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January 11, 2011, 05:53 PM ET
Rethinking Foul Trouble

by Kevin Pelton

Across sports, one of the common criticisms of coaches from the analytical community is that they are overly conservative in their decision making. In large part to avoid criticism, coaches tend not to go for it on fourth down as much as the statistics indicate they ought to, for example. If there’s a basketball equivalent, it is probably the way coaches handle player foul trouble. The argument goes like this: By taking out a player in foul trouble, coaches do exactly the very thing foul trouble threatens–rob themselves of the services of one of their better players.

A new study, however, suggests that the coaches might have had right all along. Philip Maymin of NYU-Poly, along with co-authors Allan Maymin and Eugene Shen, used play-by-play provided by basketballgeek.com to study how having a starter in foul trouble affected a team’s chances of winning the game during the 2006-07 NBA season. By using a model that accounted for score, team strength, time remaining and home-court advantage (as well as the number of starters on the floor not in foul trouble), they were able to isolate the impact of foul trouble on the ultimate outcome of the game.

Their finding, as explained in an extended abstract available now, is that teams play worse when they leave starters in foul trouble on the floor, especially during the third quarter. Why? The obvious explanation is that players in foul trouble play differently, avoiding the necessary plays–especially on defense–that carry the risk of drawing another foul. From this perspective, the issue is less about maximizing the total number of minutes the player is on the floor and more about maximizing the effectiveness of those minutes.

It would be a mistake to read too much into this latest study. It generally seems to suggest that coaches should not be particularly worried about foul trouble in the first and second quarters, except to the extent that it produces subsequent second-half foul trouble. It also operates under the rule of thumb that foul “trouble” exists only when a player has more fouls than the current quarter, so coaches who bench starters who pick up their second foul in the second quarter are still being overly conservative by this heuristic. Lastly, this kind of study is too general to apply to every situation. It’s much more sensible to bench a marginal starter than the team’s star player. Still, these results provide an interesting new perspective on how coaches should respond to foul trouble.

I’d also suggest checking out the extended abstract to see how different coaches dealt with foul trouble during the 2006-07 season, including one who gambled more with fouls than any other.

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