# Mathletics: How Gamblers, Managers, and Sports Enthusiasts Use Mathematics in Baseball, Basketball, and Football

By Wayne Winston | Go to book overview

35

In 2006 Wharton professor Justin Wolfers created a stir by claiming that around 5% of all college basketball games are fixed by players who intentionally slacken their effort (often called point shaving). Wolfers argued that for games in which the favorite is favored by S points, we should find that the probability of the favorite winning by between 1 and S — 1 points should equal the probability of the favorite winning by between S + 1 and 2S — 1 points. This follows because statisticians usually find that forecast errors about an unbiased prediction (like a point spread) should be symmetrically distributed, like a normal or Bell curve. For strong favorites (defined as teams favored by more than 12 points), Wolfers found that the forecast errors were not symmetrical about the point spread. He found that 46.2% of the time, strong favorites won by between 1 and S — 1 points, and 40.7% of the time, strong favorites won by between S + 1 and 2S — 1 points. Wolfers thus argues that 46.2% — 40.7% = 5.5% of the time players shaved points. This would account for more games ending under the spread than over the spread. The idea is once victory is in hand some of the favored team's players do not play at their optimum level. This causes more games to end with the favorite winning by a number of points in the range [1, S — 1] than the range [S + 1, 2S — 1]. Wolfers's conclusion seems a bit strong, since there may be other factors that might cause the asymmetry in forecast errors.1

Rebuttal

Heston and Bernhardt (HB) provide other explanations for the asymmetry in forecast errors Wolfers found for strong favorites.2 HB looked at games

1 See Wolfers, “Point Shaving in College Basketball.”

2 See Heston and Bernhardt, “No Foul Play.”

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