- Jan 15, 2007
What are y'alls thoughts on foul trouble? I strongly believe that the conventional wisdom of sitting players is dead wrong. I think you should implement your most effective substitution patterns regardless of your players being in foul trouble. If they foul out, they foul out and at least you got as many minutes as you could you of them. On the other hand look at Key last night, picked up 3 fouls before she was able to log 5 minutes in the game (2 early in the first half and 1 early in the second half), then she plays the whole 4th quarter without a foul. I think this author explains it best:
Is the rule of thumb reasonable? No! First let’s consider a simple baseline model: Suppose I simply want to maximize the number of minutes my star player is in the game. When should I risk putting him back in the game after his nth foul? It’s a trick question: I shouldn’t bench him at all! Those of you who haven’t been brainwashed by the conventional wisdom on “foul trouble” probably find this obvious. The proof is simple: if he sits, the only thing that has changed when he gets back in is that there is less time left in the game, so his expected minutes have clearly gone down. In fact, the new distribution on minutes is first-order stochastically dominated, being just a truncation of the alternative. This assumes only that his likelihood of getting a foul is time-invariant, which seems reasonable. [...]
Conventional wisdom seems to regard foul management as a risk vs. safety decision. You will constantly hear something like, “a big decision here, whether to risk putting Duncan back in with 4 fouls.” This is completely the wrong lens for the problem, since the “risky”* strategy is, with the caveats mentioned, all upside! Coaches dramatically underrate the “risk” of falling behind, or losing a lead, by sitting a star for too long. To make it as stark as possible, observe that the coach is voluntarily imposing the penalty that he is trying to avoid, namely his player being taken out of the game!
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