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Observers of the NBA know that the direct effect of fouling out actually has less impact than the indirect effect of “foul trouble.” That is, if a player has a dangerous number of fouls, the coach will voluntarily bench him for part of the game, to lessen the chance of fouling out. Coaches seem to roughly use the rule of thumb that a player with n fouls should sit until n/6 of the game has passed. Allowing a player to play with 3 fouls in the first half is a particular taboo. On rare occasions when this taboo is broken, the announcers will invariably say something like, “They’re taking a big risk here; you really don’t want him to get his 4th.”
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Re: Game Theory and Foul Trouble
Thanks for the interesting read overall, Anthem.
I think, though, that the author fails to take into account what probably led to the player being in foul trouble to start with, whether it be the style of play employed by the opposition either offensively or defensively, mismatches with that player or others on his team that frequently leave the player in a position that has led to his foul trouble to begin with.
Also, a coach with other knowledge of a particular game may lead the coach to believe that if all things are equal that his team will be better served by the additional aggressiveness the player can play with in latter stages of the game with less likelihood of fatigue leading to a given player fouling out and damaging momentum down the stretch of a game.
So, while interesting, I would punt on 4th and two and take my chances that my good defensive team can hold off Peyton Manning on the last drive of the game, despite statistics that might be interpretted to mean that I should go for it against a Colts defense that has risen to the occasion throughout the course of the second half of that particular game.