Hot hand theory, updated?

One spot where statistics and sports have commonly intersected is the so-called ‘hot-hand’ theory. Statisticians have argued that athletes – whether a basketball player at the free-throw line, or a baseball player at the plate – don’t get ‘hot.’ Instead, athletes are just subject to the same fluctuations and streaks that a roulette table or slot machine would. Of course, TV commentators argue the opposite: ‘he’s hot, feed him the ball,’ is heard probably once a quarter on most TNT broadcasts.

While the original hot-hand debunking occurred in the 1980’s, two papers have chipped in recently. The first, written by Attali in Psychological Science, suggested that hot-hands don’t exist, and, instead, basketball players believing they are “hot” take, and miss, a disproportionate percentage of their teams’ shots after making a shot. 

The second was written by Gur Yaari in PLOS one, and is linked here and blogged by the NY Times here. This study looks at the probability of shooters hitting their second (and third, on occasion) free throws, conditional on what happened in their first attempt. The authors use several seasons worth of NBA data, and several thousand free throws, and find shooters who have made their first free throws are significantly more likely to make their second. In other words, the hot-hand may still exist. My quick notes & comments on this paper follow.

1) Several researchers (including’s @SIDavidEpstein) have commented that with large data sets, the researchers were bound to find statistical significance, and that what’s really important is effect size. This is a good point, but the effect size is easy to find in the paper (especially because its free for everyone). Aggregated across the league, there is least a 4% higher percentage of hitting the second free throw after hitting the first, a difference which is fairly strong and worth of significant results. Accounting for individual player strength, which is obviously fairly important to do, the results are not as strong: between 1.4% and 4.6% increases in the probability of hitting the second free throw. With roughly 45 free throws in an NBA game, that’s a few points a game that can be attributed to a ‘hot’ hand.  I’d say that’s a worthy effect size.

2) One frequent problem with studying sports & statistics is that it is often difficult to account for changes in opponent behavior. For example, in the Attali paper, opponents are likely play better defense on players who just scored baskets, perhaps causing them to miss future shots. This behavior change is often tough to account for. The strength of the Yaari article is that in using free throws, there is no issue with behavior changes. 

3) That said, a strength of the paper – studying free throws, which aren’t subjective to behavioral variables – is also its weakness. The hot-hand is more plausible, but less impactful, in short sequences of time, as in free throw attempts. The true value of the hot hand comes not in two-event sequences, like free throws, but over the course of a game, like Kobe Bryant hitting 12 three-pointers in a game.

Further, an individual’s free throw success may also be tied to game and time specific changes, most specifically how tired he is and/or how long he has been on the court. A tired individual is more likely to miss the first free throw and subsequently miss the second…is that being cold or just being exhausted?

Thus, while the Yaari paper is an important advancement in the hot-hand literature, it far from proves the hot-hand theory. Like most everything else, more research is needed. 


Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s