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An Overview of the Economics of Sports Gambling and an Introduction to the Symposium

Victor matheson.

College of the Holy Cross, Worcester, USA

Gambling in the Ancient World

Gambling likely predates recorded history. The casting of lots (from which we get the modern term “lottery”) is mentioned both in the Old and New Testaments of the Bible, most famously when Roman soldiers cast lots for the clothes of Jesus during his crucifixion. In Greek mythology, Hades, Poseidon, and Zeus divided the heavens, the seas, and the underworld through a game of chance.

Organized sports also have a long history. The Ancient Olympic Games date back to 776 BCE and persisted until 394 AD. The Circus Maximum in Rome, the home of horse and chariot racing events as well as gladiatorial contests for over one thousand years, was originally constructed around 500 BCE, and the Colosseum in Rome began hosting sporting events including gladiator fights in 80 AD. Variations of the ball game Pitz were played in Mesoamerica for nearly 3000 years beginning as early as 1400 BCE (Matheson 2019 ).

Given the prevalence of both sporting contests and gambling across many ancient civilizations, it is natural to conclude that the combined activity of sports gambling also has a long history. And, indeed it is widely reported that gambling was a popular activity at the Olympics and other ancient Panhellenic events in Greece and at the racing and fighting contests in ancient Rome. Problems associated with gambling were also widely reported. As early as 388 BCE, the boxer Eupolus of Thessaly was known to have paid opponents to throw fights in the Olympics. Rampant gambling in Rome led Caesar Augustus (c. BCE 20) to limit the activity to only a week-long festival called “Saturnalia” celebrated around the time of the winter solstice, while Emperor Commodus (AD 192) turned the royal palace into a casino and bankrupted the Roman Empire along the way (Matheson et al. 2018 ).

Just as in the modern day, gambling was often looked down upon by societal leaders in antiquity. Horace (Ode III., 24; 23 BCE) wrote, “The young Roman is no longer devoted to the manly habits of riding and hunting; his skills seem to develop more in the games of chances forbidden by law.” Juvenal (Satire I, 87; 101 AD), well-known for coining the term “bread and circuses” wrote, “Never has the torrent of vice been to irresistible or the depths of avarice more absorbing, or the passion for gambling more intense. None approach nowadays the gambling table with the purse; they must carry their strongbox. What can we think of these profligates more ready to lose 100,000 than to give a tunic to a slave dying with cold.” (Matheson 2019 ).

Gambling in Renaissance and Pre-industrial Revolution Europe

Gambling in Europe persisted into the Middle Ages and Renaissance. For example, although the true origins of the famous columns in Venice’s Piazza San Marco are lost to the mysteries of time, at least one history suggests they were erected around 1127 by Nicholas Barattieri, who was rewarded for this task by the local government with an exclusive right to operate a gaming table between the columns, an activity otherwise officially prohibited in the Republic (Schiavon 2020 ).

However, without the large sporting events of the ancient world, gambling turned more toward to precursors of modern casino games. Indeed, the gambling that occurred in the “small houses” or “casini” of the city of Venice is the origin of the modern term “casino,” and in 1638 Il Ridotto, “the Private Room,” became the first public, legal casino in the region (Schwarz 2006 ).

Until the formation of professional sports leagues in the mid- to late nineteenth century, horse racing was the predominant type of sports gambling across Europe and North America. The Newmarket Racecourse near Cambridge, UK, was founded in 1636 although races at the location date to even earlier. The racetrack was frequented by King Charles II earning horse racing the title of “the Sport of Kings” (Black 1891 ). The first racetrack in North America was established on Long Island in 1665, and horse racing has persisted in the USA since that time.

Prior to the mid-1800s, bets in horseracing were handled by bookmakers who set odds on individual races. This carries risk for the bookmaker who may be forced to pay out large winning bets as well as the bettor who may find that the bookmaker lacks the funds to cover all payouts. This problem was solved in 1867 in Paris when Joseph Oller, who later went on to open the famous Parisian nightclub the Moulin Rouge, developed pari-mutuel betting.

Under pari-mutuel betting, the returns are based not on independent odds set by a bookmaker but instead are endogenously generated by the gamblers themselves based upon the number and size of the bets made on various race participants (Canymeres 1946 ). This betting system rapidly became wildly popular for racing in Europe and USA and remains the standard for horse racing today throughout the world.

Gambling Throughout US History

Gambling was a common activity throughout colonial and early American history. Lotteries funded activities such as the original European settlement at Jamestown, the operations of prestigious universities such as Harvard and Princeton, and construction of historic Faneuil Hall in Boston. Card rooms were not unusual at taverns and roadhouses across the country, and the activity moved west onto riverboats and into saloons as westward expansion occurred during the 1800s (Grote and Matheson 2017 ).

However, the late 1800s and early 1900 witnessed a widespread decline the legality of all types of gambling throughout the USA. In the sports realm, by 1900 betting on horse races was made illegal except in Kentucky and Maryland, states that to this day host two of the three Triple Crown events in American horseracing, the Kentucky Derby and the Preakness Stakes. States began to relegalize gambling on horse racing in the 1930s as a method of economic stimulus during the Great Depression. Total horse racing handle peaked in the 1970s and has generally declined since that time due to increased competition from alternative forms of gambling such as state lotteries and casinos (and, in fact, many racetracks nationwide, known as “racinos,” are permitted to offer alternative forms of gambling such as slot machines on their grounds (Nash 2009 )). In 2019, horse racing’s handle in the USA totaled $11.0 billion (Jockey Club 2020 ).

The birth of professional sports leagues in the USA also gave immediate rise to new betting opportunities, as well as problems associated with corruption. The oldest professional league in the USA, baseball’s National League, formed in 1876, and by 1877 the Louisville Grays ended the season mired in a betting scandal and ceased operations. Similarly in football, the Ohio League, a forerunner to the modern National Football League (NFL), began play in 1903, and by 1906, the league was embroiled in a match fixing scandal between the Canton Bulldogs and the Massillon Tigers (Grote and Matheson 2017 ).

During the early years of professional sports leagues in the USA, betting on games, although generally illegal like most gambling in the period, was common either through direct bets made with bookies or through “pool cards” allowing gamblers to bet on a slate of games. Nevada, which in 1931 became the first state to relegalize most forms of gambling, authorized sports gambling in 1949, but high tax rates on wagers prevented major casinos from running sports books until 1974. Following the elimination of a 10% tax on sports gambling revenues in the state, the sport betting handle rose dramatically from $825,767 in 1973 to $3,873,217 in 1974, to $26,170,328 in 1975 (Grote and Matheson 2017 ). By 2019, Nevada’s 192 sportsbooks took in $5.3 billion in wagers or roughly 2.7% of total gaming revenues for the state (Nevada Gaming Control Board 2019 ).

While Nevada remained the only state offering full sports books, Montana, Oregon, and Delaware all offered pool cards through their state lotteries beginning in the 1970s. Montana first offered legal pool cards in 1974. Delaware followed in 1976 (even winning a court case against the NFL for the right to offer sports gambling), but its games folded in the following year due to difficulties in adhering to the state’s statutory guidelines about lottery contributions to state coffers. The Oregon Lottery sold NFL pool cards from 1998 to 2007 and National Basketball Association (NBA) game tickets in 1998 and 1999 (although the NBA ticket did not include games featuring Portland’s local NBA team). Pressure from the National Collegiate Athletic Association (NCAA) eventually led the state to terminate its sports gambling offerings under the threat of losing the opportunity to host NCAA post-season men’s basketball tournament (March Madness) games (Grote and Matheson 2017 ).

The Professional and Amateur Sports Protection Act (PAPSA), passed in 1992, prohibited states from legalizing sports gambling in any form including lotteries, casinos, and tribal casinos while grandfathering in the four states with existing sports gambling operations. In mid 2010s, the state of New Jersey, in an effort to revive its flagging casinos in Atlantic City, sued to overturn PAPSA, and in May 2018, the US Supreme Court declared PAPSA unconstitutional. While this ruling did not legalize sports gambling in any states, it did allow states the option to legalize sports gambling if they so choose. This symposium examines some of the economic issues facing the sports gambling industry as the American market opens up.

Issues Facing the New Sports Gambling Industry

The first and perhaps easiest question facing the industry is how quickly and how widely will sports gambling be adopted by states? Here it seems clear that sports gambling will follow the pattern seen in lottery and casino adoption, although almost certainly at a much faster pace. As noted by Garrett and Marsh ( 2002 ), once states began to legalize state lotteries, neighboring states began to feel pressure to legalize their own state games or otherwise lose consumer spending to lottery players crossing the border to buy tickets.

By 2020, this pressure had led all but 6 states to adopt lotteries after the first state lottery was reestablished in New Hampshire in 1964. Among the holdouts, Alaska and Hawaii are protected geographically from cross-border purchases, Nevada’s powerful gambling industry has successfully prevented the adoption of a state-sponsored competitor, and conservative religious cultures in Alabama, Mississippi, and Utah have stopped lotteries there. (Religious concerns have not stopped Mississippi from legalizing sports gambling, however. Perhaps God just really wants to put a few bucks down on Ole Miss to upset the Tide this year.)

With respect to sports gambling, New Jersey and Delaware legalized the activity immediately upon the Court’s decision in 2018, and many states followed suit. By the end of 2020, 20 states and the District of Columbia had legalized sports gambling, 6 had legalized sports gambling but were pending launch, and over 20 more states were considering legislation (Rodenberg 2020 ). It appears that sports gambling will soon be legal nearly nationwide.

The next big question facing the industry is assessing the potential size of the sports betting market. If sports wagering is restricted to in-person betting at existing casinos, the impact of nationwide legalization is likely to be quite modest. Extrapolating Nevada’s sport wagering data to the national casino market suggests that nationwide legalization might lead to as much as $20 billion in annual wagers and just under $1 billion in net casino revenues. While these figures may seem high, they pale in comparison to gambling figures in the UK where sports betting has been legal (although highly regulated) since 1960 and is widely available through over 8300 (as of March 2019) small, commercial betting shops spread throughout the country as well as through online betting sites.

In the most recent fiscal year prior to shutdowns caused by the COVID-19 pandemic, in-person betting shops in the UK generated $3.7 billion and online gambling generated another $2.8 billion in net gambling revenues (UK Gambling Commission 2020 ). This implies that UK bettors placed roughly $130 billion in wagers in 2019 or about $2000 per person in the country. If industry were to achieve a similar level of popularity in the US market, this would suggest over $600 billion in annual wagers and $32 billion in net sport gambling revenue. The $32 billion figure would be roughly twice the net gambling revenue generated by state lotteries across the country and slightly less than the $42 billion in net casino gaming revenue generated across the USA. Such revenue figures would likely only be possible with widespread adoption of legalized mobile sports gambling as well as within-game betting on individual plays as opposed to wagering solely on game outcomes.

Obviously, another major question facing the industry is the extent to which expanded access to sports gambling will bring in new players to the gambling industry overall or whether it will simply cannibalize existing gambling options such as state lotteries, horse racing, or casino gaming. The first paper in this symposium examines this topic by analyzing the determinants of sport gambling handle and its effects on other casino gaming at West Virginia casinos during roughly the first year of legalized sports betting in the state (Humpheys 2021). Brad Humphreys finds that the introduction of sports gambling seems to have significantly decreased overall state gaming tax revenues as gains from sport gambling taxes were far outweighed by decreases in tax revenues from video lottery terminals.

Of course, even if the problem of cannibalization is avoided by sports gambling attracting a new customer base, this is not without its own set of problems as sports wagering may introduce an entirely new population to the problems associated with pathological gambling and problem gaming (McGowan 2014 ). The second paper in this symposium examines health outcomes in Canada related to participation in gambling activities (Humphreys et al. 2021 ). Brad Humphreys, John Nyman, and Jane Ruseski show that recreational gambling has either no effect or even actually reduces the probability of having certain chronic health conditions and has a positive impact on life satisfaction suggesting the possibility that expanded sport gambling in the USA may not be associated with significant adverse health outcomes.

Legalized sports gambling is certain to bring about winners and losers. As noted above, depending on the level of cannibalization, other forms of gambling are likely to be losers such as horse racing, which is likely to continue its long-term decline in gambling handle (Nash 2009 ), and potentially casino gaming as identified by Humphreys ( 2021 ) in this symposium. On the other hand, sports book operators and mobile application developers are likely winners, so casinos themselves may either be either winners or losers in sports gambling legalization. It is interesting to note that established casinos have not been the only players to enter the online sports gambling market. In many states, the companies FanDuel and DraftKings, who prior to sports gambling legalization operated online fantasy football competitions of controversial legality, have already been able to leverage their fan bases in the online fantasy sports gaming communities into more traditional online sports gambling opportunities.

The sports leagues themselves may also be either winners or losers. Historically in the USA, leagues strongly opposed legal sports betting due to the potential for corruption. The history of sports in the USA is littered with betting scandals from the earliest days of the previously mentioned Louisville Grays and Canton Bulldogs to the infamous 1919 “Black Sox” World Series scandal to the 1948 NCAA basketball point-shaving scheme to the more recent actions of Major League Baseball (MLB) player and manager Pete Rose or NBA referee Tim Donaghy.

More recently, however, leagues have become more supportive of sports betting. In part, leagues acknowledge that legal betting markets make it easier for regulators to uncover suspicious betting behavior that could suggest corruption. More importantly, teams and leagues have also slowly recognized the potential for higher fan interest if fans have the opportunity to gamble on games. There is no doubt that the NCAA can attribute a significant portion of its 23-year, $19.6 billion television contract for March Madness on the popularity of “bracket pools,” and likewise the NFL understands the degree to which the explosion of fantasy football leagues has increased the popularity of its games. Humphreys et al. ( 2013 ) developed evidence of a significant correlation between betting and television viewership for regular season men’s NCAA basketball games.

Furthermore, the dramatic increase in professional athlete salaries over the past several decades in the USA has reduced worries of corruption. It is highly unlikely that star players in any major US league would jeopardize their massive earning potential as an athlete by accepting a bribe to alter a game outcome (and non-star players to whom a bribe could potentially be profitable are rarely in a position to influence games).

Those sports that remain at more significant risk to corruption are those with a high level of fan interest but low player salaries. This describes the working conditions of athletes prior to free-agency in the USA such as during the 1919 Black Sox scandal, referees like Tim Donaghy, and players in minor leagues or small national leagues as well as cricket players prior to the relatively recent formation of the Indian Premier League. It also describes the conditions of college athletes in the USA as the NCAA has successfully operated a cartel restricting the ability of even top college players from earning money as a player despite playing for teams generating millions or tens of millions of dollars annually for their host institutions. Thus, it comes as no surprise that the NCAA remains adamantly opposed to sport gambling in contrast to the major professional leagues in the USA.

Sports leagues are naturally eager to take steps to protect themselves against potential corruption in the wake of expanded gambling opportunities. The third paper in the symposium (Depken and Gandar 2021 ) explores the topic of integrity fees, payments by sports books to leagues, supposedly to pay for monitoring to ensure against match fixing. Craig Depken and John Gandar find evidence that integrity fees might influence sports books to establish lines that would minimize the chances for payouts in certain game situations.

Finally, legalized sports gambling will provide researchers with troves of new data to analyze one of the oldest questions in gambling economics: are sports betting markets efficient? The final paper in this symposium provides an excellent example of this type of research (Brymer et al. 2021 ). Rhett Brymer, Ryan M. Rodenberg, Huimiao Zheng, and Tim R. Holcomb examine whether referees in college football’s major conferences can be shown to have particular biases and if these biases are appropriately accounted for in the gambling markets. Studies like these will remain a fertile area for continued economic research.

As guest editor, I wish to thank Eastern Economic Journal co-editors Cynthia Bansak and Allan Zebedee, participants in the sports economics sessions at the 39th annual Eastern Economic Association Conference in New York City, February 2019, and numerous anonymous referees for their assistance in putting together this symposium. Most importantly, thanks go out to Eastern Economic Association Vice President Brad Humphreys who both proposed this symposium and collected and reviewed the participating papers. His name should really be on this guest editor’s introduction, but I guess he will have to settle to being co-author on two fine contributions within this symposium.

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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.

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( 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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Expert Commentary

Sports betting in the US: A research roundup and explainer

We look at the landscape of legal sports betting in America, explain what the research says about how legalization affects tax revenues, and provide a brief history of the activity.

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by Clark Merrefield, The Journalist's Resource October 25, 2022

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On Nov. 8, Californians will vote on two ballot measures that would allow for different forms of sports betting in the state.

Proposition 26 would allow sports betting at licensed casinos and horse tracks on tribal lands and run by federally recognized Native American tribes.

Prop. 27 would allow tribes licensed to offer gambling and major gaming companies to offer online sports betting. These companies include FanDuel and DraftKings, which together make up roughly two-thirds of the U.S. online sports betting market.

“If both pass, they might both go into effect or the result could be decided in court, depending on which one gets more yes votes,” writes CalMatters economics reporter Grace Gedye in an article from June.

Although California is the only state with sports betting on the midterm ballot , it’s not the only state where sports betting is a topic of political discussion — and relevant for journalists across beats to understand. For example, Georgia gubernatorial candidate Stacey Abrams recently expressed support for legalized sports betting in her state. Abrams’ opponent, Gov. Brian Kemp, is opposed.

In Missouri, state lawmakers from both parties support legalizing sports betting , but Gov. Mike Parson is hesitant. Vermont lawmakers are considering taking up a sports betting bill during the next legislative session. Gubernatorial candidates in South Carolina and Texas support legal sports betting. In Florida, there is an ongoing lawsuit over whether the state should be allowed to give the Seminole Tribe the exclusive right to run online sports betting there.

Legal sports wagering in the U.S. has grown vertically in recent years — from less than $5 billion worth of bets placed in 2018 to $57 billion in 2021 — despite sports betting remaining illegal in nearly half of states. Sportsbooks, the entities that take sports bets, bring in about $4 billion yearly after wagers are settled.

The reason for this growth: a May 2018 Supreme Court ruling. Justice Samuel Alito, in delivering the 6-3 decision , reasoned that 1992 federal legislation banning states from allowing sports betting was unconstitutional.

Under the 1992 law, the Professional and Amateur Sports Protection Act, the federal government did not “make sports gambling itself federal crime,” Alito writes in the 2018 decision. “Instead, it allows the [U.S.] Attorney General, as well as professional and amateur sports organizations, to bring civil actions to enjoin violations.” Other than legislative powers the Constitution grants Congress, the federal government cannot “issue direct orders to state legislatures,” Alito writes. The majority interpreted the Professional and Amateur Sports Protection Act as doing so.

Here is how John Holden , an assistant professor of business at Oklahoma State University who has written extensively on sports gambling, explains the 2018 ruling:

“If the federal government wants to make sports betting illegal, they’re free to do so, but they can use the [Federal Bureau of Investigation] and the [Department of Justice] to enforce that,” Holden says. “They can’t tell a state legislature that you need to keep that law on the books and use your state police to go out and bust up gambling rings.”

A fundraising breakdown from the Los Angeles Times shows about $132 million has been raised to support Prop. 26, with about $43 million in opposition funding. Top backers include the Federated Indians of Graton Rancheria, the Pechanga Band of Indians and the Yocha Dehe Wintun Nation. Non-Native American casino and gaming interests are largely opposed — conversely, they have backed Prop. 27, which would open up sports betting to all gambling interests, not just Native American-run casinos.

Tribal gaming brings in nearly $40 billion a year across all tribes that operate gambling enterprises, according to the National Indian Gaming Commission . “Gaming operations have had a far-reaching and transformative effect on American Indian reservations and their economies,” write the authors of a 2015 paper about how the act affected tribal economic development. “Specifically, Indian gaming has allowed marked improvements in several important dimensions of reservation life.”

The landscape of legal sports betting

If California legalizes sports betting, it would represent a major coup for gaming interests in the state. In California, the most populous state, horse racing is the only legal form of sports betting.

Sports wagering is legal in 28 states plus the District of Columbia, according to a recent Washington Post analysis. Seven states prohibit online sports betting and only allow in-person wagers at licensed locations, such as casinos: Delaware, Maryland, Mississippi, Montana, New Mexico, North Carolina and North Dakota. Sports betting is legal but pending rollout in four states: Maine, Massachusetts, Nebraska and Ohio. Kansas is the most recent state to implement legal in-person and online sports gambling, as of Sept. 1.

States place a range of licensing fees on operators and tax rates on sports betting revenue, from a low of 6.75% in Nevada and Iowa to a high of 51% in New Hampshire and New York. States use tax revenues for a variety of purposes . Some, like Delaware, put sports wagering taxes toward their general fund. Colorado uses sports betting taxes to pay for its statewide water plan, Illinois funds transportation infrastructure and New York funds education programs.

In states where sports betting is legal, bettors can wager on nearly any major sporting event, both professional and amateur. For example, bettors can wager on the outcome of a baseball game, as well as events within the game, such as whether a particular player will hit a home run.

Polling indicates California may be unlikely to join the legal betting club. CalMatters reported earlier this month that despite various campaigns raising more than $440 million in marketing related to Props. 26 and 27, each measure is garnering support from less than a third of likely voters, according to October polling from the Institute of Governmental Studies at the University of California, Berkeley.

Below, we explore recent research on sports betting. Among the findings of the seven studies featured here:

• Sports bettors are more likely to be white, male, and exhibit psychological traits consistent with narcissism.
• Tax revenue from sports betting may appear substantial in raw numbers, but the impact on tax coffers is muted when compared with income and sales taxes, or tax revenue from other gambling offerings.
• Evidence is mixed as to whether introducing sports betting cannibalizes — eats away at — revenue from other types of gambling.
• Some college football referees may more heavily penalize betting favorites.

The nonprofit National Council on Problem Gambling estimates as many as 8 million adults in the U.S. may have a mild, moderate or severe gambling problem. However, there is a lack of comprehensive, recent academic research on the extent of gambling addiction in the U.S., and the societal costs.

If you feel you may have a problem with gambling you can get help from the National Council on Problem Gambling by call or text at 1-800-522-4700, or online chat at ncpgambling.org/chat .

Research roundup

The Income Elasticity of Gross Sports Betting Revenues in Nevada: Short-Run and Long-Run Estimates Ege Can and Mark Nichols. Journal of Sports Economics, October 2021.

The study: The authors analyze quarterly sports betting data from Nevada covering 1990 to 2019, to explore whether sports betting might be a viable tax revenue stream for other states. Sports betting has been legal in Nevada for decades, so it is the only state with long-run data that can potentially provide insight on the tax base future in states that have legalized sports betting since 2018. The authors note that Nevada is a “mature” market for sports betting, meaning industry growth is relatively stable year to year. A state that newly legalizes sports gambling is likely to see an immediate jump in sports betting revenue, with industry growth levelling off over time.

The findings: In the short-run, quarter-to-quarter, the rise and fall of sports betting revenue in Nevada is most closely tied to changing sports seasons. The authors suggest this is due to differences in how much bettors wager on various sports — the NFL, for example, is “the most popular sport to place wagers on,” with revenues rising and falling as an NFL season begins and ends. In the long run, taxable income in the state and sports betting revenues tend to grow at similar rates. Sports betting revenue in Nevada is a small fraction of revenues from other sources.

The authors write: “Total sports betting revenue in Nevada, the amount kept by the casinos, was $329 million in 2019, implying $22.2 million in tax revenue for the state. In contrast, casino gambling in Nevada in 2019 was $12 billion, generating $810 million in tax revenue. Sports betting is a gambling activity where the amount retained by the casino, and consequently retained by the state, is relatively small as most of the money from losing bets is transferred to those with winning bets. Therefore, sports gambling is a smaller contributor to tax coffers compared to more traditional tax sources such as income and taxable sales or, if applicable, casino revenue.”

A Comparative Analysis of Sports Gambling in the United States Brendan Dwyer, Ted Hayduk III and Joris Drayer. International Journal of Sports Marketing and Sponsorship, August 2022.

The study: The authors explore whether there are psychological differences between bettors and those who do not bet, as well as differences in how closely bettors identify with social institutions, such as religious organizations and far-right or far-left politics.

The authors surveyed 377 bettors and 402 non-betting sports fans from 47 states and explored differences between bettors and non-bettors in states with legal gambling and states where gambling is banned. They also asked about narcissism, which past research has found “is associated to gambling behavior especially as it relates to risky behavior such as participating in illegal gambling,” the authors write. Bettors in the sample were 81% male, compared with 69% of non-bettors. Among bettors, 64% were white and 27% were Black, while 77% of non-bettors were white and 17% were Black.

The findings: In legal gambling states, bettors felt more self-worth than non-bettors, though in states where gambling is illegal the difference in self-worth was almost nil. In legal gambling states, bettors reported a stronger personal identity, “or the importance with which an individual identifies with their relationship and career,” than non-bettors. This relationship flipped in illegal gambling states, with non-bettors showing a stronger personal identity than bettors. In both illegal and legal gambling states, bettors reported slightly higher levels of social uselessness — “an individual’s perceived lack of worth related to social institutions” — than non-bettors, though the gap was wider in illegal gambling states.

The authors write: “Bettors look different and come from different backgrounds and locations. Psychographically, they were clearly more narcissistic. They also indicated a higher social identity and self-worth, yet perceived themselves as less worthy members of important social institutions. In general, sports bettors out consumed non-bettors as it relates sports spectatorship.”

Game Changing Innovation or Bad Beat? How Sports Betting Can Reduce Fan Engagement Ashley Stadler Blank, Katherine Loveland, David Houghton. Journal of Business Research, June 2021.

The study: Legal sports betting means more than $4 billion in additional yearly revenue across the four major sports leagues, according to research the authors cite from the American Gaming Association. At the same time, there may be drawbacks that come with the financial windfall. The authors conduct two studies to explore how sports betting affects fan engagement — the emotional connection fans have with their favorite teams.

The first study included 325 people recruited from Mechanical Turk and focused on betting on a team to win, also called moneyline betting. The second was among 167 Mechanical Turk-recruited participants and focused on prop, or “proposition” bets. Prop bets are bets made on the outcome of some action during the game — whether the next foul ball is caught, missed or goes into the stands, for example. The study is among the first to explore whether there are negative emotional responses from fans related to sports betting.

Participants read a scenario — they were to imagine watching a Major League Baseball game, then randomly they were told they placed either no bet on the game or one of several types of bets. These bets included a $20 bet for the home team to win, along with prop bets. Gaming experts, according to the authors, contend that prop bets can potentially keep fans engaged even if the outcome of the game is obvious — if a team is up by 10 runs by the middle innings, for example. In each study, the participants were asked questions to gauge their emotional investment before and after being told the outcome of the game and their bets. Questions broadly asked about team loyalty, feelings of connectedness to the team and the likelihood participants would watch the team or attend a game, along with other measures of fan engagement.

The findings: In the short run, immediately after a game, the study indicates that betting and losing can decrease fan engagement. Participants who placed no bet were more likely to exhibit loyalty and purchase team-branded merchandise when the team lost, compared with those who placed a moneyline bet. Those who won a prop bet were slightly more likely to be engaged with the team than those who did not bet — but those who lost a prop bet were much less engaged than those who did not bet.

The authors write: “Although industry experts expect sports betting to increase fan engagement, results from two studies do not support this expectation. Instead, we find that when fans lose a bet, positive emotions and subsequent fan engagement decrease.”

College Football Referee Bias and Sports Betting Impact Rhett Brymer, Ryan Rodenberg, Huimiao Zheng and Tim Holcomb. Eastern Economic Journal, January 2021.

The study: The authors explore whether betting lines are related to bias in officiating in the six major Division I college football conferences across 6,598 games from 2005 to 2012. Betting lines indicate whether a sportsbook thinks a game will be close, will favor one team or the other, or be a blowout. The authors note that “college football and basketball are the only major U.S. sports in which conferences have primary managerial responsibility for officials.” If there is a game late in the season with an undefeated team playing a middling team, the conference will benefit financially if the undefeated team wins and goes on to play in a high-profile bowl game. “Referees, as employees of the conferences, are theoretically more likely to have implicit bias favoring the team with higher revenue potential,” the authors write. They use penalty yards per game as a proxy for whether an officiating crew exhibits bias toward one team or the other.

The findings: The authors find signs of bias during in-conference games in two conferences: the Atlantic Coast Conference and the Big East, which reorganized in 2013 and no longer sponsors football. In-conference games are those where two teams from the same conference play each other. In those ACC games where there one team was favored to win by three touchdowns or more, the authors find officials call 6.5 more penalty yards per game against the favorite. In the Big East, the penalty yards increase to 5.7 for the heavy favorite. Further, ACC officials appeared to flag fewer penalty yards against teams that had been in the league longer and enjoyed historic success, rather than newer teams enjoying more recent success. The authors found no officiating bias when an out-of-conference opponent was heavily favored.

The authors write: “… with increasing state regulation, there will likely be more scrutiny of officiating given that a wider spectrum of consumers will have a financial interest in game outcomes. Increased fan engagement via legal sports wagering highlights the importance of pinpointing evidence of bias and undertaking measures to ensure unbiased officiating and game integrity.”

Legalized Sports Betting, VLT Gambling, and State Gambling Revenues: Evidence from West Virginia Brad Humphreys. Eastern Economic Journal, January 2021.

The study: In one of the only studies to examine state-level sports betting revenue after the 2018 Supreme Court ruling, Humphreys looks at sports betting tax revenues in West Virginia and whether gamblers shifted their wagering from video lottery terminal games in casinos to sports betting.

The findings: From September to December 2018, casinos in West Virginia introduced five new sportsbooks, one at each of its licensed casinos. The year before, the state saw a windfall of $253 million in tax revenue from video lottery games. In the year after sports betting was introduced, the author estimates $45.4 million in lost video lottery revenue, with new sports betting revenue pegged at only $2.6 million. The state taxes video lottery revenues at 53.5%, while sports betting revenues are taxed at 10%.

The author writes: “These results should give state policy makers considering legalization of sports betting pause. While new revenue streams from legalized sports betting appear attractive on the surface, states already generate substantial tax revenues from gambling, and the introduction of sports betting to this mix does not leave spending on other forms of gambling untouched.”

Sports Betting’s Impact on Casino Gambling: Cannibalization or Expansion? Ernest Goss and Peyton Miller. University of Illinois Law Review, October 2021.

The study: Another one of few papers to examine how tax revenues and the games bettors played changed after the 2018 ruling, the authors analyze what happened after Iowa allowed sports gambling after August 2019. Iowa casinos that offer sportsbooks pay 6.75% of their sports betting revenue to the state, “a rate tied with Nevada for the lowest nationally,” the authors write. Like in West Virginia, taxes on all other forms of casino gambling are much higher — 22% on revenue over $3 million. The authors do not look at the specific effects of sports betting on other types of gambling, but rather whether there were any changes in overall revenues after August 2019.

The findings: Mobile sports betting and sports betting in casinos did not affect statewide gambling revenues from August 2019 to March 2020. After March, casinos shuttered due to the COVID-19 pandemic.

The authors write: “While these results do not indicate cannibalization within the Iowa gambling market, there are relevant implications for both casinos and the state. Conditions within the state of Iowa may limit the applicability to other states. For example, the varying tax brackets across gambling forms differ from casino taxing in other states.”

Frameworks of Gambling Harms: A Comparative Review and Synthesis Virve Marionneau, Michael Egerer and Susanna Raisamo. Addiction Research and Theory, August 2022.

The study: The authors gather and analyze “harm frameworks” related to problem gambling. A framework in this context refers to a way of categorizing and thinking about an issue with an ultimate goal of understanding the issue in a comprehensive way and finding solutions. A harm is simply an outcome that most of society would classify as negative — losing one’s house, for example, because of gambling-related losses.

While not specifically related to sports betting, the frameworks explored in the paper are useful for those who want to better understand what can happen to individuals and families affected by problem gambling. After searching major academic research databases, the authors settled on seven papers published between 2000 and 2021 that developed an original harm framework related to problem gambling — four of the papers focused on developing the same framework, leaving four frameworks total. The authors, while applauding the research that has already been done, note that further research is needed.

The findings: Two of the frameworks discussed problem gambling harms related to the workplace and personal relationships. One framework separated psychological and cultural harms, and harms related to crime. Another framework mostly focused on risk factors related to problem gambling, risks which “also occur on the individual, familial, community, and societal levels,” the authors write. They note none of the models explore the degree to which problem gambling harms individuals, families, communities and society — all the harms or risks were “treated as somewhat equal,” they write. Financial harms, they argue, might be a relatively worse harm since they “can be seen to precede or even cause many of the other harms, including criminal acts or emotional suffering.” The authors argue for more research on social harms, where, on the whole, the existence of high levels of problem gambling, “can cause harms irrespective of individual participation, including corruption, economic substitution, match fixing, environmental damage related to tourism, or animal suffering.”

The authors write: “We have found that while existing conceptualizations include a wide definition of harms, most harm items are still seen to stem from individual engagement with gambling. Further incorporation of social and societal harms is still needed to conceptualize and operationalize gambling as a public health issue. This includes the development of societal-level harm measurement and harm minimization.”

A brief history of U.S. sports betting

Americans have a long tradition of gambling. College of the Holy Cross economist Victor Matheson recounts in a January 2021 article in the Eastern Economics Journal:

“Lotteries funded activities such as the original European settlement at Jamestown, the operations of prestigious universities such as Harvard and Princeton, and construction of historic Faneuil Hall in Boston … In the sports realm, by 1900 betting on horse races was made illegal except in Kentucky and Maryland, states that to this day host two of the three Triple Crown events in American horseracing, the Kentucky Derby and the Preakness Stakes. States began to relegalize gambling on horse racing in the 1930s as a method of economic stimulus during the Great Depression.”

By the early 1960s, illegal gambling enterprises run by organized crime groups were worth a combined $7 billion . For more than 30 years, the Wire Act , enacted in September 1961, was the only federal law that addressed sports gambling. The law prohibits the use of a wire — a phone, or, more recently, the internet — to transmit information about placing sports bets across state lines.

The Indian Gaming Regulatory Act, which became federal law in 1988, allowed federally recognized Native American tribes to operate casinos on their land. Sports betting in tribal-run casinos, however, was not allowed unless a tribal-state compact was signed. This is the root of the current legal dispute in Florida. Such compacts were in effect in 22 states as of June 2021, according to the International Center for Gaming Regulation at the University of Nevada, Las Vegas.

By the early 1990s, federal legislators were expressing moral panic over the possibility of states allowing sports betting within their borders, to take advantage of billions being wagered illegally.

Illegal transactions are, by nature, difficult to track. People who bet illegally and their bookies do not typically share receipts with the government or trade groups, so it is difficult to say with precision how big the illegal gambling market was before 2018.

Noting that caveat, the American Gaming Association estimated illegal sports betting as a $150 billion-a-year business before the 2018 Supreme Court ruling. It is an oft-repeated figure in news stories and on websites devoted to sports betting.

In 1991, when overall illegal sports bets were estimated in the tens of billions, a Senate report declared sports gambling a “national problem.” The report continued:

“The harms it inflicts are felt beyond the borders of those states that sanction it. The moral erosion it produces cannot be limited geographically. Once a state legalizes sports gambling, it will be extremely difficult for other States to resist the lure. The current pressures in such places as New Jersey and Florida to institute casino-style sports gambling illustrate the point. Without federal legislation, sports gambling is likely to spread on a piecemeal basis and ultimately develop an irreversible momentum.”

Professional sports league commissioners and former athletes were publicly and adamantly against legal sports betting. They objected that sports integrity would be irreparably harmed, including the possibility of fixed games.

Gary Bettman, the top lawyer for the National Basketball Association, made clear to federal lawmakers in 1990 that sports betting was at odds with the league’s profit motive: “Bettors do not care about the win of their team,” Bettman said during a Senate committee hearing. “They only care about the spread being covered and winning their bets. That is not our product. That is not the product we are selling.”

President George H. Bush signed the Professional and Amateur Sports Protection Act on Oct. 28, 1992. It went into effect on Jan. 1, 1993. Bettman became commissioner of the National Hockey League a month later — and, eventually, a fan of sports betting.

“What we’ve learned is that [sports gambling] is another point of engagement for the fans,” Bettman said during a 2019 American Gaming Association conference. “Ultimately, I think if you’re interested in sports betting, you’re going to have an increased opportunity to engage with the game.”

After 1992, some limited sports betting was grandfathered in Delaware, Oregon and Montana. Delaware, for example, allowed a certain type of bets on National Football League games. States were given one year to legalize casino sports betting after the federal law went into effect, but none did. Nevada was the only grandfathered state that fully allowed sports betting. For nearly three decades, the 1992 federal legislation enshrined Las Vegas as the U.S. sports betting hub.

“[Legal] betting was pretty much happening in Nevada, in a regulated market, and you’d have to be at casino to do it,” says Holden, who wrote a comprehensive overview of the rise of legal sports betting published February 2019 in the Georgia State University Law Review. “That gave us sort of the image of sportsbook-style betting that you would see in the movies, you would see on TV. You go to the counter, you place a bet and you watch the game on 50 different screens.”

Constitutional cracks emerged in the 2010s. In 2014, New Jersey legislators voted to reverse their law banning sports betting there. The National Collegiate Athletic Association brought the state to court. This was the case the Supreme Court heard years later, leading to the fall of the Professional and Amateur Sports Protection Act.

Major sports leagues today are on board with gambling. It is impossible to watch professional sports without encountering advertisements encouraging betting. Online sportsbooks spend $154 million yearly in local TV spots, according to Nielsen. Aside from accepting ad dollars from sportsbooks, every major sports league and numerous individual teams have lucrative partnership deals with sportsbooks.

About The Author

Clark Merrefield

The Gambling Behaviour and Attitudes to Sports Betting of Sports Fans

• Original Paper
• Open access
• Published: 01 February 2022
• 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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The ghosts of the Kentucky Derby: From Lewis & Clark to the race’s near demise

An earlier version of this article misstated the year of death of Meriwether Lewis Clark Jr. He died in 1899.

The Athletic has live coverage of the 2024 Kentucky Derby , the 150th anniversary.

LOUISVILLE, Ky. – On an unnaturally summer-like Sunday morning, six days before 20 horses will break from the starting gate for the vibrant and very much alive 150th running of the Kentucky Derby, the deceased rest largely unperturbed at Cave Hill Cemetery.

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The sprawling cemetery, a quick 6-mile ride from Churchill Downs, is the first stop of six on a very particular graveyard shift. Kentucky loves to celebrate the great steeds that have made its commonwealth famous. Secretariat is immortalized in a park in Paris, Ky., and Barbaro, the Derby winner who fought valiantly after shattering his leg in the Preakness, is remembered out front of Churchill Downs, where his remains are interred. Aristides, the first Derby winner, is memorialized in bronze in the Churchill paddock, and down the road in Lexington, Alysheba stands tall in bronze at the Kentucky Horse Park, War Admiral at Faraway Farms and Seattle Slew at Hill ‘N Dale.

But to find the real roots of the Kentucky Derby – the people who started, captured and continued it – you have to know where the bodies are buried.

Cave Hill Cemetery, Louisville

A green line painted on the road leads visitors directly from the administrative offices to the gravesite of Louisville’s beloved son, Muhammad Ali. There are no such markers to find a small, ordinary gravestone atop a hill in Section A that sits parallel to the ground, its markings facing away from the road.

Only a collection of French-speaking women gathered beneath a tree tip off where Meriwether Lewis Clark Jr. lies. “Bonjour,’’ they say warmly, before shuffling off with their tour guide to the next stop.

In a city that plasters buildings with pictures of its famous homegrowns – you’ll find Paul Hornung, Diane Sawyer, Ali and others – Clark remains comparatively anonymous. Yet he arguably might be more responsible for making Louisville famous than any of them. Six miles away from where Clark lies buried sits Churchill Downs, site of the Kentucky Derby, celebrating its 150th running this week. Without him, none of it might ever have happened.

Clark is of that Lewis & Clark – grandson of William Clark and named for the explorer’s famed traveling partner. Meriweather, who went by Lutie, did not exactly have his forefathers’ sense of forbearance. Instead, he found an appreciation for the finer things in life after moving in with his wealthy uncles, John and Henry Churchill. Clark enjoyed fancy clothes, a sip of Champagne and gambling on the horses.

Louisville always had a penchant for horse racing, but by 1870, the city had no track after Woodlawn Race Course shuttered its doors. A group of investors approached Clark to see if he could help revive the industry. He used that as an excuse to visit Europe for a year and pick the brains of famous horsemen there. He settled on a plan modeled after England’s Epsom Derby, pitching not just the creation of a track, but a grand day of racing with a fancy grandstand that ended with the 1 ½ mile Kentucky Derby (it was later shortened to today’s 1 ¼ mile length).

He leased the land from the Churchills, both also buried at Cave Hill, who were considered “two of Louisville’s most picturesque figures, distinguished-looking men, and practically always together,’’ according to a 1920 account in The Standard Printing Company. Clark founded the Louisville Jockey Club, charging $100 for membership, and used the money to turn the 80 acres into a racetrack.

On May 17, 1875, 15 horses entered the starting gate for the first running of the Kentucky Derby in front of a “grand stand being thronged by a brilliant assemblage of ladies and gentlemen.”

Coldstream Research Campus, Lexington

A historical marker explains that what is now a campus devoted to lab and office space once served as the pastures where Aristides, the first Derby winner, grazed. As for the men who made it happen, well, one gets a parkway. McGrathiana Parkway is named for the farm that is named after the man who owned the horse that won the first Derby.

To be fair, Henry Price McGrath, known as H.P., was … complicated. “McGrath is one of the long heads on the turf; a compactly built, cold-eyed, steel-gray whiskered man, who loves a horse and the money he can win so equally that we hardly know whether to consider him wholly or half mercenary,’’ offers one newspaper account.

Born poor in nearby Versailles, Ky., he worked dice games to earn a buck, parlaying his successes to the more established gambling houses in New Orleans (though he was once jailed there for snookering Union soldiers). McGrath eventually made his way to New York, where “army and navy men, and sutlers and contractors, gambled like horseback beggars,’’ according to the Owensboro Monitor. Aligned with more like-minded folks, McGrath made a fortune – enough, in fact, that he gave some to another gambler, John Chamberlain, who used it to establish Monmouth Park race track in New Jersey.

Legitimized with his cash flow, McGrath returned to Kentucky and bought up land on what sits now alongside busy Lexington thoroughfare, Newtown Pike. He established his stud farm, and the man raised in poverty and dismissed as a fleecer, soon entertained politicians at his new mansion fashioned after Saratoga’s grand United States Hotel, the parties so lavish one person referred to them as having a “restless ocean of Champagne.’’

McGrath bred Aristides (named not for the Athenian statesman but for his friend Aristides Welch, a breeder from Pennsylvania) at his farm, though the owner did not think much of his small-ish horse. In fact in the first Derby, Aristides was meant to set the pace for his stablemate, Chesapeake.

Ansel Williamson, who was born an enslaved person in Virginia, trained the horse for Robert Alexander, owner of the prestigious breeding farm, Woodburn Farm. Black trainers were common then, most tasked with tending to the horses. Williamson remained with Alexander after emancipation, and after Alexander’s death worked for McGrath, where he was given Aristides, leading the horse and himself to victory and a place in history. Though remembered fondly in newspaper accounts that reported his passing, Williamson’s final resting place remains a mystery.

African Cemetery No. 2, Lexington

Two black wrought-iron gates sprung open lead to tire-worn ruts carved into the grass that serve as the roadway to a piece of history tucked just off of downtown Lexington. The magnitude of African Cemetery No. 2 lies in its simplicity. It is just 7.7 acres (compared to 296 at Cave Hill), but more than 5,000 people are buried here; only 600, however, have headstones.

One marker belongs to the Lewis family, and though only the names of Eleanora and William Lewis are chiseled into the monument, Oliver Lewis is buried here, too.

On that first Derby race day, Aristides wore a green blanket with an orange stripe, “McGrathiana” also spelled out in orange. He stood alongside 14 other horses at a line drawn in the dirt, who “started at the first tap of a drum,’’ according to the May 21, 1875, retelling in the Kentucky Advocate, with Oliver Lewis, a 19-year-old jockey born in Lexington, at the reins.

Lewis followed his instructions, leading Aristides out to the front to set the pace, but the expected challenge from Chesapeake never came. Instead, McGrath urged Lewis to keep on, and Aristides held the lead to win the first Kentucky Derby wire to wire.

The horse, owner and trainer would go on to more victories – Aristides finished with nine wins in his 21-race career; McGrath’s horse, Calvin, won the Belmont Stakes that same year; and Williamson, who also trained undefeated Asteroid and Norfolk, was posthumously inducted into the National Museum of Racing and Hall of Fame. Lewis rode Aristides to a second-place finish at the Belmont but, like many of the people buried here, his story got lost until people salvaged the cemetery from disrepair and gave the influential people buried there their proper due.

As for Clark, though his race was deemed an immediate hit, he was considerably less popular. Stubborn and hot-tempered, he clashed with locals frequently. In 1879, he was “shot and painfully but not dangerously wounded’’ at the Galt House, a downtown hotel, over a dispute involving a horse, per the Tri-Weekly Kentucky Yeoman. Though he was revered in his obituary (he died in 1899) as “one of the most notable figures of the America turf,’’ Clark also was remembered for his “spells of melancholy’’ and his inability to properly run the actual business of horse racing.

Sauerkraut Cave, E.P. “Tom” Sawyer Park, Louisville

The fitness trail, stuffed with dog walkers, joggers and cyclists, starts not far from where parents lug chairs from their trunks to the nearby soccer fields. It winds its way past the people quietly practicing tai chi and onward to an archery range. Just off the trail, a small opening into a dense area of overgrowth and woods is closed off by a chain link fence and a strong suggestion not to enter.

Here Derby history wasn’t so much buried, as it was razed. Before these sprawling 550 acres became a park, they were home to the Central State Hospital, which in its prior iterations was known less politically correctly as the State House of Reform for Juvenile Delinquents, the Home for the Feeble Minded, and the Lakeland Asylum for the Insane and the Central Kentucky Lunatic Asylum.

Conveniently, a limestone cave on the property provided convenient natural refrigeration and over the years housed not only the food produced on site but canned goods, including sauerkraut. The so-called Sauerkraut Cave is all that remains of the hospital; the building was knocked down in the 1990s.

Though the history of the hospital is horrific, filled with allegations of mistreatment and deaths, the building was considered an architectural marvel. Designed by Harry Whitestone, an architect with D.X. Murphy, the imposing three-story building was topped by two identical towers.

Twin spires, if you will.

By 1894, the Derby’s 20th anniversary, Clark’s lousy business skills combined with a competition from a boon in racetrack construction across the country and a dismal Derby that threatened to derail the whole thing. That year, Chant won what The Capital called “the slowest and poorest ever run’’ version of the race and the Frankfort Advocate rued that the “Classic Event of the Kentucky turf seems to be in its dotage.” A group of investors, led by William Applegate, bought the Jockey Club and went about trying to save it.

They targeted $100,000 toward a new grandstand and hired D.X. Murphy to design it; the firm turned the project over to 24-year-old Joseph Dominic Baldez. A fan of symmetry, Baldez added the spires to give the new grandstand a more impressive look. Though he was rather nonchalant about his iconic creation, referring to them only as “nicely proportioned,’’ future Jockey Club president Matt Winn promised that upon Baldez’s death, “there’s one monument that will never be taken down, the Twin Spires.’’

St. Louis Cemetery, Louisville

A mere two miles separates the man who started the Kentucky Derby and the man who saved it. Like Meriweather Lewis Clark Jr.’s gravesite, Matt Winn’s is easy to miss. Perched high atop the hill of this massive cemetery, Winn’s nondescript headstone, alongside the curb in the front of the family plot, is darkened by weather.

The ordinariness of Winn’s burial spot doesn’t do him justice. As a 13-year-old, he watched Aristides win the first Kentucky Derby. Twenty-seven years later, he saved the race from possible extinction.

Though Applegate’s new ownership group revolutionized the track, they still couldn’t make the race profitable. In an effort to conserve cash, they cut the purses, but that only made for smaller fields and lousier horses. Applegate turned to Winn, a tailor by trade but a serious horse fan, for assistance. In October 1902, Winn was named vice president and eventually became executive director, ushering the Kentucky Derby into all of its glory.

Winn would rid the race of the bookmakers in exchange for pari-mutuel betting. He dropped the minimum bet from $5 to $2 in 1911, and made savvy marketing decisions to raise the Derby’s profile, such as inviting Regret, a filly, into the 1915 field. Winn also shepherded the race through both World Wars, set up the first national radio broadcast of a horse race and helped cement the Triple Crown schedule.

Upon his death, the Courier Journal wrote, “It was business to be sure, and at times a tough one, what with the rivalries and contentions. But nobody may gainsay the romance and the charm, the high bravura, that Matt Winn brought to an outstanding and characterizing event.’’

(Illustration: John Bradford / The Athletic ; photos: Andy Lyons / Getty Images)

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Dana O’Neil, a senior writer for The Athletic, has worked for more than 25 years as a sports writer, covering the Final Four, the Super Bowl, World Series, NBA Finals and NHL playoffs. She has worked previously at ESPN and the Philadelphia Daily News. She is the author of three books, including "The Big East: Inside the Most Entertaining and Influential Conference in College Basketball History." Follow Dana on Twitter @ DanaONeilWriter

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