Why pull players in foul trouble?

We all know the answer to this, but it does make for some interesting theorizing.

Every shot counts the same no matter when it is made in the game. (The only difference in that would be shots made after 1-and-1 is in effect.) Let's assume that a player is as likely to make a shot at the beginning of the game as at the end of the game. What difference does it make when he makes it? Assume you pull your best player with five minutes left because he gets his fourth foul, and put him back in with one minute left, on the theory that the score at the end of the game is the only one that counts and you want him in the game when it comes time for the final score. The other side of the coin, though, is that in the four minutes he was out of the game he might have accounted for several points so that your team would be in better shape on the score board when it did come to crunch time. You want him in the game when the game is tied, but if you had left your better player in the game you might be several points ahead. Six of one and half a dozen of the other.

The answer, of course, is psychological. A coach is taking a gamble to do that, and most of them are not willing to make that gamble. Sort of like always going for it on fourth down in football.