell you if the manager will start his strongest lineup or try to rotate it.

#4 — Watch Prior Matches of the Two Teams

The next step would be to look at how both teams have done in their previous matches. The most recent games are the most revealing, but recent statistics should not be overlooked. Another thing you may notice is that particular teams or even certain players may have a strong streak against a specific opponent. Plenty of instances can be seen in the English Premier League, where Sunderland has been on a roll over local rival Newcastle in recent years. The Magpies are also a favorite opponent of Arsenal striker Olivier Giroud, who regularly scores against them.

#5 — Pay Attention to the Experts

Nowadays, there are so many different points of view on the Internet that it may be overwhelming. Most of them will merely confuse you and add little to your analysis. However, there are certain professionals who may be valuable. There are those who are adept at evaluating and forecasting football matches, whether they are successful punters or well-known journalists.

We don’t advocate exactly copying someone else’s viewpoint, but reading a preview isn’t a terrible idea. Seeing things from a fresh viewpoint may support your own assumptions or reveal a new angle you were unaware of.

Bet and Win

Proper research will put you closer to the long-awaited football bets. So take your time and arm yourself with the key data for your next football betting session.

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DealBook Newsletter

Sports Leagues Bet on Gambling. Now They’re Facing Its Risks.

A string of gambling situations involving athletes leaves leagues in a tough spot.

By Lauren Hirsch and Ephrat Livni

Major League Baseball held its season openers this week under the shadow of a gambling scandal . Reports surfaced that the National Basketball Association is investigating a player over irregular bets . And college basketball fans await results from a review into unusual betting on a men’s basketball game .

The incidents have highlighted a trade-off that professional sports leagues made when they embraced gambling.

Leagues have signed lucrative marketing deals with betting apps like FanDuel and DraftKings and use gambling to amp up fan engagement. But this new source of revenue has also opened the doors to a fundamental danger: that an explosion of sports betting could threaten the assumption of fairness at the core of athletic competitions.

“The risk is that the game becomes like professional wrestling — which is rigged. And nobody bets on professional wrestling,” said Fay Vincent, the M.L.B. commissioner from 1989 to 1992. “And if baseball becomes professional entertainment the way wrestling is, it’s dead.”

Leagues are unlikely to abandon gambling completely. But is there a way for them to protect their image as they profit from betting?

Clubs can no longer blame gambling itself for scandals. When Pete Rose was barred from baseball in 1989 for betting on games, in one of the most famous gambling scandals in sports history, Commissioner A. Bartlett Giamatti, Vincent’s predecessor, denounced gambling as corrosive. But after a 2018 Supreme Court decision paved the way for states to legalize betting, leagues are now working directly with sports books. The N.B.A. signed an estimated $25 million contract with MGM Resorts in 2018 , and M.L.B. has an exclusive multiyear deal with FanDuel.

“There is no putting the toothpaste back in the tube,” said Patrick Rishe, a professor in the business of sports at Washington University in St. Louis. “The money flows too thick.”

Leagues may support limits on prop bets, which allow gamblers to bet beyond the results of games on components like the first player to score. Since the outcome of these bets can often be decided by only one player, they leave individual athletes vulnerable to more pressure from bookies and others. The president of the N.C.A.A., Charlie Baker, encouraged states this week to ban prop bets , sending shares of DraftKings and FanDuel’s parent company, Flutter, tumbling. (Some analysts said a ban would only minimally affect the sports books’ bottom lines. )

Better self-monitoring could help. The largest U.S. sports books announced this week that they were forming the Responsible Online Gaming Association , an organization that will allow them to share information about customers who have been excluded because of problematic gambling.

“This is real money, real participation,” said Chris Grove, an analyst at Eilers & Krejcik Gaming. “But, with that said, it shouldn’t also just be a free pat on the back. There are a lot of questions, especially around what kind of information are you going to be sharing about individual players and then what kinds of actions are you going to be taking based on that information sharing.”

Leagues could also extend bans against in-sport betting to individuals with ties to players , like personal assistants. Anyone who works at the teams “should probably be subjected to the same rules as they’re subjecting the athletes to,” said Jeffrey Kessler, a sports law lawyer at Winston & Strawn.

More taxes may be on the table. “State governments are also major beneficiaries of regulated gambling,” Grove said. “They have an obligation to step up and to help to mitigate whatever problems are emerging.”

States could raise taxes on sports betting, which range from 6.75 percent in Iowa to 51 percent in New York, Rhode Island and New Hampshire , and use the proceeds to fund oversight initiatives such as real-time data monitoring or state-supported teletherapy for gambling addicts.

A flat tax increase might be welcomed by FanDuel and DraftKings, the largest betting sites, which are better equipped than smaller rivals to afford the impact — “though they would never say that out loud,” Grove said.

But many are doubtful this will happen any time soon, given the pushback that higher taxes would most likely elicit from others. Professional sports teams and casinos both “have a very strong track record in terms of lobbying state legislatures,” said Marc Edelman, a professor of law at Baruch College who studies gambling history.

Will the latest incidents damage leagues? Given the lengthy nature of TV contracts and relative steadfastness of fans, any immediate impact may be subtle. Attendance at Cincinnati Reds games dipped only slightly after Rose, who managed the team, was ousted for betting, said Keith O’Brien, author of “Charlie Hustle: The Rise and Fall of Pete Rose.” A year later, it jumped about 25 percent.

“Does that mean that fans wanted to come because they were washing away the scandal? I don’t know,” O’Brien said. “I can tell you, having lived in Cincinnati in 1989, that it ruined baseball. It ruined it. And it was a lost season.” — Lauren Hirsch

IN CASE YOU MISSED IT

Jay Powell says economic resilience gives the Federal Reserve more flexibility on when to start cutting rates. The Fed chair signaled yesterday that robust consumer spending and a strong labor market allowed the central bank to be patient. He reiterated that it wanted to be more confident that inflation was coming down sustainably before taking action.

Sam Bankman-Fried is sentenced to 25 years in prison. The FTX founder was convicted of stealing $8 billion from his customers and faced a maximum sentence of 110 years . He vowed to appeal the conviction.

Visa and Mastercard agreed to reduce swipe fees for five years. The proposed class-action settlement to a long-running fight with retailers could have wider consequences, like making the credit card reward programs that many travelers use for free travel less lucrative .

Disney ended its legal fight with Ron DeSantis. The entertainment giant and the Florida governor have been sparring for two years over control of a tax district that encompasses Walt Disney World. Both sides have now agreed to cooperate on new growth plans for the 25,000-acre area.

Blockbuster spending

Wednesday is the deadline for Disney shareholders to vote in what is expected to be the most expensive proxy fight in history. The company’s board faces attacks from two sets of activist investors — Trian Partners and Blackwells Capital — and all sides are putting their money to work to try to win over retail investors. Trian has spent about $25 million, Blackwells Capital about $6 million and Disney upward of $40 million.

Because a large portion of Disney’s shareholders are retail investors , the battle has morphed into what is effectively a modern-day marketing campaign. And if you’ve been searching for information about the fight, you’ve probably been barraged by online ads. Here’s how the price to bid on Google Ads keywords tied to the fight has jumped over the past year.

How any business can use A.I.

Ethan Mollick, a professor at the Wharton School of the University of Pennsylvania, has built a big following for his research into how to apply artificial intelligence at work and his popular newsletter, One Useful Thing.

He spoke to DealBook about his new book, “Co-Intelligence: Living and Working With AI,” in which he spells out how to get the most out of the transformative new tools. The conversation has been edited and condensed.

What mistakes do companies make with A.I.?

They tend to view this as something that has to be highly centralized. So it ends up being some sort of high-end working group, usually with the I.T. department and the legal department, to define rules and uses. What they often do is lock down use.

Companies also believe that somebody has answers about how to use A.I. They’re hiring consulting companies, and the consulting companies don’t know anything. Even the A.I. companies don’t know how this can be used best.

Have you seen companies use generative A.I. to make big improvements in how they work?

What’s really happening is large numbers of their employees are secretly doing their work with A.I. and just not telling anyone. So a lot of companies are actually being automated and getting huge efficiency gains.

You write that we should strive to use A.I. like a “cyborg” instead of a “centaur.” What do you mean?

Centaur work is divided. There’s some work you give the A.I and some work you keep for yourself. So let’s say I’m not a good writer but I’m good at analysis. I’d say to the A.I.: “You do the writing. I do the analysis.”

Cyborg work is more blended. When I wrote this book, if I got stuck on a sentence I’d ask the A.I., “Give me 10 ways of resolving this issue.” I had it read through part of my books and give me feedback on it, or suggest analogies that might be useful. That is more effective.

If an executive wants to incorporate A.I. into my business, what should be that person’s first step?

You just have to use it. The first use case I see from many, many people is using a chatbot to write children’s stories or wedding toasts. I think the thing to actually start with is everything you legally, ethically can at work. Ask it questions about what you’re working on. Have it brainstorm ideas with you. Have it give you feedback on a meeting that you recorded on Zoom with permission. And that’s how you learn how to work with it.

On our radar: The ancient maritime principle of ‘general average’

Insured losses from the collapse of the Francis Scott Key Bridge, which a cargo ship struck on Tuesday, could reach $4 billion , and sorting out who will foot that bill may take a decade of litigation. Part of that fight may involve a little-known ancient principle of maritime law called “general average.”

The principle, attributed to the mariners of Rhodes in a text from 533, dictates that when there is disaster, cargo shippers and vessel owners jointly share the costs. “General average is a shared sacrifice,” said William Fennell, chair of the Marine Insurance and General Average Committee for the Maritime Law Association of the United States. The principle dictates that “everyone’s in it together.”

Classic cases involved jettisoning cargo — if the crew had to lighten a ship’s load to avoid sinking and tossed some but not all cargo, under general average everyone chipped in for the loss. In modern times, the notion applies more broadly, and it could arise in the case of this week’s tragedy, Fennell said.

If the ship’s owners invoke the principle and are not ultimately found to be at fault for the accident (in which case it would not apply), companies that had cargo on the ship could end up paying for some of those losses.

Thanks for reading! We’ll see you Monday.

We’d like your feedback. Please email thoughts and suggestions to [email protected] .

Lauren Hirsch joined The Times from CNBC in 2020, covering deals and the biggest stories on Wall Street. More about Lauren Hirsch

Ephrat Livni reports from Washington on the intersection of business and policy for DealBook. Previously, she was a senior reporter at Quartz, covering law and politics, and has practiced law in the public and private sectors.   More about Ephrat Livni

Inside the World of Sports

Dive deeper into the people, issues and trends shaping professional, collegiate and amateur athletics..

Minor League Baseball’s Real Estate: The fight over a new stadium for the Eugene Emeralds  highlights a wider challenge for cheaper alternatives to big-league live sports.

New York’s Favorite Soccer Team: Some people splurge on vacations, fancy shoes and motorcycles. A group of dozens of friends, neighbors and co-workers decided to try something better (or maybe worse): They bought a middling soccer team in Denmark .

Here Comes Padel: The sport is played with a racket on a court with a net, but watch out for those bouncing shots from the back wall. Reporters take a look at the padel scene in New York City .

Have the Brands Gone Too Far?: Runners at the Boston Marathon are disappointed that the new finisher medals feature a large bank logo  across the bottom.

How Soccer Embraced Ramadan: In competitions like the Premier League, Muslim pros who once faced pressure to avoid daily fasts  during the monthlong holiday now benefit from custom diets and in-game breaks.

The Gambling Behaviour and Attitudes to Sports Betting of Sports Fans

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• Volume 38 , pages 1371–1403, ( 2022 )

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Survey responses from a sample of nearly 15,000 Australian sports fans were used to study the determinants of: (i) gambling behaviour, including if a person does gamble and the type of gambling engaged with; (ii) the number of sports and non-sports bets made over a 12-month period; and (iii) attitudes towards betting on sports. The probability of betting on sports decreased with increasing age and was lower for women and people with a university education. This gender difference varied with age, with the greatest difference found among the young. Similar effects were observed for the number of sports bets made, which declined with age. The gender difference in the number of sports bets also varied with age with the greatest difference found among the young arising from the high propensity of young men to bet on sports. Attitudes to sports betting were also analysed, with a key finding that, within friendship circles, the views that sports betting is perceived as harmless, common and very much a part of enjoying sports were stronger among young men. These permissive attitudes were stronger among people who bet on sports and those who bet on sports more frequently. The analysis of sports fans provides insights into the characteristics of the target market most likely to bet on sports, which can be used to inform public health initiatives and harm reduction campaigns.

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Introduction

Harm from gambling is a significant global public health issue, with negative impacts on the health and wellbeing of individuals, families and communities (Gainsbury et al., 2014 ). Researchers have argued the harm to health and wellbeing caused by gambling is equivalent to that associated with major depressive disorders, and substance misuse and dependence (Browne et al., 2016 ). There is an array of research linking harmful gambling to health and social issues, including an individual’s health and wellbeing (Rockloff et al., 2020 ; Suomi et al., 2014 ), impacts on families and relationships (Dowling, 2014 ), and an association with intimate partner and family violence (Dowling et al., 2019 ). Generally, harms related to gambling reflect social and health inequalities, with negative effects unequally skewed towards economically and socially disadvantaged groups (Cowlishaw et al., 2016 ; Raybould et al., 2021 ; Wardle et al., 2018 ). Further, Deans et al., ( 2017a , 2017b ) argued that older adults, young men, and children are most vulnerable to harm from gambling.

In this paper, we explore the gambling choices of a diverse group of sports fans from Victoria, Australia, aged 18 and over, based on data from a survey of almost 15,000 members and fans of elite sporting clubs. In doing so, we investigate the relationship between individual demographic characteristics, the gambling behaviour of these sports fans and differences in attitudes to sports betting. Australia is recognised globally as having one of the most accessible and liberalised gambling environments, with policy and regulation, online platforms and the diversification of gambling products all increasing the availability and uptake of different gambling opportunities (Deans et al., 2016a ; Hing et al., 2017 ; Pitt et al., 2017a ). However, this trend is reflected elsewhere, with similar issues reported in the United Kingdom (McGee, 2020 ), Spain (Lopez-Gonzalez, et al., 2020 ) and Ireland (Fulton, 2017 ), implying our analysis is of international importance for those seeking to understand gambling choices and attitudes, and mitigate harm through appropriate policies and programs.

Recent evidence from the Household, Income and Labour Dynamics in Australia survey (a nationally representative longitudinal survey) demonstrated that there were 6.8 million regular gamblers in 2015, of whom an estimated 1.1 million were at risk of harm from gambling-related problems (Armstrong & Carroll, 2017 ). The National Australian Gambling Statistics Report highlighted that total gambling losses rose 5% between 2017 and 2018 to $24.89 billion. These statistics demonstrate gambling is an ongoing and increasing threat to individual and public health. Not only are individuals at risk of harm from gambling, for one person with problematic behaviour, an estimated five to ten people are adversely affected (Productivity Commission, 1999 ), implying widespread economic and social costs of gambling (Wardle et al., 2018 ).

Rise and Normalisation of Sports Betting

This research focuses on sports betting, a rapidly emerging sector of the gambling industry. Its impact on normalising gambling, especially among the young, has been of increasing concern over the last decade in countries like Australia and the United Kingdom (Purves et al., 2020 ). Sports betting is one of the few forms of gambling that has shown a substantial increase in participation in recent years (Hare, 2015 ). In Australia, sports betting resulted in the largest year-on-year percentage increase (16.3%) in gambling losses during 2017–2018. The relationship between sports and gambling is increasingly symbiotic, with teams from Australia’s two major professional sports, the Australian Football League (AFL) and National Rugby League (NRL), significantly involved in the ownership and promotion of gambling products and services. Activities include formal sports partnerships, uniform naming rights, stadium signage and the promotion of odds during televised broadcasts. This general trend has been termed the ‘gamblification’ of sports by McGee ( 2020 ) and has become ubiquitous across a variety of sports settings, from elite to community level.

As a consequence of the pervasiveness of sports betting, researchers have increasingly sought to identify and describe the ‘normalisation’ effect of sports betting and its acceptance as part of peer-based socialisation and general sports fandom (Bunn et al., 2019 ; Raymen and Smith, 2017 ). A growing body of evidence has started to address the factors that lead to sports betting being perceived as an everyday part of sports, fostering its uptake. This is aligned with an increasing focus within broader gambling research on the influence of the environment and social determinants on people’s behaviour, as opposed to concentrating on a problem or pathology within the individual (Johnston and Regan, 2020 ).

There has been a strong research focus on the rise and prominence of sports betting marketing, quantifying how prevalent gambling promotions are during sports broadcasting (Milner et al., 2013 ), on social media platforms (Thomas et al., 2018 ), in live events within stadia (Thomas et al., 2012 ), and exploring how online platforms have been harnessed by wagering companies to encourage consumption (Deans et al., 2016a ). Thomas et al. ( 2012 ) highlighted there were very few visible or audible messages to counter overwhelmingly positive messages about sports betting during matches. Their research also addressed how sports betting advertising and associated strategies affect the attitudes of specific community sub-groups, including young people, parents, and young males. Pitt et al. ( 2016a ) found children could recall sports betting brand names, places they had seen betting advertising and associated plot details of advertisements. Deans et al. ( 2017b ) conducted similar work with young men and demonstrated sports betting marketing influences their betting behaviour.

Research has also focused on people’s attitudes to sports betting advertising, to improve understanding of community sentiment. Generally, this has shown that both parents and young people disagree with the increase in sports betting advertising and have concerns about how these messages promote a seemingly natural affinity between gambling and sports (Nyemcsok et al., 2021 ; Pitt et al., 2016b ). However, Pitt et al. ( 2016b ) reported that young people’s discourses about sports increasingly involve discussions about gambling ‘odds’ and that some young people believe that gambling is a usual and valued consumption activity during sports. Alternative evidence suggests young men feel particularly overwhelmed and bombarded by sports betting advertising (Thomas et al., 2012 ). This is unsurprising because this group is the target market for most Australian wagering operators. Hing et al. ( 2016 ) argued that such operators deliberately position sports betting as an activity engaged in by single, professional, upwardly mobile young men.

Other environmental or ‘normalisation’ issues investigated in the research literature include the availability and convenience of sports betting on mobile phone apps or online, with ease of access facilitating gambling (McGee, 2020 ), the socio-cultural alignment between sports betting and sports (Deans et al., 2017a ; Thomas, 2014 ), and how physical and online environmental factors influence the gambling risk behaviours of young men (Deans et al., 2016b ). For example, Deans et al. ( 2017a ) conducted semi-structured interviews with a convenience sample of 50 Australian men, aged 20–37, who were fans of and had bet on either NRL or AFL matches (games). These young male sports bettors reported their betting was normal and socially accepted, especially among sports fans, and ‘gambling-related language had become embedded in peer discussions about sport’ (p. 112). As such, Deans et al. concluded an exaggerated normalisation of wagering might exist in male sports fans’ peer groups. The young men in their study had established rituals (e.g. punters’ clubs) that reinforced their social connection to sports betting, but also enhanced the peer pressure to bet—an outcome that is perhaps inevitable given the role of social interaction in normalising behaviour (Russell et al., 2018 ).

Understanding ‘Sports Bettors’

A separate but connected branch of research literature has concentrated on profiling groups most at risk of experiencing harm from sports betting, particularly describing their attitudes and characteristics. As indicated previously, two groups of major concern are men and youth in general (both male and increasingly female). Studies and reviews have consistently found that young adult males are at greater risk of problem gambling (Hing et al., 2015 ; Williams et al., 2012 ). Recently, such research has also explored sports betting specifically. For example, Hing et al. ( 2016 ) in a quantitative study with a purposive sample of 639 Australian adults, identified key demographic risk factors for problem sports bettors included being male, younger, never married, and living either alone, in a one-parent family with children, or in a group household. Other risk factors included having a higher level of education and working or studying full-time. Numerous, frequent, and larger bets appeared to characterise high-risk sports bettors, as opposed to those deemed at low risk of experiencing harm. This is supported by recent research by Ayandele, Popoola and Obos ( 2019 ), who surveyed 749 Nigerian tertiary students aged 16–30 years to explore how socio-demographic factors, peer-based gambling and sports betting knowledge interact to shape young adults’ attitudes to sports betting. They found a favourable attitude towards sports betting was associated with being older and male, having a knowledge of sports betting and was positively related to the betting attitudes and behaviours of friends.

Whilst understanding normalisation factors and processes is important, alongside the attitudes and characteristics of different sub-groups, what is missing from current research is a large-scale examination of the attitudes of sports fans specifically, and the key demographic factors that are associated with their sports betting behaviour. This study addresses the gap. To the best of our knowledge, this research, conducted with almost 15,000 unique respondents, is the largest quantitative study operating at the nexus of sports fans and gambling behaviour. Arguably, the issues described above are more impactful in this cohort because they are highly engaged with sports and very exposed to marketing and the gambling economy. It is imperative to understand how such environmental and socio-cultural processes influence sports fans’ betting behaviour and to identify the sub-groups where these behaviours are most apparent.

Using quantitative research with a broad demographic group of sports fans (aged 18 and over), we aimed to compare attitudes between sports bettor, non-sports bettor and non-bettor cohorts, and examine the factors that would make it more likely for a sports fan to be a sports bettor. Broadly, we focused on attitudes to betting in sports, the risks associated with sports betting and perceptions about how much of a social norm this activity is. The research was guided by the following questions:

What demographic factors make it more or less likely for a sports fan to bet on sports? How does this correlate with the number of sports bets a person makes?

What is the impact of described normalisation processes on the attitudes of sports fans that bet on sports, compared with those that do not bet at all, and those that bet but not on sports?

Understanding the demographic profiles and risk factors for sports bettors and their attitudes is an increasingly important area of research. The results from this research could inform public health interventions and policy to help ensure they appropriately address areas of concern.

The research questions above are addressed as part of a broader project undertaken in partnership with the Victorian Responsible Gambling Foundation (VRGF). The project involved a survey that was distributed in collaboration with 17 professional sporting clubs from Australian Football, Basketball, Cricket, Soccer, Netball and Rugby Union in the state of Victoria, Australia. The survey was targeted at members, fans, and supporters of these clubs. In each instance, the survey was shared via social media channels (including Facebook and Twitter) and electronic direct marketing using email to each club’s membership base. Depending on the sporting code and relevant season (summer or winter), the survey was shared either between 30th October–3rd December 2020 or 25th February–18th March 2021. Data were collected in the context of the COVID-19 pandemic and research has demonstrated an increase in sports betting and a decrease in other types of gambling (e.g., casino, horse racing, pokies, etc.) during this period (Jenkinson et al., 2020 ). Whilst this could have impacted the behaviour and attitudes of respondents in this survey, the results still highlight the groups most at risk from engaging in sports betting and their associated attitudes. The survey took on average 15 min to complete and elicited a total of 17,228 responses. However, due to incomplete survey responses, the estimating sample is restricted to at most 14,950 observations in the analysis below. Three components of the survey were used in this study. First was data on gambling behaviour comprising responses about (i) whether an individual gambles or not and whether any gambling is sports betting, non-sports betting or both; and (ii) the number of bets in a given period.

Participants were asked about gambling activity in general first. They were advised: “Gambling includes activities in venues such as casino table games, pokies, TAB, Keno etc ., as well as raffles, lotteries and scratchies. It also includes gambling online or via apps such as sports betting, race betting and online pokies and casino games, where you bet with money.”

This was followed with the questions:

Thinking of all these types of gambling, in the past 12 months, have you spent any money on these gambling activities?

In the past 12 months, how often have you gambled? (with a number of times per week, month or year options available)

Participants were then asked about sports betting activity. They were advised: “ Sports betting refers to legal wagering with bookmakers on approved types of local, national or international sporting activities, (other than horse or greyhound racing both on or off the course) in person, via the telephone or via an app or online.”

Thinking of all these types of sports betting, in the past 12 months, have you spent any money on these sports betting activities?

In the past 12 months, how often have you taken part in sports betting? (with a number of times per week, month or year options available)

This data are summarised in the first six rows of Table 1 under the sub-headings ‘betting category’ and ‘number of bets’. For clarity, when referring to the specific participant groups involved in the research, we will use the terms sports bettors, non-sports bettors, or non-bettors to avoid referring to gambling and betting interchangeably. Table 1 shows that about 35% of the sample are non-bettors while another 35% are non-sports bettors (i.e. they bet on lotteries, raffles, poker or slot machines and casino gambling). The remaining 30% of the sample are sports bettors divided evenly between those that engage in sports betting only and those that engage in both sports and non-sports betting. The average number of bets in a year for the full sample is 19.6 for non-sports and 14.5 for sports bettors. Footnote 1 This data are also presented by betting category, showing that sports bettors, on average bet many more times per year than non-sports bettors. However, those that bet on both have a much higher betting frequency again, betting nearly twice as often as those who bet only on sports. The much higher standard deviation among sports bettors is also notable, suggesting there is much greater variation in betting frequency among sports bettors than non-sports bettors.

The second component of the data used in this study comprises demographic characteristics. This includes gender, age, location (metropolitan or regional), marital status, education, employment status, income categories, country of birth, parents’ country of birth, Aboriginal Torres Strait islander origin and health status. The data are summarised for the full sample and the different betting categories in Table 1 . Some key features of the data are that about 70% of the sample is male but nearly 80% of sports bettors are male and the average age of the sample is 50 years, but sports bettors have an average age of 43 years for sports bettors and 46 years for those who both sports and non-sports bet. Two other notable features are the much higher proportion of non-sports bettors who are retirees (0.24) compared to the proportion of sports bettors (0.07) and the high proportion of responders who did not report their income (0.20).

The third component of the data used here comprises responses to questions about attitudes to gambling. The questions are grouped into two categories including (i) general attitudes to gambling and sports betting; and (ii) perceptions of the attitudes and behaviours of others. Responses were elicited on a scale from 0 (totally disagree) to 10 (totally agree). The questions are presented in Table 2 , where sample means and standard deviations are presented for the full sample and the different betting categories.

An important research question here is whether people in different betting categories respond to each question differently. We conducted a one-way analysis of variance (ANOVA) for each question to test whether the mean responses of each group are statistically significantly different. The p -value of this joint F -test for each question is presented in the ‘Full Sample’ column in braces; all tests have p -value of [0.000] implying we reject the null hypothesis of equality between the mean response of each group to each question. We also test the differences between means for each group using t -tests with a Sidak correction to account for the possibility of a false positive finding given the large number of t- tests. The table reports results of tests of differences between the mean response of non-bettors and each type of betting group with statistically significant differences at the 10%, 5% and 1% levels denoted by *, ** and *** respectively. The results show average responses of almost all betting groups differ from those of non-betters at the 1% level of significance. Differences are most stark in relation to the notion that ‘sports betting should not be part of experiencing sport’ and items related to the social aspects of sports betting, particularly the place of sports betting in the person’s family and friendship groups. However, responses to (i) ‘most people in society think betting on sport is harmless’ were not statistically different between sports bettors and non-bettors; and (ii) ‘odds talk is common in discussions about sport with my friends and peers’ were not statistically different between non-bettors and non-sports bettors.

An important feature of the survey is that it reached beyond people who identify as gamblers, providing insights into a more diverse sample than many previous studies. However, a limitation is that the design is focused on members, fans or supporters of a group of elite clubs or teams, implying to some degree that respondents are likely to be more engaged with sport than the average member of the Victorian population. Therefore, the differences between bettors and non-bettors identified here are potentially lower bounds and analysis of a more representative sample might uncover even greater differences. Another important benefit of the sampling frame is that it is likely the target audience for sports betting advertisers. Therefore, the analysis offers insights into a group that is likely most targeted and affected by sports betting advertising and understanding this group provides valuable insights to harm minimization policies with respect to sports betting.

Empirical Methods

The empirical analysis can be divided into two broad approaches. The first is to analyse the determinants of the betting choices of survey respondents. The second is to analyse the responses to gambling attitude questions. The approaches to these analyses are described in turn below.

Who Bets and How Often?

Each survey respondent is assumed to choose between four types of betting activity: no betting, non-sports betting, sports betting or both sports and non-sports betting. We define the gambling choice of each survey respondent \(i\) as \({G}_{i}=j\in \left\{1, 2, 3, 4\right\}\) . We want to understand the relationships between different demographic characteristics’ and gambling choices. Given these four possible gambling choices or outcomes are unordered, we used a multinomial Probit specification to estimate the relationships. The probability that individual \(i\) makes gambling choice \({G}_{i}=j\) is given by

where \({X}_{i}\) is a vector of personal characteristics (including gender, age, location, marital status, education, employment status, income categories, country of birth, parents’ country of birth, Aboriginal Torres Strait islander origin and health status, as listed in Table 1 ), \(\Phi \left(.\right)\) is the cumulative density function of the Standard Normal distribution and \({\beta }_{j}\) provides the parameter estimates on \({X}_{i}\) for gambling choice \(j\) ; see Greene ( 2018 ) Chapter 18 for more details. This model allows us to understand the influence of each characteristic on the four possible gambling choices from a model that jointly estimates the probabilities of each alternative gambling choice.

As parameter estimates do not have a clear intuitive interpretation in such models, we compute marginal effects for each \({X}_{i}\) which are given by

where \(\overline{\beta }\) is the probability weighted average of the parameter estimate across the four different possible gambling choices. The multinomial Probit results reported in Table 3 below are average marginal effects which are computed as the average of for \({\delta }_{ij}\) across all \(i\) individuals. The interpretation of these marginal effects is that they tell us the impact of a unit increase in \({X}_{i}\) (for example female versus male or a one-year increase in age) on the probability of making gambling choice \(j\) ; that is, four marginal effects will be reported for each variable, one for each of no betting, non-sports betting, sports betting or both sports and non-sports betting.

Along with the choice of gambling type, individuals choose how many bets to place, and the factors that influence this number of bets are also of interest. Since 35% of survey respondents are non-bettors, the data on the number of bets comprises a large number of zeros. To accommodate this feature of the data, a Cragg hurdle model is adopted (Cragg, 1971 ). This model involves two parts: the first is a model of the decision to gamble (selection model), while the second is a model of the number of bets. As we have data on the number of sports bets and non-sports bets, we estimate this two-part model separately for each of these choices. The first part of the model is the selection decision, given by

where \({C}_{i}\) is individual \(i\) ’s choice of whether to bet on sports (1) or not (0) or alternatively to make non-sports bets (1) or not (0). The control variables \({X}_{i}\) are as defined above for the multinomial Probit model in Eq. ( 1 ), while \(\alpha\) is a vector of parameters capturing the influence of each control variable on the decision to place bets or not and \({\epsilon }_{i}\) is a mean zero, constant variance normally distributed disturbance term. The second part of the model estimates the number of observed bets. This continuous variable is given by

an exponential specification of the Cragg hurdle model where \({B}_{i}\) is the number of bets made per year by individual \(i\) , \(\theta\) is the set of parameters reflecting the impact of variables \({X}_{i}\) , again as defined above and \({u}_{i}\) is a mean zero, constant variance disturbance term.

The key idea of this model is that the decision to gamble is modelled separately from the decision of how many bets to place. Estimates of \(\alpha\) are important determinants of the decision not to gamble and therefore choose zero bets, whereas \(\alpha\) and \(\theta\) together determine the number of bets if a person chooses to gamble. The overall marginal effect of control variables \({X}_{i}\) , which in our specification are common to the selection and number of bets equations, are computed using the margins command in STATA and presented in Table 4 below. The detailed expressions for these marginal effects can be found in Burke ( 2009 ). The interpretation of these marginal effects is that they reflect the impact of a unit change in the value of a control variable \({X}_{i}\) (i.e. gender or age) on the average number of bets in a given period of time (a year in this instance).

Factors Affecting Attitudes Towards Sport Betting

Our analysis of responses to the 12 different questions about attitudes to sports betting listed in Table 2 comprises two key objectives. First, we are interested in the relationship between individual gambling choices and attitudes to sports betting—this involves the type of betting and the number of bets. It is anticipated that sports bettors will hold more positive attitudes towards sports betting than non-bettors or non-sports bettors. Second, we are also interested in the relationship between demographic characteristics and attitudes to sports betting. Responses to each question range on a scale from 0 to 10 but are standardized to have mean zero and standard deviation of one, to enable comparisons of effects of different variables across survey questions. These standardized responses are modelled using OLS. The model estimated is given by

where \({A}_{i}\) is the response of individual \(i\) to one of the 12 questions on their attitude to gambling listed in Table 2 . For each question, two versions of the model are estimated where \({Z}_{i}\) is a vector of control variables, including all variables in \({X}_{i}\) which is as defined above, along with either (i) gambling choice, \({G}_{i}\) , (no betting, non-sports betting, sports betting or both sports and non-sports betting); or (ii) the number of sports and non-sports bets, \({B}_{i}\) , included. Model parameters are given by \(\gamma\) while \({\varepsilon }_{i}\) is a disturbance term with zero mean and constant variance. As the dependant variable, \({A}_{i}\) , is a standardized measure of responses to attitude questions, \(\gamma\) should be interpreted as the average number of standard deviations of change in \({A}_{i}\) per unit change in \({Z}_{i}\) .

In all models, we allow for non-linear age effects by including quadratic and higher order age terms, along with a linear age term, testing their significance using a likelihood ratio (LR) test. We also allow for gender effects to vary with age by including age and gender interactions and testing for their significance, again using a LR test.

Factors Affecting Gambling Behaviour

The results of estimation of Eq. ( 1 ) are presented in Table 3 . The average marginal effects of the listed control variables on different gambling choices of no betting, non-sports betting, sports betting and both sports and non-sports betting are presented in first, second, third and fourth columns respectively. The model includes linear, quadratic and third order age terms. Footnote 2 Focusing on the cases of sports betting only (third column) and both types of betting (fourth column) and on results that are significant at the 1% level (denoted by ***), we found that relative to males, females are 9.6% less likely to bet on sport and 6.2% less likely to bet on both. To test the hypothesis that gender effects vary with age, all the included age terms are interacted with the gender indictor, with these interactions supported by a LR test = 62.63 ( p value = 0.00). The marginal effect for females relative to males is plotted for each betting category in panels (a)–(d) of Fig.  1 . The difference between men and women sports betting is greatest among the youngest in the sample and the difference decreases with age. The result suggests that young men are up to 25% more likely than women of the same age to bet on sports; the difference is less than 10% for people over 50 years. In addition, the average marginal effect of a 1-year increase in age is reported in Table 3 . Comparing otherwise identical individuals with a 10-year age difference, the older person is 5.0% less likely to sports bet only and 2.0% less likely to make both sports and non-sports bets relative to the younger person.

Marginal effect of gender on the probability of each betting category plotted over age. Panels ( a )–( d ) are based on estimates presented in columns (1)–(4) of Table 3 respectively. Point estimates are denoted by dots with 95% confidence intervals for each point estimate included

Relative to self-employed, which is the base category, students are 6.7% less likely to bet on sports, while those on home duties are 7.0% less likely to gamble on both sports and non-sports. Income results are all relative to the base range of “less than $10,000”, with little difference between different income ranges in the probability of sports betting only. However, respondents above $60,000 are between 5.6 and 8.0% more likely to bet on both sports and non-sports than those in the base income range. This suggests there is little effect on gambling probability of additional income as the marginal effects are similar for each category above $60,000. Finally, respondents whose parents were both born overseas were 2.7% less likely than the base category (both parents born in Australia) to bet on both sports and non-sports.

In Table 4 , we present estimates of the model of the number of bets specified in Eqs. ( 3 ) and ( 4 ). The marginal effects of the full set of control variables on the number of non-sports bets and sports bets are presented in first and second columns of Table 4 respectively. Age is included in these models through linear, quadratic and cubic terms. Footnote 3 As the number of bets is a continuous variable, the marginal effects are interpreted as the impact of a unit change in the control variable on the number of bets per year.

Focusing first on results significant at the 1% level (denoted by ***) for the number of non-sports bets, females make on average 9 fewer bets per year than males. Betting increases with age, with a 10-year older person making on average 5.29 more bets. The model also includes an interaction between all age terms and gender to test the hypothesis that gender effects vary with age — this interaction is supported relative to the model without the interactions, LR test = 28.41 ( p value = 0.00). The marginal effect of gender on the number of non-sports bets increases with age with women over 58 placing around 20 fewer bets than men of the same age: panel (a), Fig.  2 . Further results include that someone who is married makes 4.5 fewer bets than a single person and parents place 5.0 fewer bets than people with no children. Education reduces betting with those holding trade qualifications betting 6.3 times less than someone who did not complete high school while those with university qualifications betting 15.3 fewer times than someone who did not complete high school. Employment status and income are uncorrelated with the number of non-sports bets. Respondents whose parents were both born overseas place on average 4.4 fewer bets than people whose parents were both born in Australia.

Marginal effect of gender on the ( a ) number of non-sports bets and ( b ) number of sports bets, plotted over age. Panels ( a ) and ( b ) are based on estimates presented in columns (1) and (2) of Table 4 respectively. Point estimates are denoted by dots with 95% confidence intervals for each point estimate included

Again, focusing on results significant at the 1% level, results for the number of sports bets show that women place on average 18.2 fewer bets than men per year. In contrast to non-sports bets, the number of sports bets placed decreases with age; a person 10-years older bets on average 5.0 fewer times per year. The interaction between age and gender confirms that the gender effect on the number of sports bets does vary with age—supported relative to the model without the interactions, LR test = 37.52 ( p value = 0.00). However, the marginal effect of gender on the number of sports bets decreases with age, with 18-year-old women placing 50 fewer sports bets than 18-year-old men. This difference is as low as 10 fewer sports bets per year when comparing women and men aged over 60 years: panel (b), Fig.  2 . Education effects are similar to those for non-sports bets. People with trade qualifications bet on average 6.7 (10.0) times less than someone who did not complete high school. The only employment status category that is related to the number of sports bets is being a student, who place on average 10.3 fewer bets than the self-employed. The number of sports bets is related to income with most annual income categories above $40,000 betting on average between 8 and 11 more times per year, though some differences are significant only at the 5% level and others are smaller with 5 more bets per year and significant at the 10% level. Finally, respondents whose parents were both born overseas place 4.2 fewer sport bets on average than people whose parents were both born in Australia.

Attitudes to Sports Betting

Selected results of estimating the model presented in Eq. ( 5 ) using the responses to the first set of questions on general attitudes about sports betting summarized in Table 2 are presented in Tables 5 and 6 . Full results of these models are available in Online Resource 1 and Online Resource 2 of the Supplementary Materials, where estimates for all variables included in the models are presented. In all these models, an interaction between gender and all age terms (up to third order age terms are included in all models) is considered with the result of a LR test of the restriction that the coefficients on the interactions are zero presented in the last row of each column. In cases where the restriction is rejected and the interaction is non-zero ( p value < 0.05), the model presented includes the interactions.

Results in Table 5 are for the model estimated with all the demographic control variables in \({X}_{i}\) together with a set of indicators for each type of betting behaviour, \({G}_{i}\) , including non-sports betting, sports betting and both sports and non-sports betting, with no betting the omitted base category. Each column presents estimates for a model of standardized responses (mean zero and standard deviation of one) to a separate statement about sports betting. The statements upon which each dependent variable is based are listed in the table notes. Focusing on results significant at the 1% level (denoted by ***), the results show that after controlling for a large set of individual demographic characteristics, people who bet are on average less concerned about sport betting issues than non-bettors. This is evident for all 5 statements modelled. We can see in column (1), for example, responses to the statement ‘sports betting should not be part of experiencing sport’, relative to non-bettors, the average response of people who bet on non-sport only is 0.20 standard deviations lower, while people who bet on sport (only or both sport and non-sport) have an average response that is 0.71 standard deviations lower. Other key results from these models are that females are more concerned about sports betting than males, except for in their responses to the statement ‘people who bet regularly on sport are at risk of harm from gambling’, where there is no difference between men and women. The relationship with age is statistically significant for the statements ‘sports betting should not be part of experiencing sport’ and ‘people who bet regularly on sport are at risk of harm from gambling’ but the effects are small, with a 10-year older person having on average a 0.06 standard deviation higher response to the former question and a 0.03 standard deviation lower response to the latter. People from regional locations are on average more concerned about sports betting than people from metropolitan locations; however, this concern is not evident in response to ‘sports betting should not be part of experiencing sport’. The results on education show that relative to the base case of ‘did not complete high school’, those with trade qualifications are on average more concerned about sports betting and in turn, people with university education are even more concerned with even greater differences evident than for those with trade qualifications.

The results presented in Table 6 are for models of the same questions with the same demographic controls included but with betting behaviour replaced by the number of sports and non-sports bets, \({B}_{i}/100.\) Once again, each column presents estimates for a model of standardized responses (mean zero and standard deviation of one) to a separate statement about sports betting. The statements upon which each dependent variable is based are listed in the notes to the table. The impacts of the demographic characteristics in Table 6 are qualitatively similar to those found in Table 5 . The key difference between Tables 5 and 6 is that gambling categories are replaced with the number of sports bets and the number of non-sports bets. On average, people who bet more often are less concerned about sports betting. However, 100 more sports bets per year (approximately 2 bets per week) has nearly double the impact on responses of 100 more non-sports bets. For example, responses to ‘sports betting should not be part of experiencing sport’ are on average 0.14 standard deviations lower for every additional 100 non-sports bets but are 0.30 standard deviations lower for every additional 100 sports bets.

The above analysis is repeated for the second set of statements summarized in Table 2 which focus on perceptions of the sports betting attitudes and behaviours of others. Selected results of this analysis with betting categories included are presented in Table 7 and with the number of bets included are presented in Table 8 . Each column presents estimates for a model of responses to a separate statement about sports betting. Survey responses used to estimate each model have been standardized to have mean zero and standard deviation of one. The statements upon which each dependent variable is based are listed in the notes to each table. Full results of these models are available in Online Resource 3 and Online Resource 4 of the Supplementary Materials.

Focusing on significance at the 1% level (denoted by ***), Table 7 shows, except for the first two statements that focus on attitudes in society, bettors have families and friendship groups where gambling is common and perceived as harmless. However, the difference between sports bettors and non-sports bettors is stark. For example, in response to the question ‘most people in my friendship group bet on sport’, the average response of non-sports bettors is 0.16 standard deviations higher than non-bettors whereas the average response of sports bettors is up to 0.50 standard deviations higher, with both significant at 1%. The difference between non-bettors and sports bettors (0.49 standard deviations) is nearly 10 times as large as the difference between non-bettors and non-sports bettors (0.05 standard deviations) in response to the question ‘odds talk is common in discussions about sport with my friends and peers’. The largest impact of age is on the peer and friendship group statements, columns (5)–(7), with a response of a person 10-years younger on average 0.15 standard deviations higher. The interaction between gender and age is illustrated for the results reported in column (6) which is based on the statement “most people in my friendship group bet on sport” in panel (a) of Fig.  3 . The difference between men and women is greatest at younger ages with women in the 18–45 year range responding on average 0.5 standard deviations lower than men, suggesting young men have a much stronger belief than young women that their friends are involved in sports betting.

Marginal effect of gender on response to the question “Most people in my friendship group bet on sport”, plotted over age. Panel ( a ) is based on model in column (6) from Table 7 which includes betting categories and panel ( b ) is based on model in column (6) from Table 8 which includes number of bets. Point estimates are denoted by dots with 95% confidence intervals for each point estimate included

The results presented in Table 8 are for models of the same questions analyzed in Table 7 , with the same demographic controls included but with betting behaviour replaced by the number of sports and non-sports bets, \({B}_{i}/100.\) The relationships with the demographic characteristics are qualitatively similar to the results presented in Table 7 and discussed above. The more a respondent bets, the greater their agreement with all but the first two statements that focus on attitudes in society. The relationship between responses and number of sports bets is up to 4 times as large as the relationship with the number of non-sports bets. For example, responses to the question ‘most people in my friendship group bet on sport’ on average increase by 0.10 standard deviations for people who place 100 more non-sports bets per year (2 more bets per week) but for an otherwise identical person who places an additional 100 sports bets, their response is on average 0.38 standard deviations higher. These sorts of differences are evident across all questions about family and friendship groups, with a greater number of bets associated with responses that show sports betting is believed to be more common and perceived as less harmful in these circles. It is also found the more sports bets a person places, the stronger their agreement with the statement ‘most people in society bet on sport’, though the relationship with the number of non-sports bets is statistically insignificant. The gender and age interaction for the model in column (6) in Table 8 is presented in panel (b) of Fig.  3 . The figure shows the difference between men and women is greatest among 18–28-year-olds, with the responses of women in this age range on average 0.70 standard deviations lower. This compares with differences of less than 0.30 standard deviations for those over 60 years. The results are consistent with those in panel (a) of Fig.  3 , suggesting that gender age differences are robust whether we control for the betting category or the number of bets per year.

This study builds on existing literature at the intersection of sports betting and sports, providing a comprehensive analysis of the sports betting behaviour of sports fans, including many people who choose not to gamble at all. Survey respondents’ attitudes to sports betting were analysed using betting behaviour and a wide range of demographic characteristics. The approach differs from many previous studies as we targeted a broader demographic of sports fans, rather than focusing only on those engaged in gambling (sports or non-sports), which is a strength. We did not measure whether a person’s gambling behaviour is deemed ‘problematic’, but previous research has demonstrated a connection between frequency of sports betting and problematic gambling behaviour (Hing et al., 2016 ). Therefore, our analysis of the number of sports bets provides a useful proxy to identify those most at risk of experiencing gambling harm. The research was guided by two overarching questions addressed in turn through the following discussion.

Demographic Profile of Sports Bettors

The dominant theme emerging from our analysis is the importance of gender, age and their interaction. The gender difference in the probability of sports betting is wider among the youngest in the sample; 18-year-old men are about 25 percentage points more likely than their female counterparts to bet on sports, whereas this difference is less than 5 percentage points for those over 60 years. Similar patterns are evident for the number of sports bets placed, with younger men placing more bets than similar aged women and fewer bets being placed with each additional year of age. Consequently, young men are most at risk based on their sports betting engagement and number of bets placed. This aligns with previous studies (Hing et al., 2016 ; Williams et al., 2012 ), but widens our understanding of the sports betting behaviour of sports fans. Moreover, even though this has been described in smaller-scale qualitative research studies (Deans et al., 2017b ; Waitt et al., 2020 ) our results are based on empirical analytic techniques applied to a larger and more diverse sample. The results comprehensively demonstrate sports betting is predominantly pursued by young men, in sharp contrast to other forms of gambling. Given the recent growth of sports betting, its marketing, and increasing contribution to problem gambling (Hing et al., 2019 ), as well as the need for appropriately tailored prevention and early intervention public health initiatives, this finding is significant for highlighting the distinctive sports betting behaviour of young men aged 18–35. Recent research has started to examine young women aged 18–35 as an emerging gambling cohort (see McCarthy et al., 2020 ), but our results demonstrate no significant gender or age effects for women’s sports and non-sports betting behaviour.

Other important demographic factors included education level, relationship status, and employment status. People who are widowed or separated were less likely to bet on sports, but no other relationship types were significant at the 1% level. University educated individuals were less likely to bet on sports than those who did not complete high school. Employment status did not exhibit a strong relationship with sports betting, except students and unemployed were less likely than self-employed to bet on sports. Surprisingly, income did seemingly not influence whether people engaged in sports betting only. This was more important in the context of making both sports and non-sports bets—those reporting higher levels of income were more likely to engage in these gambling types.

Whilst other studies have reported various demographic risk factors for sports betting and gambling, our results contribute by clearly demonstrating the significant interaction between age and gender. The importance of our study for public health policy and harm reduction campaign strategies is twofold. First, our sampling frame is likely the target audience of sports betting marketers, providing strong evidence upon which to base public health policy and harm reduction campaigns. Second, such campaigns should be aimed specifically at young men to help counteract the increasing environmental and social normalisation of sports betting. The next section focuses on the key attitudinal differences that emerged from the results to answer our second research question.

Attitudes Associated with Sports Betting

Our results demonstrate there are significant differences between the attitudes of sports bettors (either sports betting or sports betting combined with non-sports betting), non-sport bettors and non-bettors. Not only do sports bettors feel more strongly that sports betting has a place in sport, they are also less concerned about the risks and harms of sports betting. These results help to demonstrate the effects of the normalisation processes outlined in previous studies. Whilst existing literature has documented how sports and sports betting have become synonymous (Milner et al., 2013 ; Nyemcosk et al., 2021 ; Pitt et al., 2016a ; Thomas, 2018 ), the attitudinal differences we identified highlight how the ‘gamblification’ (McGee, 2020 ) of sports has penetrated individual perceptions about sports betting as an activity and influenced behaviour. Moreover, the differences between sports bettors and non-sports bettors suggest something unique is happening for this group; it is not necessarily related to the act of gambling, but potentially broader environmental and socio-cultural influences. Gender and age effects are also apparent, with women less likely to agree that sports betting should be part of experiencing sports and more likely to agree that sports betting can place people at higher risk of other harms. A similar pattern is evident for age, with younger people generally being more permissive of sports betting.

The influence of the social aspects of sports betting, namely the characteristics of sports bettors’ social networks, is also a strong emerging theme, underpinned by several attitudinal measures. Sports bettors are more likely to have family and friendship groups where gambling is common and perceived as relatively harmless. Additionally, they are more likely to agree that discussions about odds and the placing of bets is the norm amongst peers. In this context, there are significant differences observed between both sports bettors and non-bettors, and sports bettors and non-sports bettors. This again highlights that there are potentially distinct socialisation processes specifically influencing the attitudes and behaviours of sports bettors. Whilst this has previously been described on a relatively smaller scale (Thomas, 2017a ), our research demonstrates that these interactional and socialisation factors are highly meaningful in an extensive cohort of sports fans.

Age and gender are the key demographic factors related to responses in a similar way to that described in the previous section. Whilst women are more likely to agree that sports betting is common in broader society and amongst family members, men are more likely to indicate it is common within their peer groups. Men are also more likely to state that ‘odds talk’ is prevalent when socialising with their peers. In combination with the demographic risk factors outlined in the previous section, it is apparent that men also have different interactions with sports betting. They are more likely to agree it has a place in sports, less likely to think it is risky and can lead to other harms, more likely to have friends and peers who bet on sports, and more likely to have dialogue that supports and endorses the normalisation of sports betting. These attitudes combined suggest it is imperative public health prevention measures and harm reduction interventions target young men. The impact of peer socialisation processes and hegemonic masculine norms around sports betting have been described in previous studies (Ayandele et al., 2019 ; Bunn et al., 2019 ; Deans et al., 2017a ). Sports betting has also been related to the development of socially valorised identities for young men (Lamont and Hing, 2021 ). Our research supports and builds on these previous findings by demonstrating in a large sample that it has become a more prevalent part of sports fandom for younger adult men.

On a large and unique scale, we have demonstrated fundamental attitudinal and behavioural differences, and distinct and concerning trends, among those who engage in sports betting, thereby offering important insights about those most at risk. Most previous research has been qualitative or focused on those identified as having problematic gambling behaviours. By contrast, the scale and type of results generated from this study have afforded the ability to compare differences between non-bettors and bettors, providing compelling evidence of current issues amongst a general cohort of sports fans. Importantly, this study provides data about an emerging public health crisis in which younger men are most at risk because they are more exposed to sports betting normalisation processes, show greater engagement with sports betting and express more permissive attitudes. As such, the results of this study provide a foundation for public health interventions and programs.

One participant reported 52,000 bets per year while some others reported 5,200 and 2,600 bets per year. Such observations were treated as outliers and excluded from the analysis. This amounted to 14 observations being excluded from the analysis.

Higher order age terms are not supported by a likelihood ratio (LR) test of a model with a fourth order age term with a test statistic of 4.63 ( p -value = 0.20).

Higher order age terms are not supported by a likelihood ratio (LR) test of a model with a fourth order age term with a test statistic of 3.33 ( p -value = 0.19) for the model of the number of non-sports bets and 2.74 ( p -value = 0.25) for the model of the number of sports bets.

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Acknowledgements

We would like to acknowledge the Victorian Responsible Gambling Foundation for supporting and funding this research. We would also like to acknowledge and thank Joe Vecci and Roger Wilkins for helpful comments and suggestions.

Open Access funding enabled and organized by CAUL and its Member Institutions. This research received funding from the Victorian Responsible Gambling Foundation.

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Seal, E., Cardak, B.A., Nicholson, M. et al. The Gambling Behaviour and Attitudes to Sports Betting of Sports Fans. J Gambl Stud 38 , 1371–1403 (2022). https://doi.org/10.1007/s10899-021-10101-7

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Online Gambling Is Changing Sports for the Worse

By Jay Caspian Kang

For the past twenty or so years, my friend Chad and I have gone to Las Vegas for the first weekend of the N.C.A.A. basketball tournament. Memory often fails when it comes to gambling, but I believe the only year we’ve skipped was 2020, when COVID -19 shut down the tournament a week or so before the scheduled tipoff. March Madness in Vegas isn’t a pretty scene—picture hundreds of red-faced, middle-aged men in quarter-zip sweatshirts hugging Coors Lights to their chests in a slightly self-conscious way—but the first round has thirty-two games to bet on, and tradition is tradition, I guess.

This year, the crowds felt light. Prior to the pandemic, you’d expect a thirty- to forty-five-minute line for the betting window at the Venetian sports book. Today, most of those windows, which used to house dour tellers who would print out your bets on little tickets, have been replaced by automated kiosks, which provide you with a wider variety of bets than their analog counterparts but make the whole experience feel frictionless and disposable. These machines are run by casino companies, many of which have their own apps, which means that, if you live in one of the thirty-eight states—plus the District of Columbia—where sports wagering is now legal, you could have replicated this particular Vegas experience from your couch.

These digital changes bring a veneer of respectability. The local bookie who used to make his money by pumping degenerates, letting them gamble with high-interest loans, has been replaced by an app. The app also allows you to bet on credit, but, instead of your points going to organized crime, they go to Discover or American Express. Touts, the yelling men who would give out 1-900 numbers promising to tell you the right side to bet on in the Dolphins-Bills game, were once relegated to late-night commercials. Now we have so-called betting experts on every major sports network on television. The cleverer ones will flash a chart or talk about trend lines or whatever, then give you their pick.

None of this means that gambling has become a clean business. It just means the action is controlled by people with deeper pockets and greater influence, who can persuade more people into thinking that betting on sports is something other than what it has always been.

Last week, reality leaked out from behind the digital façade. Shohei Ohtani , the most famous baseball player in the world, got tangled up in a multimillion-dollar sports-betting scandal involving his interpreter, Ippei Mizuhara. On Monday, Ohtani, flanked by a new interpreter, said that he “never bet on baseball or any other sport” and furthermore never “asked anyone to do it” on his behalf. He expressed shock about the whole situation.

For the rest of us, shock, at this point, hardly seems appropriate. Throughout the past three years, there have been a rash of less famous athletes who have been caught and suspended for betting. The N.F.L. has suspended several players for gambling offenses, most notably Calvin Ridley, who was suspended for a full season for betting on N.F.L. games while he was injured and away from his team. Last summer, a college baseball coach was accused of giving information about an upcoming game to a gambler, and was subsequently fired. Earlier this month, a gambling watchdog company called U.S. Integrity flagged a college basketball game between Temple University and the University of Alabama at Birmingham for suspicious betting activity; Sports Illustrated reported that the company had been monitoring Temple for a while. (The school has said that it will act “in accordance with university and NCAA policies,” and that it could not comment further.)

When New York legalized sports betting two years ago, I expressed concern about the speed and the gamification of the new betting apps. But, at the time, I was skeptical that broad legalization would lead to, as I put it then, a “long-term epidemic of problem gambling.” As for cheating scandals, if Romans were gambling at the Colosseum, some hustler was probably out there trying to convince a gladiator to throw a fight. And, though there were more improprieties after legalization than there had been before, the scale and the salaciousness of these scandals didn’t compare to the decades of match-fixing that we’ve seen in Europe and Asia.

I still believe that gambling should be legal, but it appears that the mess that came with legalization might be around longer than I initially thought. The spread of legal sports betting across the country has revealed problems that can’t easily be brushed aside or cloaked in minimizing context. The question for lawmakers today doesn’t seem to be whether these problems exist—they do—but whether those problems are permanent features of legal sports betting or things that will subside once the initial frenzy dies down.

The legalizations of vices can be followed by gleeful oversaturation, and that period of chaos and moral myopia may obscure what is good about letting people openly engage in something that was previously hidden. The rollout of marijuana dispensaries in New York City, for instance, has been a disaster , dimming the promise of legal weed as a well-regulated, tax-generating industry. This doesn’t prove that marijuana should have remained illegal or that the arguments for legalization are invalid. What it means is that New York screwed up and should enforce its own laws. You can make a similar point about the sale of high-dosage THC edibles that are packaged to look like candy. There’s no need to ban edibles . There’s also no need to allow packaging that might confuse young children who stumble on a stash.

When it comes to sports betting, there are at least two legitimate worries, although it’s still difficult to know exactly how persistent these concerns will be. The first is that the ubiquity, speed, and structure of app-based betting—which favors high-risk, high-reward “parlays” that combine multiple bets—will create an enormous population of young gambling addicts. I remain largely unconvinced of this. Most people aren’t problem gamblers, just as most people can navigate a world of beer ads without becoming alcoholics.

The second worry is more abstract, but also, I think, more substantiated. It involves what commentators like to call the “integrity of the game,” and professional sports leagues aggressively partnering with betting companies, which are currently blitzing the country with a seemingly endless marketing budget. Last week, for example, the N.B.A. announced that it would add in-game betting to its popular League Pass streaming app. This means that a viewer could watch nearly any N.B.A. game on any given night and bet, say, ten dollars that LeBron James was going to miss his first free throw. Maybe James hits it, and the viewer doubles down on James’s next one; perhaps, having lost some money in the first half, the viewer tries to win it back in the second.

Not long ago, if someone told me that they were troubled by this sort of thing, I would have said that the integrity of the game had been undone long ago by exploitative labor conditions in college sports and by a slew of non-gambling scandals in the pro leagues. I would have noted that N.F.L. broadcasts have been revolving beer ads since I was a child, and pointed out that soccer teams in England have had conspicuous betting-company logos on their uniforms for years. How did this latest violation of decorum change anything?

Now I think that legal betting really is changing how people experience sports, in part because of the way sports are now broadcast to them. Gamblers sometimes forget how many people, including children, still watch the games for something other than parlays and prop bets, or that teams, such as the Yankees, the Cowboys, and the Crimson Tide, really do represent more than their business concerns. When every game gets presented as a point spread, and when every shot becomes merely an input in a degenerate’s parlay math, the game feels cheapened. For someone who wants to watch the best athletes in the world compete against one another, it can be alienating to listen to the announcer read stilted ad copy about the upcoming slate of same-game parlays.

And there’s a much more concerning subset of the integrity problem, one that feels more permanent and specific to the style and ubiquity of online gambling. Sports betting may be a trenchant vice, but the bets themselves have changed dramatically. Single-game parlays, or S.G.P.s, in which a bettor strings together multiple wagers on individual statistical outcomes—how many points, rebounds, turnovers a certain player will accumulate—for potentially lottery-like payouts, have exploded in popularity. These bets are far more profitable for the books. According to a study by the University of Nevada, Las Vegas, a typical bet on whether a team will cover the spread will deliver a five- or six-per-cent return for the casino. An S.G.P., by comparison, will typically return up to thirty per cent. As a result, nearly every sports-betting company relentlessly pushes S.G.P.s, which, in turn, has led to a greater focus on individual players. It’s not that easy to fix a basketball game—you have nine other guys on the court affecting the outcome, not to mention the coaches and the officials. It’s a lot easier to fix your own performance. You just have to grab an extra rebound away from a teammate or maybe kick the ball out of bounds at the end of a blowout, and the odds will be ever in your favor.

On Monday, while I was typing the first draft of this column, the news broke that Jontay Porter, of the N.B.A.’s Toronto Raptors, was under investigation for possible gambling infractions involving prop bets—which include wagers based on the stats a player will accrue over a game. N.B.A. Twitter, perhaps the fastest archivists on the Internet, quickly uncovered amusing footage of Porter engaged in all sorts of on-court activity that now seemed suspicious. (Porter, who has not been available for the Raptors’ past three games for what the team describes as “personal reasons,” has yet to comment on the allegations.) Many of these clips were offered in jest, but, truthfully, this is how many fans now interact with sports. When the player is the prop and the prop fails, the player then becomes suspect. And, when an increasing number of bets are props based on individual player performances, rather than team outcomes, it doesn’t take much to prompt cheating, or to trigger the suspicion of misconduct. At some point, that toxic cloud changes the whole atmosphere of sports fandom. “To half the world, I’m just helping them make money on DraftKings or whatever,” Tyrese Haliburton, an all-star guard for the Indiana Pacers, recently told a reporter. “I’m a prop.”

What will all this look after another two years of players as props and another handful of Jontay Porter stories, throughout all levels of American sports? This past Thursday, I stood at the Yahoo Sportsbook by William Hill kiosk at the Venetian and noticed that I could bet props on college players, including those at small schools, the sort where players will never sniff the N.B.A. and don’t get offered the lucrative name, image, and likeness deals that are available to players at larger programs. (This concern, at least, has reached the offices of the N.C.A.A.: on Wednesday, the organization’s president said that he was taking steps to ban prop betting on college athletes.) The next night, I watched parts of an entirely meaningless N.B.A. game between two teams that are actively trying to lose as much as possible in order to secure a better position in next year’s draft. Some of the players on the court were on partial deals that will pay them about as much as a first-year partner at a mid-level law firm. It’s decent money, but that check may only come once for these guys.

There will be more scandals. And there will be things that we never hear about. Sports media has been so overrun with gambling money that you can’t turn on a broadcast or a debate show without seeing a betting segment. Journalists will continue to chase scandalous stories, but, having worked in sports media myself, I can imagine a scenario in which stories get shelved, or upper management quietly reassigns reporters to different beats—not out of an aversion to the truth, or because the stories don’t sell, but because they want to avoid the awkwardness of running a segment about a betting scandal followed by three gambling-app ads and a chatty, mostly nonsensical three-minute segment on the night’s best prop bets. But any such suppression won’t work. The social-media detectives will keep posting their Zapruder-like videos, and everyone will become a suspect, whether they deserve to or not. ♦

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Effects of expertise on football betting

Yasser khazaal.

1 Geneva University Hospitals, Grand-pré 70 C, 1206 Geneva, Switzerland

Anne Chatton

Joël billieux.

2 Psychological Sciences Research Institute, Catholic University of Louvain, Louvain-La-Neuve, Belgium

Lucio Bizzini

Grégoire monney, emmanuelle fresard, gabriel thorens, guido bondolfi, nady el-guebaly.

3 Addiction Division, University of Calgary, Calgary, AB, Canada

Daniele Zullino

Football (soccer) is one of the most popular sports in the world, including Europe. It is associated with important betting activities. A common belief, widely spread among those who participate in gambling activities, is that knowledge and expertise on football lead to better prediction skills for match outcomes. If unfounded, however, this belief should be considered as a form of “illusion of control.” The aim of this study was to examine whether football experts are better than nonexperts at predicting football match scores.

Two hundred and fifty-eight persons took part in the study: 21.3% as football experts, 54.3% as laypersons (non-initiated to football), and 24.4% as football amateurs. They predicted the scores of the first 10 matches of the 2008 UEFA European Football Championship. Logistic regressions were carried out to assess the link between the accuracy of the forecasted scores and the expertise of the participants (expert, amateur, layperson), controlling for age and gender.

The variables assessed did not predict the accuracy of scoring prognosis (R 2 ranged from 1% to 6%).

Conclusions

Expertise, age, and gender did not appear to have an impact on the accuracy of the football match prognoses. Therefore, the belief that football expertise improves betting skills is no more than a cognitive distortion called the “illusion of control.” Gamblers may benefit from psychological interventions that target the illusion of control related to their believed links between betting skills and football expertise. Public health policies may need to consider the phenomenon in order to prevent problem gambling related to football betting.

Introduction

Football is one of the most popular sports in the world, Europe included. It is associated with important monetary transactions and financial sponsoring [ 1 ].

Sports betting is associated with pathological gambling [ 2 ] and is widely available on the Internet [ 3 ], one of the most important means for seeking general, medical, and gambling information [ 4 , 5 ]. There, one can find messages such as “To win at sports betting, you have to prognosticate correctly. Don’t forget that a sports bet is not the lotto. Sport is not only a question of chance, far from it. To place your bet efficiently, you must learn about football as a sport and follow a minimum of its championships.”

Football competition is, unmistakably, a sport based on a high level of training and specific skills. This assertion may lead to the belief that football knowledge and expertise will allow better prediction of match scores. If unfounded, however, this belief should be considered a form of “illusion of control.” This term was defined by Langer [ 6 ] as “an expectancy of a personal success probability inappropriately higher than the objective probability would warrant.” This type of distorted thinking was considered a major factor in gambling persistence and severity [ 7 , 8 ], and led to the development of cognitive restructuring therapies for pathological gamblers [ 6 ].

As suggested by Cantinotti, Ladouceur, and Jacques [ 9 ], to a certain degree, the utility of sport expertise in sport betting cannot be fully ruled out. For example, it was previously found that factors such as the home field advantage, team rankings, most recent results of teams, and injuries of key players significantly affect game results [ 10 - 14 ]. It was then suggested that skills could be helpful when betting on sports events [ 15 ].

Probably in connection with these considerations in sport and football betting, defeats have been shown to be more often discussed than wins [ 16 ] and were commonly attributed to unlikely or random events [ 5 ] or were considered a “near win” [ 11 ], whereas wins were attributed to skills in selecting the victorious players. This interpretation probably contributes to an overestimation of betting skills [ 5 ].

It would be relevant to determine whether expertise is essential for determining game scores. If this were not the case, the alleged skills in sports betting could be regarded as no more than a manifestation of the illusion of control, as observed in most gambling activities.

With several exceptions, such as horse betting [ 17 ] and hockey [ 7 ], the relation between gamblers’ skills and betting outcomes has been rarely studied. Studies that evaluated gambling skills rather than the role of expertise in sports for betting activities showed that monetary gains from gambling skills were not significantly higher than would have occurred by chance. Because of the wide popularity of football and football betting, it seems important from a public health policy perspective to assess the links between football expertise and prediction of match results.

The present study examined whether football experts were better than non-experts for predicting the scores of the first 10 matches of the 2008 UEFA European Football Championship.

During the 3 weeks prior to the beginning of the first match of the 2008 UEFA European Football Championship, a questionnaire was completed anonymously by 258 study participants recruited through local advertising and direct contact of football professionals (players, handlers, and referees) and sports reporters. The questionnaire assessed professional and amateur activity in relation to football. It also included five questions (Table ​ (Table1) 1 ) related to the degree of football interest (questions 1, 2, and 3), the degree of belief in the link between a good knowledge of football teams and accuracy of match-related prognoses (question 4), and sport betting habits (question 5). In addition, participants predicted outcomes for the first 10 matches of the 2008 UEFA European Football Championship.

Questions related to football and sport betting

Participants were classified as being in one of three categories:

(a) “Experts”: The experts are professional or semiprofessional football players, coaches, or football sport journalists whose work was related to the 2008 UEFA European Football Championship.

(b) “Amateurs”: These participants have an amateur link with football (e.g., amateur referee) and/or play football as amateurs.

(c) “Laypersons”: This group has neither professional nor amateur connections.

The forecasts were analyzed for winning accuracy (accuracy of the prognosis: winning team 1, winning team 2, or draw) and score accuracy (good score prediction).

Statistical analyses were performed with SPSS for Windows (version 15.0). An initial exploratory analysis involved the calculation of proportions, as well as means and standard deviation of the outcome values. Spearman correlations with Bonferroni’s correction ( p  = 0.05/4 since four correlations were analyzed; p  = 0.0125) were carried out to assess the links between each of the first four questions related to football interests and the fifth related to sports betting (Table ​ (Table1). 1 ). Moreover, one-way analyses of variance (ANOVAs) were performed to compare the distribution of the mean numbers of correct outcomes and correct score predictions as dependent variables with regard to the above-cited first four questions as factors, adjusting for multiple pairwise comparisons.

We also used a paired samples t -test to test whether gamblers had a greater number of correct outcomes than chance when forecasting the results of the games. Indeed, by chance, that is to say in the absence of any information, the probability of a gambler predicting 7 correct outcomes out of 10 games (0.016; the exact formula for the binomial distribution is given by p x = ( x n ) p x 1 − p n − x , where x is the number of successes and n the number of trials) is not the same as the probability of predicting 7 outcomes out of 10, given all the information in the bettor’s possession (0.7; given by the assumption: 7 correct outcomes out of 10 games). This last probability, referred to as conditional probability, means that before making a choice, the bettor will take into account all relevant information at their disposal. In addition to each participant’s observed probability of making the right bet, one may compare this to the expected probability based on chance.

Finally, a binary logistic regression for each of the 10 matches was done to predict the accuracy of the scores (correct vs. incorrect score) with the participants’ expertise categories (expert, amateur, or layperson) as predictor, controlling for age and gender (female vs. male). For the categorical factors “gender” and “expertise,” the reference groups were levels 2 and 3, respectively.

After checking for multicollinearity and outliers, we assessed the goodness of fit of these logistic models by considering the following:

The classification table of the intercept-only model (baseline or null model) with that of the full model, where a significant improvement should be expected over the null model.

The Nagelkerke R-square statistic with all the independent variables. This statistic attempts to quantify the proportion of explained variation in the logistic regression.

The statistical tests of the predictors, using the Wald chi-square statistics. P-values less than 0.05, or alternatively, confidence intervals that exclude the “1” value, are suggestive of significant predictions.

Two hundred and fifty-eight persons participated in the study (57% were men; mean age: 36.6 years ± 11.2). Fifty-five (21.3%) were classified as football experts, 140 (54.3%) as laypersons, and 63 (24.4%) as amateurs.

Answers to the five questions in the questionnaire are reported in Table ​ Table2. 2 . After Bonferroni’s correction was performed, the Spearman correlation showed significant associations between the first three questions related to football interest and sports betting (Spearman’s r = 0.49, r = 0.43, r = 0.41; p  < 0.0005, respectively). Sports betting appeared to be associated with football interest. There was no correlation found between question 4 (believed role of football expertise for prognosis skills) and sports betting.

Distribution of participants’ answers to the five questions reported in Table ​ Table1 1

The numbers and percentages of accurate outcomes and scores by category of participants are reported in Table ​ Table3. 3 . The mean number of correct outcome or score prognoses and the relative frequency of the distribution of correct outcomes by category of participants are reported in Table ​ Table4 4 and Figure ​ Figure1, 1 , respectively.

Number and percentage of correct outcomes and scores by categories of participants and by match

Comparison of mean number (standard deviation) of correct outcomes and scores exactly predicted by each group of participants

Distribution of relative frequencies of correct outcomes.

The ANOVAs that were used to compare the distribution of the mean numbers of correct outcomes and correct score predictions with regard to the first four questions showed a statistical significant between-group difference for the mean number of correct outcomes (F (3,253)  = 2.8 and p  = 0.04) in question 4 (“I think that a good knowledge of the teams allows me to predict with accuracy the match score results”). But after adjusting for multiple comparisons, this difference was no longer significant. No significant difference before or after adjustment was observed for the other three questions.

The paired sample t -test that was used to evaluate whether gamblers had a greater number of correct outcomes than chance when forecasting the results of the games showed a statistical significant difference (t = 39.15 and p  < 0.0005). We conclude from the data that the bettors were more accurate in their predictions than chance.

The logistic regressions, which were done to test the research hypothesis, yielded poor results. The classification table of the full models showed no improvement over the baseline models, meaning that the classification rates were exactly the same in both situations (Table ​ (Table5, 5 , column 2). The Nagelkerke R-square measures ranged from 1% to 6%, leading us to conclude that these models were not useful in explaining the outcome variable (Table ​ (Table5, 5 , column 3). Finally, the predictor variable “expertise” (Table ​ (Table5, 5 , column 4) did not prove significant except for the model involving the game Germany-Poland ( p  = 0.03, odds ratio = 2.57 and 95% CI for odds ratio = [1.08; 6.14]). This result means that compared with a layperson, being an amateur increases the likelihood of accurate score prediction by 2.57, assuming that the other factors in the model are held constant. There was no significant difference between experts and laypersons since the confidence interval includes “1” (exact results not shown).

Evaluation of model’s goodness of fit

*Maximum iterations reached and final solution not found because group sample size too small.

It is worthwhile noting that no expert was able to correctly predict more than seven outcomes and no participant more than eight (Figure ​ (Figure1 1 ).

In the present study, the results of the logistic regressions, although poor, were consistent across matches. Experts do not appear to be better than non-experts at predicting football match scores. Similarly, ANOVA results indicated that the average number of correct outcomes with respect to accurate scores were not significantly different across the four conditions (first four questions in Table ​ Table1). 1 ). The belief that expertise is useful for sports gamblers seems to be simply an illusion of control.

By chance alone, the probability of someone predicting 10 correct outcomes (first winning team, second winning team, or draw) out of 10 games is estimated to be 1.7 100 , 000 , i.e., P X = 10 = 10 ! 10 ! 0 ! × 1 3 10 × 2 3 0 . The exact formula for the binomial distribution is given by p x = ( x n ) p x 1 − p n − x , where χ is the number of successes and n the number of trials. This is an interesting probability for the sports betting business, which mostly offers big monetary winnings on a combination of match results. Thus, in consideration of this probability and the lack of impact of expertise on football betting outcomes, sports betting appears to be nothing other than a game of chance, as suggested by other studies [ 7 , 15 ].

As reported elsewhere [ 18 ], sport interest, rather than the athlete’s status [ 19 ], is possibly linked to sport betting. The finding of a lack of association between sports bets and the belief assessed in question 4 (“I think that a good knowledge of the teams allows me to predict with accuracy the match score results”) may result from the present sample being participants from the community and not problem or pathological gamblers. About 6% of the subjects did, however, consider this declaration as extremely correct and more than 30% as fairly correct, showing the wide diffusion of such beliefs.

One possible limitation of the present study is that it was not carried out as a real gambling condition. The results should be then taken with caution. Further studies may include measures of gambling-related cognitions (e.g., fallacy, superstitious beliefs, biased evaluation of outcomes), participants’ betting behaviors and habits, and more detailed measures of expertise and self-confidence related to a sense of expertise, as suggested by wagering models [ 20 ]. Further studies may also include betting related to other sport activities.

Another limitation was the small sample of games surveyed and the non-random selection of these games, which resulted in a non-probability sample. Out of all matches that were played during the 2008 UEFA European Football Championship, only the first 10 were selected for analysis. The possibility that, by pure chance, the games selected happened to be more or less predictable than the standard ones should not be ignored.

Finally, the logistic regression models set up to predict the accuracy of the number of goals scored by each team may have failed to take account of other possible significant predictors, such as the quality of the teams (ability to attack and/or to defend), the team’s league position at the time of playing, and the “home effect” (advantage in playing at home). The absence of these potential predictors may explain the small predictive power of our models.

Expertise, gender, and age did not have an impact on the accuracy of the football match prognoses. Consequently, the belief that football expertise improves betting skills seems to be a cognitive distortion.

Clinicians may inform gamblers about the limited help of football expertise in match-outcome predictions and the relative fallacy of commercial advertisements for sport betting, such as “….a sports bet is not the lotto… to place your bet efficiently, you must learn about football as a sport and follow a minimum of its championships.” Gamblers may benefit from psychological interventions that target the illusion of control related to their believed links between betting skills and football expertise. Furthermore, public health prevention policies may need to consider the present results in order to prevent problem gambling related to football betting.

Competing interests

The authors declare that they have no competing interests.

Authors’ contributions

YK and DZ participated in the design of the study. YK and NG drafted the manuscript. AC performed the statistical analysis. JB, LB, GM, EF, GT, RK, and GB participated in recruitment and data collection. All authors read and approved the final manuscript.

Acknowledgements

We thank the study participants, the football experts who agreed to participate in the study, GREA and Mr. Pascal Savary, the “Rien ne va plus,” the Geneva Health Department, Dr. Christine Davidson, Mrs. Alessandra Horn, and Mr. Christian Osiek.

Funding source

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