Basketball and economics: ah, a marriage made in heaven. In grad school, I had the privilege of taking a class from the late Amos Tversky (who would presumably have been the co-winner, with Daniel Kahneman, of the 2002 Nobel Prize in economics, had he not died in 1996), one of whose famous studies demonstrated that there’s no evidence for “hot shooting” in basketball. As statistical studies go, this one wasn’t a bad assignment: a large part of it involved tracking every single shot taken by the Philadelphia 76ers for an entire season.
Another article by an economist on basketball has apparently attracted a lot of attention. By Jonathan Weinstein, it’s available here: http://theoryclass.wordpress.com/2010/04/27/foul-trouble/. His basic idea is one that I’ve thought about previously: why do coaches remove players from a game when they’re in foul trouble? If you leave him in, he might foul out and play fewer minutes overall; if you bench him, he will play fewer minutes.
(Jonathan’s post plus his follow-up appropriately note various caveats, including 1) maybe the player won’t have his “head on straight” after a foul call and 2) edge cases involving players one-foul-away-from-disqualification and saving him for “crunch time”, which may be a bit different from normal play with regard to length and nature of possessions, more foul shooting, and so on. To his list, I’d add the idea that referees may be more or less likely to call another foul on the same player shortly thereafter, though it’s not clear in which direction this would fall.)
I’m highly sympathetic to Jonathan’s post, at least “in a vacuum”. (My biggest practical concern with implementing his suggestion is actually referee behavior - it’s been documented that basketball officials (unfortunately) are significantly influenced by fans, “momentum”, foul disparities, and other factors. In particular, officials often seem to make calls to make a game closer than it “should” be. If the referees show some inclination to keep a game tight for you, even if you have your subs in, then it does make some sense to hold your best players out until the final few minutes if they’re in foul trouble.)
However, Ken Pomeroy, whose basketball analysis and writings I admire very highly, doesn’t agree with Jonathan: http://kenpom.com/blog/index.php/weblog/all_points_are_not_created_equal/. As someone who appears to be on the far end of the Ruthless Objectivity scale, his opinion isn’t to be discarded lightly. That said, I think he’s wrong.
Ken correctly notes that the objective isn’t to maximize point differential - it’s to win the game - but, as someone whose analysis is based heavily on tempo-free statistics that, basically assess Stat X Per Possession - it’s surprising that he goes on to say “It’s difficult to defend that all points are worth the same”. (Ken, your whole model is based on the premise that all points/stats (per possession) are worth the same!).
His illustrative comparison: a missed three-pointer early in the 1st half of the Duke-Butler national championship, if made, would have altered the win probability for Butler by a small amount. The end-of-game missed three by Hayward, if made, would have changed the win probability from zero to 100%. Ergo, the crunch-time three mattered a lot more than the early three.
Ken’s logical flaw: the three at the buzzer mattered hugely - but only because the team taking it was down by two. Had Butler been down by 4, or 10, or 20, or up by 1 or 20, it wouldn’t have mattered at all. Furthermore, at the moment of the early three-point attempt, Butler’s being down by 2 was only one of many possible “futures”. Had that first three gone in, the chance of a “future” in which Butler was ahead at the buzzer would have gone up a bit. To connect this to the foul-trouble argument, it’s not a question of choosing between my star hitting a minor shot now or hitting a winning shot at the buzzer: it’s whether playing my star for a minute right now will increase the team’s chance of winning.
The key is that, if you play your star _now_, you get the benefit of his play, right now, with certainty. If you bench your star, you lose that benefit. In return, you get an increased chance that he’ll be able to play in the final minute - but a) he might have been able to play in that final minute anyway, if he doesn’t foul out, and b) there’s a significantly-less-than-100% chance that that last minute will matter.
I think it’s that last piece that Ken’s missing. Yes, Hayward’s last three was a game-decider - but what were the odds that the game would end up in that situation (Butler down 1 or 2 with the last shot)? Perhaps 5%? That’s why, generally, points are points, whenever you get them. Again, “crunch time” may play out a little differently - teams fouling to get the ball back, more possessions, teams ahead with the ball holding it and then rushing a shot at the end of the 35-second clock - so I can see an argument for benching a player who is one foul away from elimination until the last few minutes. In general, though, I think coaches bench players in foul trouble way too much, and way too early. (In fact, as a Stanford fan, I was pleased to see Coach Dawkins eschewing conventional wisdom often this season, continuing to play players with 2 fouls in the first half. Of course, his lack of depth may have been a contributing factor, too…)
This raises Ken’s second flaw, which is that he has (IMO) too much faith in coaches’ understanding and motivations. He says: “While I don’t doubt that some coaches at the college level have counter-productive biases in this area, I would be surprised if taken collectively, the 347 Division I coaches are significantly more conservative than is warranted.”
Thou art far more optimistic than I, Ken. :) Gregg Easterbrook’s Tuesday Morning Quarterback continuously makes the point that coaching behavior is 1) flawed and 2) absolutely not designed to win games - it’s designed to deflect criticism and second-guessing that, in the moment, is painful and unpleasant and, in the long run, shortens coaching careers. (The canonical football example of win-percentage-deficient coaching behavior is punting on fourth-and-short. Punt and lose, and the fans/media/front office blame the players. Go for it and lose, and everyone blames the coach. Of course, in the long run, wins tell the story - but in football, where seasons offer a small sample size of games, the extra job risk of defying conventional wisdom isn’t worth the small added win percentage of being more aggressive.)
I suspect basketball coaches have the same mentality. Conventional wisdom says bench the player in foul trouble; if he abides thus, and the team loses, then (in the short run) it’s the player’s (or even the official’s) fault. If the coach keeps the player in, he fouls out, and the team loses, then the coach was an idiot. Let’s say this foul-trouble situation happens 15 times per year, and correct behavior (keeping players in) results in 8 expected-value wins, whereas benching players results in 7 expected-value wins. I wouldn’t be at all surprised if the coach is more likely to lose his job in the former scenario compared to the latter, because of those six “idiotic losses” where the coach kept his stars on the floor. (I say six losses, because the stars won’t foul out in all the games.) Fans and media and athletic department types may be less likely to recall the other times when the star stayed in, helped maintained a lead, and fouled out with 3/5/7 minutes to go with their team up by 9 and the team won without too much problem.