August 25, 2010
Each time a team is on defense leading by three points in the final seconds of a game, the coach faces an unenviable but unavoidable quandary.
Does he instruct his team to defend against a three-pointer and risk the opposing squad hitting a buzzer-beating shot to tie the game? Or does he have his team commit an intentional foul in hopes of depriving them of any chance of a comeback?
Rather than argue back and forth over that issue with anecdotal evidence, the Harvard Sports Analysis conducted what it calls the "first comprehensive empircal study of the issue for college basketball." What the study found was that teams have just as good a chance to win whether they foul or whether they don't.
In the 2009-2010 season, I found 443 instances where a team held the ball down three points during their last possession of a period (either the end of the 2nd half or an overtime period). In 391 of those cases, the team leading did not foul. In 52 cases, the team chose to foul. [...]
Of the 52 teams that committed a foul, six lost the game for a winning percentage of 88.46%. Of the 391 teams that did not foul, 33 lost the game for a winning percentage of 91.56%. Both a two sample t-test of proportion and a Chi-squared test fail to reject the null hypothesis that there is a difference in winning percentage between the two strategies. In this sample, teams that did not foul won slightly more often. For the less statistically inclined, this means that there is no significant difference between the two strategies.
The results of the study lend perspective to a situation that comes up in crucial games every college basketball season.
In the national title game in 2008, Kansas' Mario Chalmers was able to tie the score at the end of regulation on a memorable top-of-the-key three-pointer because Memphis opted not to foul. On the other hand, Cal State Northridge did foul in a similar situation in triple overtime against Cal State Fullerton last February and wound up surrendering four points on the possession and taking the loss.
While most of us still don't know a Chi-squared test from a Chai tea, we now know we shouldn't criticize a coach for his decision based on statistics. Regardless of whether a coach chooses to foul or not to foul, the Harvard study says he's right.
(Thanks, Rush the Court)