(*In honor of the upcoming NBA playoffs, a brief post on, for my money, the big paradox of professional basketball: the myth of the hot hand.)
Despite a long and fruitful career full of notable findings, Cornell psychologist Thomas Gilovich is perhaps most well known for a study he conducted with psychologists Amos Tversky and Robert Vallone 25 years ago when he presented a devastating debunking of the sports phenomena known as the “hot hand.”
The hot hand refers to the belief that success in basketball (and elsewhere) is self perpetuating. That is, a player can “get into a groove” after making a couple of shots such that making a shot leads to the higher likelihood of making the next shot. String together a bunch of these and you’ve got yourself a hot hand. Tune into any basketball game and you’ll inevitably hear an announcer say, “he’s in the zone” or “he can’t miss right now” about a player with a hot hand.
If this is true, one should look at a set of all made shots and all missed shots for some entity, such as one team for an entire year, and see that players made more shots after hits than they did after misses. Gilovich and his colleagues did just that, and that’s not what they found. They found that a player was just as likely to miss as make a shot after a previous make. But what about the possibility that opposing defense becomes tougher after a guy has made a few? Or what if he starts taking more difficult shots?
To control for these possibilties, they looked at free throws, which control for both of those factors in that there is no defensive pressure and shots are always taken from the same distance. A look at two seasons worth of free throws from the Boston Celtics showed second shots were completely independent of first shots. That is, if a player made the first free throw, he was no more likely to make the second one than if he missed the first one.
As a sports fan, I’ve always had a difficult time accepting this. (I’m not alone: the famed coach Bobby Knight responded to the study by saying, ” … there are so many variables involved in shooting the basketball that a paper like this really doesn’t mean anything.” Red Auerbach was even more blunt: “Who is this guy? So he makes a study? I couldn’t care less.” ) It just seems so counterintuitive that success or failure wouldn’t have some systematic effect on subsequent performance.
It’s a seeming truism that professional athletes (and performing artists, for that matter) perform best when they’re not thinking about how they’re playing. And it’s widely known by sports psychologists that thinking too much about one’s form in any given sport, whether it be shooting the basketball or attempting to sink a putt, can have deleterious effects on performance. So it seems plausible to imagine that success (or lack thereof) on the basketball court could alter one’s mental state in a way that could systematically alter performance. But, that’s not what the data says.
In the two decades plus since Gilovich, Vallone and Tversky’s seminal paper, the hot hand fallacy has been subject to a great deal of scrutiny and doubt, but the original finding has generally held up. One study controlled for time between shots but still found no evidence for the hot hand (Adams, 1992). Others have suggested that statistics are insufficient to handle the complexity of the game (Larkey, 1989). In 2009, John Huizinga from the Chicago Booth School of Business and Sandy Weil analyzed almost a million shots from 49 star players (unpublished; here for more details) and found, contrary to the existence of the hot hand, that NBA stars were more likely to miss after a made shot than after a miss. According to their analysis, this was more likely to happen after jump shots than non-jump shots (layups or dunks).
The implications of all this are that teams shouldn’t be looking to feed the ball to a guy just because he’s made a few in a row. But despite the ample support that hot hands don’t exist, you won’t have any easy time convincing many players or coaches of this.
A post game synopsis from an LA Lakers game last fall:
Jackson’s rationale for leaving Vujacic out entails the fact that Shannon Brown scored 16 points on six of nine shooting in 21 minutes. That led Jackson to “ride the hot hand,” as he called it, even if he had planned for Vujacic to defend against Houston guard Kevin Martin…
Even Phil Jackon, probably the most successful NBA coach in modern times, cites “the hot hand” as basis for his personnel decisions.
In Gilovich’s book summarizing the work, How We Know What Isn’t So, he talks to former NBA star World B. Free about the hot hand. “If I’m on, I find that confidence just builds . . . you feel nobody can stop you. It’s important to hit that first one, especially if it’s a swish. Then you hit another, and . . . you feel like you can do anything.”
This line of thinking, that success breeds success, is certainly feasible in many aspects of one’s life. Financial success can lead to further success, as profit can lead to more profit through increased capital. In one’s professional life, success can have a powerful effect on how one is perceived by others and promote increased success through an enhanced reputation. But, on the basketball court, the implications are quite clear. There are many factors that go into deciding – say, during crunch time of a close game – who should get the ball. A simple heuristic might be to give the ball to the guy with the highest shooting percentage. But what if he’s having an off night due to injury? Or being consistently double teamed? Perhaps your second best shooter gets the call. Many factors might inform the decision. But, according to everything the data is telling us, the “hot hand” should not be one of them.
References
GILOVICH, T. (1985). The hot hand in basketball: On the misperception of random sequences Cognitive Psychology, 17 (3), 295-314 DOI: 10.1016/0010-0285(85)90010-6
Adams, R. (1992). The “Hot Hand” Revisited: Successful Basketball Shooting as a function of intershot interval.Perceptual and Motor Skills, 74 (3) DOI: 10.2466/PMS.74.3.934-934
Larkey, P. D., Smith, R. A., & Kadane, J. B. (1989). It’s okay to believe in the ‘‘hot hand’’.
Chance: New Directions for Statistics and Computing, 2, 22 – 30.
Neuropoly 
Shouldn’t they be looking at, not 2 shots at a time (is the good shot preceded by a good or bad one), but whether streaks occur with greater frequency than chance would predict? Because I don’t think two in a row is considered “hot” by anyone– the idea is more that a mental momentum builds with success (until maybe it hits overconfidence or fatigue or something).
I don’t follow sports at all, so I’ve got no interest in the outcome, but I do think that if you’re talking about streaks you need to look at streaks, not patterns of 2.
@Samantha: Looking at pairs is probably the best way to understand whether “streakiness” is occurring in a given data set, in this case basketball shots.
Over thousands of shots, you would expect to see long spans of makes based on chance alone (Imagine flipping a coin 1000 times – you might get some spans of 10 heads or tails in a row, but we know that the probability of getting a head or tail on any given flip is .5 and we wouldn’t think of those spans as streaks. If, however, we looked at flips just after flipping a head and found that the probability was no longer .5, that would certainly be a sign of something non-random going on)
The same concept would apply when looking at basketball shots. (except the probability in this case wouldn’t be .5 but each individual player’s shooting %)
One direct indicator of systematic “streakiness” is the conditional probability of success if on the prior attempt, the player had achieved success. For a true streaky player, the chance of success after a prior success should be higher than his /her normal rate of success. In other words, if a make following a make is just as likely as a miss following a make, we can explain long stretch of makes as random effects.