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September 25, 2009

To Foul Up Three?

Filed under: Uncategorized — Kevin Pelton @ 1:41 pm

Wayne Winston, the Indiana University professor who collaborated with rankings guru Jeff Sagarin to introduce the NBA’s first version of adjusted plus-minus, has a new book out called Mathletics. In addition to discussing adjusted plus-minus, Winston has other basketball-related studies. I’ve yet to get a chance to check out the book, being too busy finalizing our own forthcoming effort, but Henry Abbott blogged today at TrueHoop about one of them–revisiting the old debate over whether to intentionally foul when leading by three points.

Then Winston does something delightfully simple. He asks: Has it worked? He presents, for the first time I’m aware, the evidence:

A student in my sports and math class, Kevin Klocke, looked at all NBA games from 2005 through 2008 in which a team had the ball with 1-10 seconds left and trailed by three points. The leading team did not foul 260 times and won 91.9% of the games. The leading team did foul 27 times and won 88.9% of the games. This seems to indicate that fouling does not significantly increase a team’s chances of winning when they are three points ahead.

He adds a key footnote:

We believe more work needs to be done to determine the definitive answer to this question. We are working on a simulation model of the last minute of a basketball game that should help settle the issue.

(The doubly-indented text is from the book.)

While the study by Klocke and Winston is a nice start to this research, Winston is correct to say more work needs to be done. There are two reasons that the percentages don’t tell us very much. The first is the small sample of times teams chose to foul. They went 24-3 in those games. Change one outcome either way and fouling either looks substantially worse than not fouling or slightly better.

Second, as David Thorpe points out later in Henry’s post, the best strategy may not be to have a hard and fast rule. That is, coaches are taking the situation into account when deciding whether to foul. Coaches are less likely to foul a poor-shooting team that will be hard-pressed to make a three, since a win is already almost assured in these situations. On the other hand, they’re also more likely to foul when less time is on the clock, which means the leading team’s chances of winning are better. So, as Henry says, the situation is still awfully complicated to study. A model might give us a better look at the issue than real-life situations.

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