(In basketball, that is.)  You shouldn’t, says Jonathan Weinstein at Leisure of the Theory Class.

This is actually pretty obvious, and benching your starters fails the opposing coach test.  Namely: will the opposing coach be happy or sad when it happens?  The fun part of the article is coming up with situations where the conventional wisdom makes sense.  Here’s my best attempt: can we imagine a situation where minutes at the end of the game are especially valuable?

Suppose two teams are separated by a modest gap in average skill, so that team A would be expected to outscore team B by (let’s say) 5 points over 100 possessions.  In this case, the underdogs would benefit from a high variance in skill.  If they spend enough time above their average skill, they might be able to pull off the upset.  On the other side there’s no downside risk if they underperform: they’ll just lose by more.  By the same reasoning, team A would want to minimize their variance.

Now suppose it’s late in the game and the underdogs are holding a lead.  This lead is large enough that team B is now favored to win.  (Team A is still expected to outscore B slightly over the rest of the game, but there’s not enough time left for A to make up the gap.)  In this case, team B would maximize their chances to win by minimizing their variance.  So a low-variance player is now especially valuable.  And team A has the opposite problem.

In other words: you always want to maximize the average skill on the floor, but the optimal amount of variance changes with game situation.  So you may want to reserve some low- or high-variance players for the end of the game, if you can do so without drastically changing your average skill.

P.S. In soccer, you could actually make a pretty legitimate case for substituting a player with an early yellow card, since you can’t replace the player when he’s sent off.  Yet I have never heard anyone advocate this strategy.  (Of course, you need the probability of getting a second yellow to be pretty high before this makes sense.)

(HT: Marginal Revolution)

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