Incentives in Sports

I just read an interesting piece using game theory models to argue that NBA coaches are pulling their stars too early because of foul trouble, and not shooting enough three-pointers at the end of close games. It reminds me of the stats showing that NFL coaches punt or kick too often on fourth downs. But what do studies like this really show?

The standard interpretation is a kind of Freakonomics/Moneyball storyline: the coaches are being irrational because of loss aversion or superstition or what have you. Or they’re responding to owners, press and fans who will judge them irrationally, e.g. by criticizing them more for a turnover on downs than they would praise them for converting.

In what sense are all these behaviors and preferences “irrational”? In that they don’t maximize wins, of course. But the goal of maximizing wins is itself just another preference, not some Platonic ideal. Given these preferences that come into conflict — one for maximizing wins, one for playing it safe — why do we tend to privilege the first and assume that the second is somehow wrong?

Michael Lewis, following this pattern, considers various incentives-driven explanations for the fourth down phenomenon, and decides that coaches just don’t want to stand out — even if they go for a risky first down and it pays off, they may feel like they’re showing up their more conservative fellow coaches, and that bond among the coaching fraternity is greater than their bond with their teams — maybe somewhat the way that aristocratic military officers in Europe once felt more kinship with the officer class in other countries than with their own enlisted men.

It’s an interesting theory and he’s definitely thought about it more than the average sports pundit, but I prefer the simplest explanation: that maximizing victories or championships is not the sole preference of fans. We all pay lip service to those goals, but in the end we’d rather minimize the pain of defeats, even if it means more of them. You might think this preference would weaken as the season progresses and the “cost” of defeats rises, but the pain of a tough defeat is probably rising even faster. Would you rather be the coach who let your star foul out in the third quarter in December, or in a playoff series?

The three-pointer argument stood out to me in particular. Specifically, he’s talking about a situation where the team in possession is down by two with time for one more play:

Simply put, it is likely in the best interests of the losing team to shoot the three almost all the time. As long as the defending (winning) team guards the three pointer less than about 80% of the time, the losing team should seek to end the game in regulation every time. Similarly, the team that is ahead should fear the three pointer much more than overtime. As long as the team that is losing shoots the three at least a third of the time, the defending team should always defend the three.
Unfortunately, often finding the best three point shot involves working the ball around and having someone other than the team’s superstar take the shot. In today’s NBA Culture, Hero Ball — star players dominating offensive possessions — has often taken the place of team basketball in crunch time. The problem with this is that isolation plays are good for only 0.78 points per possession (ppp), as opposed to off-the-ball cuts (1.18 ppp) or transition plays (1.12 ppp). When star players do not take the last shot, or when role players miss wide open opportunities, the star is blamed for not taking the shot. However, this analysis shows that the three pointer, especially if the team is able to get off an open look, dramatically improves the team’s chances of winning the game.

It’s hard for me, or any other New York sports fan, to read this without thinking of Game 6 of the 1994 NBA Finals, in which the Knicks found themselves down by two to the Houston Rockets with five seconds remaining. John Starks took the three-point shot, a shot that would have won the title, and was blocked. Houston won Game 7 and the championship.

Now, maybe this wasn’t quite the scenario he’s talking about in that post. But it’s interesting to me that as a twelve-year-old fan, that was such a traumatic moment that even now, years after I stopped following basketball, I can’t write about it without wincing a little. The Rangers won the Stanley Cup at almost the same time, and I’m sure I watched that series too, but I’ll be damned if I can remember any of it. And if the Knicks had gone for two, tied the game, and lost in overtime, I’m sure I wouldn’t remember that either. Victory and defeat are fleeting, but those moments of real heartbreak stick with you.

When economists talk about loss aversion as an irrational human tendency, that’s part of a framework in which “rational” actors maximize their economic outcomes. Money is the external yardstick. But for sports fans, there is no absolute metric to measure the outcome of a game or even a season; there’s just the pain of loss and the pleasure of victory, and there’s no question that aggressive coaching decisions in a close game will increase both. If the pain of a dramatic loss is worse than the pleasure of a dramatic victory, maybe that’s all there is to say about it. Calling it right or wrong, rational or irrational, isn’t as meaningful without an objective framework for what those terms mean.

Again, I’m not saying we don’t want our team to maximize victories — just that it’s not the only thing we want. And if we think it is, well, it wouldn’t surprise a psychologist that we don’t have perfect access to our own revealed preferences. People lie to themselves about all kinds of things. But sports fandom in particular is based on constant suspension of disbelief. If any of us spent much time thinking about the mercenary attitude of the players, the greed of the owners, or the breathtaking commercialism of the whole pro sports machine …we’d find it pretty hard to go on caring about who wins. So we assuage our guilt with an occasional 5,000 word think piece and then go back to arguing over stats, trades and strategy. Compared to the self-deception necessary to be a modern sports fan in the first place, fooling ourselves about exactly how much we want our team to win is nothing.

Does it seem like I’m just arguing semantics? I think it’s something more, and it has implications beyond sports. The spread of quantitative social science into pop culture is leading us to experience all kinds of things in a more “meta” and emotionally detached way. For example, when you read about a movie’s box office results and demographic targeting — and it’s getting hard to avoid it — you’re going to experience the movie itself a bit less directly. A friend just sent me a link to this Kevin Kelly review of a book that makes a similar suggestion:

Years back, in CS Lewis’ essay ‘On The Reading of Old Books,’ I encountered a suggestion that has stuck with me ever since. Lewis posited that each generation of humanity takes certain things for granted: assumptions that go unexamined and unquestioned because they are commonly held by all. It was Lewis’ opinion that reading books written by prior generations would help us to see around these generational blind spots.
In her new book, Monoculture: How One Story Is Changing Everything, FS Michaels suggests that just such a blind spot has, over the course of generations, come to dominate the narrative and values that our society lives by. From education and the arts to how we eat, think, and play, Michaels asserts that we have been steeped in a single point of view, the economic, where value is reduced to what can be sold and worth is determined by financial expediency.

(Indeed, the research that Lewis cites on the fourth down effect was done by an economist, David Romer.)

These kind of statistical debates are part of the fun of being a fan, but we shouldn’t confuse quantitative arguments with qualitative ones. If some NBA fans want to see more strategy and team play, and others want to see “Hero Ball” even if it costs them a few close games, those are just two sets of preferences. Neither is right or wrong in any absolute sense, and wrapping one of them in numbers doesn’t change that.