Widespread corruption in sports gambling: fact or fiction?

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