Tuesday, May 7, 2013

It's Gotta Be the Shoes!

I remeber that when I, however rarely, got the "hot hand" in a game, my basketball coach would yell "it's gotta be the shoes!" He knew I had the hot hand, and he'd tell my teammates to get me the ball, but he couldn't attribute the hotness to me, so he joked it must be the shoes.

The truth, of course, is that I didn't have the hot hand, and neither did my shoes. That's because there's no such thing as the "hot hand." In a classic paper, Gillovich et al.1 showed this by looking at every shot taken by the 1980-81 Philadelphia 76ers in their 48 home games (including the playoffs). They found that making a shot didn't increase the probability of making the next shot. In fact, it decreased that probability slightly. In other words, Dr J was slightly less likely to make a shot if he'd made his last shot! Furthermore, looking at the "runs" (streaks of misses or makes) showed no evidence of a grouping of makes or misses above what you would expect by chance.

Why does pretty much everyone believe in the hot hand if, in fact, it doesn't exist? Well, because our brains are not very good at figuring out probabilities or perceiving randomness, and they're primed to see patterns where they don't exist, so all it takes is a small run to make us think something good is going on. Or as Gillovich et al. put it (p. 311-312):
Evidently, people tend to perceive chance shooting as streak shooting, and they expect sequences exemplifying chance shooting to contain many more alternations than would actually be produced by a random (chance) process. Thus, people "see" a positive serial correlation in independent sequences, and they fail to detect a negative serial correlation in alternating sequences. Hence, people not only perceive random sequences as positively correlated, they also perceive negatively correlated sequences as random... We attribute this phenomenon to a general misconception of the laws of chance associated with the belief that sall as well as large sequences are representative of their generating process. This belief induces the expectation that random sequences should be far more balanced than they are, and the erroneous perception of a positive correlation between successive shots.
More recently, Yigal Attali, in a paper in press, shows that even people who spend their entire lives around basketball can't get past the "hot hand" belief. Here is the abstract:
Although “hot hands” in basketball are illusory, the belief in them is so robust that it not only has sparked many debates but may also affect the behavior of players and coaches. On the basis of an entire National Basketball Association season’s worth of data, the research reported here shows that even a single successful shot suffices to increase a player’s likelihood of taking the next team shot, increase the average distance from which this next shot is taken, decrease the probability that this next shot is successful, and decrease the probability that the coach will replace the player.
So the belief in the hot hand causes players to not only be more likely to take the next shot, but to take more difficult shots just because they made their last shot, even though they're more likely to miss that second shot. Despite this, coaches are so convinced of the hot hand effect that they're less likely to punish players for the resulting poor decisions.  Again, what's amazing about this is that these people are experts in basketball, and have witnessed many thousands of in-game combinations of shots, but they're still unable to perceive that making one shot doesn't make it more likely that the same player will make the next shot, especially if that next shot is an even more difficult one.

I blame the shoes.

1 Gilovich, T., Vallone, R., and Tversky, A. (1985). The hot hand in basketball: On the misperception of random sequences. Cognitive Psychology, 17, 295-314.

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