Linking Laconically is redoing the seating chart

I think you are hitting on the key point. From an optimization theory standpoint, a star player in foul trouble should adjust his style to try to maximize the amount of remaining impact he can have on the game. That is, he’s got to continue to contribute while not fouling so much. Presumably this adjustment is at some cost to his contribution. For example, he can’t really challenge his man while on defense – and the other team knows this and is likely to go at him. And he’s got to avoid being very aggressive on offense, since defenders are likely to flop on him.

So the question becomes, is his replacement off the bench able to contribute more than the starter in his (reduced) role? That’s where having Green .

College basketball isn’t game theory of course. Here are two more wrenches to the economists that I haven’t seen in this thread. First, regular season games are at least partly educational for players and their coaches. Certainly Izzo uses the preseason that way. He might put Austin Thornton in to play significant minutes against a big time opponent just to see how Austin does – and so Austin can see how Austin does. It creates teachable moments for the guy on the court – and for the guy on the bench with 2 fouls. Bob Knight used to say that nothing got his players’ attention like a good benching (actually his direct quote is much better than that, if more explicit). Frankly, Izzo doesn’t seem to care that much about beating Texas in December. He’s doing his best to make sure they beat Tennessee in March. A longer and deeper bench makes that more likely.

Second, how does a college player know how much to dial it back when he’s in foul trouble? That article presumes that the player will make the right choice – but he might pick up foul number 4 30 seconds later, or he might play so tentatively that he’s a complete liability. These are 20 year olds – they just don’t make optimal decisions on a regular basis. Maybe there’s a better argument at the professional level – a 10-year NBA player ought to be capable of the right adjustment – but for a college player? Not sure it’s that simple.

Are you better off playing the star in foul trouble and trying to build a lead? Or is there a psychological regression to the mean over the course of games (which seems intuitively true, but may or may not be empirically true) such that you should make sure the star is on the floor in the final minutes?