Do Basketball Scoring Patterns Reflect Strategic Play or Illegal Point Shaving ? ∗

This paper develops and estimates a model of college basketball teams’ search for scoring opportunities, to provide a benchmark of the winning margin distributions that should arise if teams’ only goal is to win. I estimate the model’s structural parameters using first-half play-by-play data from college games and simulate the estimated model’s predicted winning margin distributions. Teams’ optimal state-dependent strategies generate patterns that match those previously cited as evidence of point shaving. The results suggest that corruption in NCAA basketball is less prevalent than previously suggested and that indirect forensic economics methodology can be sensitive to seemingly innocuous institutional features. JEL Codes: C61, L83 K42 ∗I am grateful to John Bound, Charlie Brown, Morris Davis, Robert Gillezeau, Sam Gregory, Dmitry Lubensky, Brian McCall, Mike McWilliams, Todd Pugatch, Colin Raymond, Lones Smith, Chris Taber, Justin Wolfers, and Eric Zitzewitz for helpful comments. All remaining errors are my own. Measuring corruption is inherently difficult because law-breakers cover their tracks. For that reason, empirical studies in forensic economics typically develop indirect tests for the presence of corruption. These tests look for behavior that is a rational response to incentives that only those who engage in the particular corrupt behavior face. The validity of these indirect tests depends critically on the assumption that similar patterns do not occur if agents only respond to the incentives generated by the institutions that govern noncorrupt behavior. Research designs in forensic economics vary to the extent that they are informed by formal economic theory. In a survey of the field, Zitzewitz (2011) proposes a “taxonomy” of forensic economic research designs that ranges from the entirely atheoretical, in which corrupt behavior is measured directly, to the formally theoretical, in which corrupt behavior is inferred from particular violations of price theory or the efficient-market hypothesis. A common intermediate approach is to posit a statistical model of noncorrupt behavior and to measure the extent to which observed behaviors deviate from that model in a manner that is consistent with corrupt incentives. The soundness of a research design of this variety depends on the plausibility of the assumed statistical model and the extent to which the study’s findings are robust to deviations from the assumed statistical model. A recent application of this “intermediate” forensic economic strategy purports to find evidence of rampant illegal point shaving in college basketball (Wolfers 2006). Point shaving is when a player on a favored team places a point-spread bet that the opposing team will “cover” the point spread – win outright or lose by less than the point spread – and then manages his effort so that his team wins but by less than the point spread.1 Because this behavior causes some games that would otherwise end with the favored team winning by more than the median winning margin to win by just below the median winning margin, point shaving tends to increase the degree of right skewness in the distribution of favored teams’ winning margins. Under an assumption that the distribution of winning margins would be symmetric in the absence of point shaving, Wolfers (2006) tests for point shaving by measuring skewness in the empirical distribution of winning margins around the point spread. The skewness-based test suggests that point shaving is rampant, occuring in about six percent of games where one team is strongly favored. Wolfers’ study garnered significant attention in the popular media2, reflecting public surprise that corruption might be so pervasive in amateur athletics. While point-shaving scandals have been uncovered with some regularity dating as far back as the early 1950s, the public’s perception seems to be that such scandals are fairly isolated incidents. To obtain a more formal benchmark of the patterns that one should expect under the no-point-shaving null hypothesis, this paper develops and estimates a dynamic model of college basketball teams’ withingame searches for scoring opportunities. Using play-by-play data from the first halves of NCAA games linked to gambling point spread data, I estimate the model’s structural parameters from play during the first halves of games. With the estimated model, I then simulate play during the second halves of games. I find that the sorts of strategic adjustments across game states (current score and time remaining) that are A point-spread bet allows a gambler to wager that a favored team’s winning margin will exceed a given number, the point spread, or bet that the winning margin will not exceed the point spread. A typical arrangement is for the bettor to risk $11 to win $10 for a point spread bet on either the favorite or the underdog. Bernhardt and Heston (2008) cite a group of media outlets in which Wolfers’ (2006) study was featured. These include the “New York Times, Chicago Tribune, USAToday, Sports Illustrated and Barrons, as well as National Public Radio and CNBC TV. ”