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.”
Is the rule of thumb reasonable? No!
The strategy of sitting a player with “foul trouble” seems to be tied in with the notion that points scored late are worth more than points scored early, so if a player can play N minutes before fouling out, you want to have some of those minutes available at the end of the game. But if (after sitting the player longer than the normal rest rotation dictates) the player doesn’t foul out, you haven’t maximized his minutes. The article also discusses some of the caveats on this approach.
I think there’s an interesting undercurrent to all professional sports coaching, where it’s more acceptable to lose if you follow the conventional wisdom approach than if you go maverick. Bill Belichick was lambasted last fall for “going for it” on 4th down instead of punting — it doesn’t matter so much that you could justify the decision as being the better one, from a risk analysis standpoint. The strategy was not the normal one, and it failed. Ergo, it was wrong.
Added: IOW, “Conventional wisdom” seems to linger longer than than the rules and strategies that gave birth to it.
“Conventional wisdom” seems to linger longer than than the rules and strategies that gave birth to it.
British and the Battle of the Somme: assemble Napoleonic infantry marches into German machine gun fire, then repeat for months. Cf: Minié ball ammo, rifles, US Civil War 50 years earlier. French and Diem Bien Phu, then US entry. US in Somalia, Iraq, Yemen, Afghanistan. When Reagan had an effective word with Muammar Kadhaffi in Libya, the French declined to allow US aircraft within French air space. A 500 lb bomb happened to enter the front window of the French Embassy in Libya. When Reagan had an effective word with Cuban soldiers in Grenada, nobody stuck around to empathize with the locals. Do we see patterns emerging?
Hey, I can think of an argument in favor of benching someone in “foul trouble.” The OP assumes “his likelihood of getting a foul is time-invariant, which seems reasonable.” Suppose this is not the case, which actually seems more reasonable to me.
In particular, assume his being in “foul trouble” causes a player to defend less intensely because doing so decreases his chances of being called for a foul and he acts in order to maximize his own minutes. This behavior in response to his number of fouls could compromise his play to the degree that it would be better to have a backup in there who doesn’t have the same worry.
Pulling a player once he gets into “foul trouble” and then reinserting him into the game late enough so he won’t lose much personally by fouling out could result in better overall play than continuing to play a star who is clinging to his minutes by playing excessively conservatively.
Perhaps there is some sense behind the “conventional wisdom” after all in this case?