Jonathan Weinstein is blogging now at The Leisure of the Theory Class. His first post is a nice one on a common fallacy in basketball strategy.
if a player has a dangerous number of fouls, the coach will voluntarily bench him for part of the game, to lessen the chance of fouling out. Coaches seem to roughly use the rule of thumb that a player with n fouls should sit until n/6 of the game has passed. Allowing a player to play with 3 fouls in the first half is a particular taboo. On rare occasions when this taboo is broken, the announcers will invariably say something like, “They’re taking a big risk here; you really don’t want him to get his 4th.”
The fallacy is that in trying to avoid the mere risk of losing minutes from fouling out the common strategy loses minutes for sure by benching him.
Jonathan discusses a couple of caveats in his post and here is another one. The best players rise to the occasion and overcome deficits as necessary. But they need to know how much of a deficit to overcome.
Suppose you know that a player will foul out in 1 minute. There are 5 minutes to go in the game. If you keep him in the game now he will have to guess how many points the opponents will score in the last 4 and try to beat that. This entails risk because the opponents might do better than expected.
If you bench him until there is 1 minute left then all the uncertainty is resolved by the time he comes back. Now he knows what needs to be done and he does it.
If Jonathan’s argument were correct then there would be no such thing as a “closer” in baseball. At any moment in the game you would field your most effective pitcher and remove him when he is tired. Instead there are pitchers who specialize in pitching the final innings of the game.
The role of a closer is indeed misunderstood in conventional accounts. Just as in Jonathan’s argument there is no reason to prefer having your best pitcher on the mound in later innings, other things equal. All innings are the same. But this doesn’t mean you shouldn’t save your best pitcher for the end of the game.
Suppose he can pitch for only one inning. If you use him in the 8th inning the opposition might win with a big 9th inning and then you’ve wasted your best pitcher. It would have been better to let them score their runs in the 8th. That way you know the game is lost before you have committed your best pitcher. You can save him for the next game.
Cheap Talk 
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May 10, 2010 at 9:27 am
Bryce
There’s actually a pretty strong consensus in the sabermetrics community that baseball managers are falling victim to the same fallacy as basketball coaches. And in the baseball case, there are some good statistics to back it up. The idea is that the closer is usually the team’s best reliever and should be brought into the game in the [probable] highest-leverage situation, which is not necessarily the 9th inning. The website Fangraphs recently had an article titled “Jim Tracy’s Creative Bullpen Management,” that reflects this consensus.
May 10, 2010 at 4:30 pm
Anonymous
Benching the star would have effect on the peers, which may depend on the situation at that moment.
May 11, 2010 at 4:12 am
bellisaurius
While in a military sense reserves matter, does a player actually increase his chance of scoring because his team is down? Perhaps it affects some managerial strategies (I just need to manufacture one run…), but the idiosyncrasies of hitting and shooting seem to confound most plans, except on the level of many, many iterations.
A lot of it seems like butt covering, or simple rule following to me.
May 11, 2010 at 9:32 am
Nate
basketball stars and relief pitchers are apples and oranges here. the pitcher will only have so many innings they can work in a given week, so rest is an important consideration. presumably long-term rest is not an issue for the basketball star. (maybe a few minutes as a breather in-game, but that’s it)
also, the evidence is piling up that there is no such thing as “clutchness” in sports, so your contention that a star will “rise to the occasion” is likely false.
May 11, 2010 at 11:06 pm
jeff
Its not clutchness that is being leveraged, it is just the resolution of uncertainty. Athletes do not have an upper bound to their performance level, there is always a tradeoff at the margin between higher performance vs costlier effort. Uncertainty about how many points need to be scored means that you resolve this tradeoff by equating marginal effort cost versus *expected* incremental probability of winning. This will entail losing if it turns out that the other team scores an unexpectedly high number of points at the end after the star has fouled out.
On the other hand if the uncertainty is resolved first, then the tradeoff is between marginal effort cost and *actual* winning margin. In those states where the opponent scored many points while the star was on the bench, he has the right incentives to exert exceptionally high effort to surmount the deficit.
May 11, 2010 at 3:09 pm
lyle_s
Generally when a player is benched for risk of fouling out the coach is trying to get by without them early in the game on the assumption that, were the player left in, he/she would foul out at some point and not be available later when they may be needed for sure. If that strategy fails, coaches will reinsert the player and assume the risk of that player failing out. If the team can swim with the player on the bench, why not wait until n/6?
I agree on the closer comments, your best reliever should go in the highest leverage situation, in theory. However, there’s lots of elements to managing a staff across a season that make it desirable to mix up who takes the high leverage innings and so the convention of a closer can work to the team’s advantage in that it gives the rest of the bullpen a chance to establish just who can and can’t handle the high leverage situations. It also provides a sense of order that is said to be good for players’ psyches. The closer knows he’s going to pitch the 9th (and maybe a little before) so he can mentally prepare for that challenge. That might be a load of hooey but I think there’s something to it.
Long story short, the baseball manager has to think beyond the context of that one game/situation. I’m not sure the basketball coach has to consider as much.