Widespread corruption in sports gambling: fact or fiction?

Borghesi, Richard

1. Introduction

While approximately $1 billion is wagered legally on college sports each year in Nevada, between 30 and 100 times more is wagered illegally throughout the United States (Public Citizen 2001). Legal and illegal gambling markets are intertwined because illicit bookmakers often balance their positions by placing bets at legitimate sports books. Furthermore, legal casinos may unwittingly play an essential role in the ability of corrupt gamblers to fix sports contests via point-shaving.

Point-shaving is a scheme in which an athlete is promised money in exchange for an assurance that his team will not cover the point spread. The conspirator then bets on that team's opponent and pays the corrupt player with proceeds from a winning wager. Given the high cost of bribing players and enormous risks inherent in violating federal laws, the orchestrator must place massive bets for conspiracy to be worthwhile. Since local bookmakers are generally unwilling to accept unusually large bets, conspirators must wager at legitimate casinos. So, ironically, while the economic viability of legal sports betting markets depends on the perception that transactions are fair, Nevada casinos are potentially instrumental to gamblers who conspire to fix games. (1)

Because few cases of point-shaving have been documented, most market participants believe that legal sports books are fair. (2) However, this perception has recently been called into question. In examining 44,120 men's college basketball games played between 1989 and 2005, Wolfers (2006) offers evidence that point-shaving occurs far more frequently than previously believed and estimates that at least 1% of games involve gambling corruption, while 6% of strong favorites (those favored to win by 12 points or more) shave points. According to Wolfers, conspirators target favorites because bribed players obtain positive utility both from profiting and from winning games, and a player can receive both only when his team is a favorite. It follows that strong favorites are ideal targets because the optimal win-but-fail-to-cover outcome is easier for a player to achieve when the spread is relatively large.

In quantifying the pervasiveness of the problem, Wolfers proposes that manipulated games have two measurable identifying characteristics that differentiate them from legitimate games. First, teams having a bribed player perform worse, not better, than expected. It is presumably far easier for corrupt players to reduce effort than to increase effort, as most players typically compete using their full abilities. This reduced effort should result in poor team performance relative to market expectations. (3)

Second, the frequency at which shaving teams narrowly miss covering the spread is higher than otherwise expected. Shaving players want to win, but they profit only when the victory comes by a margin less than the closing spread. The theory therefore predicts that if corruption is pervasive and strong favorites are ideal conspiracy targets, then strong favorites will win but fail to cover more frequently than expected.

If well founded, the point-shaving theory suggests that hundreds of college athletes have committed felonies and that legitimate sports bettors have been swindled out of hundreds of millions of dollars. However, we provide evidence that is inconsistent with the premise that point-shaving is widespread in college basketball. To examine the prevalence of corruption, we analyze point spread and game outcome data from college and professional sports leagues. These data and the methodology employed are discussed in section 2. Results are presented in section 3, and an alternative explanation is presented in section 4. Closing remarks are contained in section 5.

2. Data and Methodology

Our data set contains the final scores of 74,586 men's National Collegiate Athletic Association (NCAA) basketball games from 1990 to 2005, 30,129 National Basketball Association (NBA) games from 1978 to 2005, and 6015 National Football League (NFL) games from 1981 to 2005. Associated closing point spreads are obtained from Computer Sports World, which records lines posted at the Stardust Casino in Las Vegas. We remove from the sample all games for which no point spread is available. The final data set consists of final scores and closing point spreads for 43,656 college basketball, 28,905 NBA, and 6015 NFL games.

Wolfers's theory predicts that among favorites, the proportion of win/no cover (W/N) outcomes will be unusually high, while the proportion of win/cover (W/C) outcomes will be unusually low. A W/N occurs when 0 < favorite's victory margin < closing spread, while a W/C occurs when closing spread < favorite's victory margin < 2*closing spread. The existence of such a pattern would be interesting because, in the absence of point-shaving and assuming that the distribution of forecast errors is symmetric, the frequencies should be identical. For example, if a closing spread is five points, then the favorite should be just as likely to win outright by a margin of between zero and five points as it is to win outright by a margin of between five and ten points.

But since corrupt players do not want to cover and because favorites are most likely to shave, the widespread point-shaving theory instead suggests that a five-point favorite is significantly more likely to win outright by a margin of between zero and five points. It also implies that this pattern should be particularly pronounced among strong favorites because of the relative ease with which corrupt players can achieve both of their objectives--win the game and the bet--when their teams are heavily favored. However, if an equivalent pattern exists among strong favorites in settings in which shaving is implausible, then it is unlikely that corruption is the culprit. Professional leagues provide such a setting.

It is clear that a shaving player must find greater utility in his team not covering than in covering. While the marginal utility of monetary gains from fixing bets may be large for college players, professional players are wealthy and thus would experience relatively small utility gains from shaving. In addition, the consequences of being discovered are disproportionately severe for most professional players, as they would forgo all future financial gains from continuing their athletic careers. (4) Because the utility differential between the lifestyle of a professional athlete and his next-best option is far higher than that between a college player and his next-best option, a professional should be far less tempted to shave.

Furthermore, since median NBA and NFL salaries are over $1 million per year, conspirators would have to gamble an enormous amount of wealth to profit after paying the bribe. Large wagers, however, would likely raise suspicions among gaming authorities; thus, game fixing is unlikely to occur in professional sports. (5) To test whether differences between the frequencies of W/N and W/C outcomes are a reliable indicator of point-shaving in college basketball, we test the null hypothesis that the difference between the frequencies of W/N and W/C outcomes is not significant in professional leagues. If we find that the distributions of W/N and W/C outcomes in professional leagues are consistent with those in the NCAA basketball market, then it is likely that some phenomenon other than point-shaving is responsible.

3. Results

Wolfers's theory predicts that, since shaving teams are expected to win but fail to cover, we should observe an unusually high proportion of W/N outcomes relative to W/C outcomes among strong favorites. To test this prediction, we replicate Wolfers's analysis by plotting these rates for NCAA basketball. Results are displayed in Figure 1 as a solid (dashed) line representing the frequencies of W/N (W/C) outcomes within varying point spread deciles. Figure 1A illustrates the premise of Wolfers's point-shaving theory, as strong favorites win but fail to cover the spread more often than expected.

[FIGURE 1 OMITTED] (6)

However, if such a pattern were to exist among strong favorites in settings where shaving is implausible, then it is unlikely that corruption is the culprit. In games involving professional athletes, because the benefit of cheating is greatly outweighed by the cost of being discovered, we would not expect to observe an equivalent gap between the solid and dashed lines at high spreads. However, the pattern emerging from plots of professional basketball (Figure 1B) and football (Figure 1C) outcomes is similar to that observed in NCAA basketball outcomes. Within the largest spread deciles, the difference between W/N rates and W/C rates is largest.

Results in Table 1 formally confirm that these differences are systematically significant within the highest deciles. In the NBA data, the W/N proportions are significantly greater than W/C proportions in games having closing lines in the top two deciles. The difference between these two rates is significant at the 1% level. In the NFL betting market, while fewer subgroups are possible, we again find that W/N proportions are significantly greater than W/C proportions in deciles containing the largest closing lines (subgroups 6 and 7). In summary, results obtained from professional leagues mimic those from college basketball. Results do not support the conclusion that shaving is widespread in NCAA basketball.

4. Alternative Explanation

Survey studies support the contention that gambling corruption affects college sports. For instance, the NCAA (2004) finds that 2.1% (2.3%) of collegiate basketball (football) players claim to have been asked by gamblers to fix games. Also, Cross and Vollano (1999) find that 0.4% of collegiate football and basketball players claim to have accepted money for performing poorly in a game. However, there is no reason to believe that athletes who are targeted by gamblers typically play for strong favorites. (7) In any case, the point-shaving theory does not explain why results are similar across amateur and professional markets.

One potential explanation that is consistent with the patterns documented here is that teams with large leads decrease effort late in games. This may occur either because of sportsmanship pressures or because player and/or coach slacking is less likely to result in a loss when a team is far ahead. Strong favorites are more likely to be ahead by a large margin, so these teams are more apt to reduce effort late in the game and thus win yet fail to cover at a high rate.

However, to counter this idea, Wolfers shows that there are at least as many NCAA basketball blowouts as expected; therefore, teams with large leads are unlikely to reduce effort. Additionally, bettors should know that star players may be benched and that slacking may occur in blowout games, and these possibilities should be priced into closing spreads. (8) So these factors do not provide an adequate explanation for the difference between W/N and W/C rates.

We propose an alternative explanation--that sports books intentionally inflate the lines of games in which a particularly strong team plays against a particularly weak team. This practice, called line shading, potentially maximizes sports book revenues. In general, sports book managers are concerned primarily with balancing their books. That is, they prefer to avoid taking a position in which their profit depends significantly on the realized outcome of a sporting event. However, for a particular subset of games, sports book managers have an opportunity to improve their risk-return trade-off.

This possibility is generated by a betting clientele that steadfastly prefers to bet on strong favorites, even if the spread is too large. (9,10) To capitalize on the irrational behavior of these gamblers, numerous sports book managers in Las Vegas casinos engage in line shading (inflating). By shading a line, a sports book manager improves the likelihood that the strong favorite fails to cover and therefore increases the chance that the sports book profits not only from the vigorish it collects but also from its winning naked position on the underdog.

Until recently, the Stardust Resort and Casino sports book set the de facto opening lines for professional football. In an interview with Doc's Sports (Martin 2007), former Stardust Resort and Casino sports book manager Bob Scucci stated that shading is a common practice among legal sports books. According to Scucci, lines are most frequently shaded on games involving a strong team that has won and covered in recent weeks, and lines can actually be shaded so much that a profitable opportunity exists for those who bet against favorites. (11, 12) Sports book managers at the Hard Rock Hotel and Casino and at Terrible's Casino also tell Martin that they frequently shade. If lines involving strong teams are the most likely to be shaded, then we would observe that strong favorites perform worse against the line than otherwise expected. This result is precisely what the widespread point-shaving theory predicts.

5. Conclusions

Strong favorites in NCAA basketball win but fail to cover at a rate significantly greater than that at which they win and cover. Prior research suggests that widespread point-shaving causes this phenomenon. However, we demonstrate that the rate at which strong favorites win and fail to cover the spread is unusually high in professional basketball and football games. Given that the expected utility of point-shaving is likely to be negative for professional athletes, we conclude that the unexpectedly high rate at which strong favorites in NCAA basketball win and fail to cover is unlikely to be caused by widespread point-shaving. Instead, we suggest the possibility that sports books intentionally bias the lines against strong favorites in order to maximize profits. This practice, which is called line shading, would produce the observed underperformance of strong favorites relative to market expectations.

We thank an anonymous referee for helpful comments and suggestions.

Received August 2006; accepted February 2007.

References

Cross, Michael, and Ann Vollano. 1999. The extent and nature of gambling among college student athletes. University of Michigan Department of Athletics.

Gillespie, Rob. 2003. Why bet basketball? Gambling Times Winter 2002 2003.

Golec, Joseph, and Maurry Tamarkin. 1991. The degree of inefficiency in the football betting market: Statistical tests. Journal of Financial Economics 30:311-23.

Gray, Philip, and Stephen Gray. 1997. Testing market efficiency: Evidence from the NFL sports betting market. Journal of Finance 52:1725 37.

Lacey, Nelson. 1990. An estimation of market efficiency in the NFL point spread betting market. Applied Economies 22:117-29.

Levitt, Steven. 2004. Why are gambling markets organised so differently from financial markets? The Economic Journal 114:223-46.

Martin, Jeremy. 2007. "Going against Public Teams Can Be Winning Strategy." Ultimate Capper, Accessed 15 November 2006. Available http://www.ultimatecapper.com/sports-betting-articles-49-htm.

McCarthy, Michael. 2005. Football bettors put billions on the line. USA Today, 8 September.

National Collegiate Athletic Association. 2004. 2003 NCAA national study on collegiate sports wagering and associated behavior. Indianapolis: National Collegiate Athletic Association.

Public Citizen. 2001. Folding to the casino industry: How soft money buys Congress. 15 March.

Vergin, Roger. 2001. Overreaction in the NFL point spread market. Applied Financial Economics 11:497-509.

Wolfers, Justin. 2006. Point shaving: Corruption in NCAA basketball. American Economic Review 96:279-83.

Woodland, Linda, and Bill Woodland. 1994. Market efficiency and the favorite-longshot bias: The baseball betting market. Journal of Finance 49:269-79.

(1) Legal casinos have also been instrumental in alerting authorities to suspected point-shaving conspiracies.

(2) In the past 50 years, there has not been a single documented case of a player fixing games in any of the four major American professional sports (basketball, football, baseball, and hockey).

(3) Expected performance is quantified by the closing point spread, which represents the market's wealth-weighted forecast of the difference in points to be scored by two teams.

(4) Notorious point shaver Stevin Smith was expelled from Arizona State University and sentenced to a year in prison. A professional player found guilty of conspiracy would presumably face league expulsion and a prison sentence.

(5) Approximately $969 ($543) million was bet on football (basketball) in Nevada in 2004 (McCarthy 2005), and bet volume is roughly equally distributed between professional and collegiate leagues (Gillespie 2003). Because betting markets in professional sports are not materially larger, it is implausible that conspirators could avoid detection when betting the enormous amounts of money that would be required to compensate professional athletes for shaving.

(6) A large proportion of NFL closing lines are within [+ or -] 0.5 of three points (28.81%) or seven points (15.96%).

(7) In addition, such contact is meaningful only if the shaving player has the ability to significantly affect final score differentials. At minimum, this requires that the bribed athlete be highly talented. It is also likely that top collegiate players overestimate their abilities and thus overestimate their chances of becoming professional athletes. Thus, even fewer college players would find it optimal to engage in point-shaving. Furthermore, for top collegiate teams vying for seeds in the NCAA national basketball championship tournament, margins of victory are important. Presumably, players on these teams receive utility from national exposure and thus would receive additional disutility from shaving.

(8) The fact that the strongest players are the most capable point shavers raises additional concerns with the theory that strong favorites are the most likely to shave points. Star players are often pulled from games in which their teams are winning or losing by large margins, the goal being to reduce the likelihood of injury. Therefore, conspirators may avoid games having the largest spreads, as the bribed player(s) would be unable to influence outcomes were he benched. We thank an anonymous referee for this observation.

(9) For instance, Woodland and Woodland (1994) show that baseball gamblers overbet favorites despite unfavorable odds. The authors also interview Michael Roxborough, then president of Las Vegas Sports Consultants, which played a large role in setting Las Vegas lines in the 1980s and 1990s. Roxborough states that football bettors overvalue favorites.

(10) Levitt (2004) finds that bookmakers systematically exploit bettor biases by taking large positions that depend on game outcomes.

(11) Prior literature has identified betting patterns that are consistent with anecdotal descriptions of line shading. For instance, Lacey (1990) and Vergin (2001) find that gamblers overbet on teams that have recently exceeded performance. In addition, Golec and Tamarkin (1991) and Gray and Gray (1997) find that bettors often fail to recognize persistent biases in closing lines.

(12) In order for a betting strategy to be profitable, a win rate of 52.38% (11121) must be surpassed.

Richard Borghesi, Texas State University, McCoy College of Business Administration, Department of Finance and Economics, 601 University Drive, San Marcos, TX 78666, USA; E-mail rickborghesi@txstate.edu.

Table 1. Outcomes by closing lines. This table shows differences
in frequencies between W/N (0 < favorite's victory margin < closing
spread) outcomes and W/C (closing spread < favorite's victory margin
< 2*closing spread) outcomes in NCAA basketball, NBA, and NFL games.
The data for NCAA basketball and the NBA are divided into closing
spread deciles. As a large proportion of NFL closing lines are around
three points or seven points, relatively fewer subgroups are possible.
We use a binomial test to identify statistical differences. Graphical
depictions of the relationships are presented in Figure 1.

 NCAA Basketball

Decile N W/N W/C Difference p-Value

 1 3567 1.09% 2.16% -1.07% 0.0005
 2 4075 5.72% 6.65% -0.93% 0.0992
 3 3787 10.25% 10.11% 0.13% 0.8855
 4 5110 14.95% 13.78% 1.17% 0.1236
 5 3175 20.85% 18.61% 2.24% 0.0479
 6 4166 24.56% 24.05% 0.50% 0.6567
 7 4648 29.67% 30.34% -0.67% 0.5700
 8 4451 35.30% 34.26% 1.03% 0.4187
 9 4356 43.32% 36.94% 6.38% 0.0000
10 4576 49.04% 42.50% 6.53% 0.0000

 NBA

Decile N W/N W/C Difference p-Value

 1 1957 1.48% 1.79% -0.31% 0.5323
 2 2782 5.64% 5.43% 0.22% 0.7758
 3 3146 10.11% 10.36% -0.25% 0.7827
 4 3115 12.62% 14.35% -1.73% 0.0674
 5 2920 15.62% 18.60% -2.98% 0.0065
 6 2726 20.18% 22.89% -2.71% 0.0331
 7 2437 23.14% 25.89% -2.75% 0.0562
 8 3011 27.20% 27.17% 0.03% 1.0000
 9 2675 34.92% 31.48% 3.44% 0.0308
10 3079 44.43% 35.34% 9.09% 0.0000

 NFL

Decile N W/N W/C Difference p-Value

 1 1857 4.15% 5.55% -1.40% 0.0621
 2 791 12.64% 8.47% 4.17% 0.0130
 3 628 17.36% 15.61% 1.75% 0.4871
 4 565 20.35% 14.34% 6.02% 0.0182
 5 657 22.53% 15.37% 7.15% 0.0035
 6 536 30.60% 19.96% 10.63% 0.0006
 7 708 34.75% 27.54% 7.20% 0.0172
 8 -- -- -- -- --
 9 -- -- -- -- --
10 -- -- -- -- --