Hot hand fallacy
Claim assessed: Belief in athletes' streaks of success is an illusion.
Published · how we work
In short
The hot hand is the idea that an athlete who has succeeded a few times in a row has, for a while, a better chance of succeeding again. A 1985 study concluded that the idea is an illusion: successes would come as independently as coin tosses, and people see streaks where there are none. The conclusion became a classic example of a judgement error, called the hot hand fallacy. In 2018, Miller and Sanjurjo showed that the study’s method had a statistical bias that is hard to spot. After correction, the same data show a real hot hand.
What it says
The classic study. Gilovich, Vallone and Tversky (1985) started from the fact that basketball players, coaches and fans almost all believe in the hot hand. Besides NBA game data, they ran an experiment with 26 players from Cornell University’s teams. Each shot 100 times from a distance at which they made about half their shots. After three hits in a row, players made 49% of their shots on average; after three misses, 45%. The difference was not significant, and the authors called belief in the hot hand “a powerful and widely shared cognitive illusion”. We have not read the study; we describe it from Miller and Sanjurjo, who reproduced its results from the raw data.
The hidden bias. Miller and Sanjurjo (2018) proved mathematically a surprising property of short sequences. If you toss a coin several times and look only at the tosses that follow a heads, the share of heads among them will, on average, be below 50%. With three tosses, the average is 5 in 12. For a player who makes 50% of 100 shots, the difference between “after three hits” and “after three misses” should average −8 percentage points even if there is no hot hand. Gilovich et al. compared the difference with zero, not with −8.
The corrected result. Taking the bias into account, the average difference in Gilovich et al.’s experiment rose from +3 to +13 percentage points, a significant difference. The authors compare it with the gap between the median and the best NBA three-point shooter, 12 percentage points in the 2015–2016 season. After correction, 19 of 25 players shot better after a streak of hits, and for 5 of them the effect was significant. Another test, which the bias doesn’t affect, gave the same result. A replication of the experiment also reverses its conclusion after correction. Over 28 years of the NBA three-point contest, the corrected difference was +8 percentage points.
In games and in other sports. Lantis and Nesson (2021) analysed every shot from 12 NBA seasons: over 500,000 free throws and two million field goal attempts. For free throws, after three or four makes in a row the chance of the next one rose by about 4.5 percentage points. For field goals it didn’t rise at all; after three makes in a row it even fell slightly, by 0.6 points. Teams nonetheless reacted as if the hot hand existed. The player who had just scored shot sooner and from further away, and the defence guarded him more closely. In darts, Ötting et al. analysed 167,492 throws by 73 professional players. They found a strong link between the three darts thrown quickly in the same turn, but almost none between turns. The authors note this isn’t the hot hand as fans usually understand it.
Example
A basketball coach tells the team to pass more often to the player who has scored three times in a row. NBA game data suggest that, during play, the defence adapts and the next shot doesn’t go in more often. In practice, with repeated shots and no defence, the decision would have more support. The example is an illustration, not a study cited here.
How to apply it
The steps below are a practical approach we propose, based on the studies cited.
- Don’t automatically dismiss “good form” as an illusion. Under controlled conditions, the corrected data show a real hot hand.
- Don’t overestimate it either. The measured effects are a few percentage points and can disappear when the context changes, for example when the opponent adapts.
- Be careful when analysing what follows a streak. In short sequences, even a completely random process seems to “turn back” after a streak. The right comparison isn’t with zero.
- Ask for a lot of data. A few successes in a row are a weak signal of someone’s form.
Limits and nuances
- Whether people estimate the hot hand correctly remains open. Miller and Sanjurjo note that players and coaches may still see a hot hand where there is none, or exaggerate how much it matters.
- Studies define the effect differently. Some ask whether a success directly raises the chance of the next one, others whether there are periods when a player is in form. The results can’t be compared directly.
- Game data are observational. Lantis and Nesson control for many shot characteristics, but defence and shot selection remain hard to separate from the effect itself.
- What we read. We read Miller and Sanjurjo (2018) in full, from the published version posted on OSF. Of Lantis and Nesson we read the 2021 NBER working paper: the abstract, introduction, main results and conclusion. We read Ötting et al.’s 2018 arXiv version in full. Their published versions may differ slightly. We have not read Gilovich et al. (1985); we describe it from Miller and Sanjurjo.
Sources
- Thomas Gilovich, Robert Vallone, Amos Tversky (1985). The hot hand in basketball: On the misperception of random sequences
- Joshua B. Miller, Adam Sanjurjo (2018). Surprised by the hot hand fallacy? A truth in the law of small numbers
- Marius Ötting, Roland Langrock, Christian Deutscher, Vianey Leos-Barajas (2020). The hot hand in professional darts
- Robert Lantis, Erik Nesson (2021). Hot shots: An analysis of the “hot hand” in NBA field goal and free throw shooting
See also: Conjunction fallacy, Gambler's fallacy, Regression to the mean