Basketball Theory And Truncation Of The Alternative

The Sporting Blog espouses on an issue that is theoretical in nature but completely relevant in its application: At what point should basketball coaches take a star player out of the game because of foul trouble?

Coaches of course, think it should be as soon as a player picks up two fouls. Goodness knows, it’s better to have him sit on the bench than risk a third foul. But an item from Northwestern University’s Kellogg School of Management disputes this notion. If you want to win the game, shouldn’t you maximize the minutes from your best players?

Now, there may very well be no better source of basketball theory than the Kellogg School of Management. After all, the “new distribution of minutes is first-order stochastically dominated, being just a truncation of the alternative.” And who can argue with that?

Apparently, this guy can. And he’s right. The fact is that all minutes of a basketball game are not created equal.

It’s like running a marathon. Not that I would know what it’s like to run a marathon, but stick with me here for a minute. I don’t think you would argue that runners should go as fast as they can at the beginning of the race in order to maximize the use of their energy. The same goes for basketball teams.

Or consider this analogy: Why does every team in baseball employ a closer? Why not use your best available pitchers in descending order of quality, bringing in your best reliever for the sixth or seventh inning? It’s because if the closer does his job in the ninth, your chance of winning goes to 100 percent.

All of this is theoretical, and I’m all in favor of questioning conventional wisdom. But it seems as if every manager and every basketball coach believes the end of the game is more important than the middle, there’s probably a great deal of truth behind that philosophy.