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

By Wayne Winston | Go to book overview

36
DID TIM DONAGHY FIX NBA GAMES?

In July 2007 shockwaves rippled through the sports world when NBA referee Tim Donaghy was accused of fixing the outcome of NBA games. If bettors attempt to fix a game, after the opening betting line is posted the line would move substantially as the “fixers” put their bets down. A move of two or more points in the line is generally considered highly unusual. For example, on November 14, 2007, when the Toronto Raptors played the Golden State Warriors, the opening line on total points (referred to hereafter as the Total Line) was 208 points. This means that if you bet the “Over” you would win if the total points scored were 209 or more. If you bet the “Under” you would win if the total points scored were 207 points or fewer. If the total points scored were 208 neither would win. The closing Total Line was 214 points, a six- point increase. This means that near game time a large amount of money was bet on the Over. If, as was alleged, Donaghy had been trying to fix the game (causing the game to exceed the Total Line), he probably would have to have called lots of fouls. (Fouls create free throws and in effect make the game longer.) Using publicly available data, we can determine whether significantly many more free throws were attempted in games Donaghy officiated and in which the Total Line moved up two or more points than were attempted in the rest of the games Donaghy officiated. We adjusted the number of free throws attempted in each game based on the teams playing and on the other two game officials. Figure 36.1 displays the results of these calculations. For example, in the first listed game, Chicago had 32 free throw attempts and Miami had 22. An average NBA team had 26.07 free throw attempts per game during the 2006–7 season. Figure 36.2 gives the average number of free throw attempts for each team and their opponents.

The Bulls shot (25.40 26.07) more free throws than average while the Heat shot (24.62 26.07) fewer free throws than average. The Bulls'

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