Last updated September 2026
The evidence now says yes, at least in controlled shooting. The 1985 study that called it a myth compared each player's hit rate after streaks of hits with the rate after streaks of misses, and that comparison is biased against finding a hot hand. In a 100-shot sequence, a player with no hot hand at all is expected to score about 8 points worse after three hits than after three misses. Correct for that bias and the original data point to a real hot hand.
Most people who have played a sport know the feeling: a few successes in a row, and the sense that the next one is more likely. In 1985 three psychologists tested that feeling, found nothing, and gave us the “hot hand fallacy”, one of the best-known examples of human bias. In 2018 two economists showed that the way the streaks were measured was itself tilted, and that the corrected 1985 data support the hot hand. A coin and a spreadsheet are enough to see the tilt for yourself: download the workbook and try it.
Gilovich, Vallone and Tversky asked 26 Cornell University basketball players to take 100 shots each, from distances chosen so that each player would hit about half. For each player they compared two numbers: the hit rate on shots taken straight after three hits in a row, and the hit rate straight after three misses in a row.
A hot hand would make the first number clearly higher. On average it was higher by only about 3 percentage points, too little to be significant. The conclusion, repeated in textbooks for the next three decades, was that the hot hand is an illusion: we see patterns in random sequences because we expect to.
The arithmetic was fine. The problem is subtle enough to have gone unnoticed for thirty years: in a finite sequence, if you look only at the outcomes that follow a streak of successes, you will on average see fewer successes than the true rate. Miller and Sanjurjo published the proof in Econometrica in 2018.
The simplest version needs only a coin. Flip a fair coin four times, look at every flip that comes straight after a head, and write down what share of them were heads. Ask a thousand people to do the same and average their answers. The average is 40.5%, not 50%. We checked this by listing all 16 possible sequences, and again with two million simulated ones.
Nobody cheated and the coin is fair. The tilt comes from measuring within each short sequence and then averaging across people, which is exactly what a study of individual players does. A run of heads uses up heads, so the flips that follow it come from what is left, and what is left leans towards tails.
We rebuilt the 1985 experiment and ran it 400,000 times with a shooter who has no hot hand at all, where every shot is an independent 50% chance. The 1985 method still reports a clear “cold hand”:
The fair benchmark for the 1985 study was therefore about −8 points, and measured against it, Cornell's +3 is about 11 points better than a coin would have scored. Miller and Sanjurjo's bias-corrected estimate for the Cornell data is +13 percentage points, and it is statistically significant.
The bias shrinks as sequences get longer, which helps it hide:
We then gave our simulated shooters a real hot hand, with a higher chance of hitting after three hits and a lower chance after three misses, and measured them the 1985 way.
A shooter who really is 8 points better when hot comes out looking like a coin. When we ran whole 26-player panels in which every player was truly hot by 13 points, about one panel in three still came out at +3 points or less, which is what Cornell recorded. The 1985 result is roughly what a real hot hand of that size produces when you measure it this way.
Not entirely. The bias is a mathematical fact. How large the hot hand is, and whether it carries over from a practice gym to real games with defenders and shot selection, is still argued over, and people may still overestimate streaks even if streaks are real. What has changed is the famous evidence: once corrected, the study that “proved” the fallacy points the other way.
The flaw was in the method, and businesses apply the same method to their own data all the time. Whenever a short track record is analysed one unit at a time (a salesperson's quarters, a fund manager's months, a supplier's deliveries, a project team's last few jobs), asking “what happened after a good run?” is tilted in the same direction. A review that compares each person's results after strong periods with their results after weak ones will tend to find slumps that are not there, and, as the 8-point shooter shows, it can miss real momentum entirely. Decisions on bonuses, supplier contracts or which team gets the next project can rest on that tilt without anyone noticing.
The remedy is the check the 1985 study never ran. Before trusting what a method says about your data, run it on simulated data where you already know the answer: generate a thousand records with no effect in them, apply the same analysis, and see what it reports. Anything it finds there is bias, and you now know its size and direction. It is the same habit behind our boarding race, where one run of an uncertain process turned out to be only a sample.
A single replay of the experiment shows almost nothing. The bias appears across thousands of replays, which is what a Monte Carlo engine is for, so the workbook runs in Excel with ModelRisk:
Download the Hot Hand Test workbook (.xlsx). It is free and needs no registration. No ModelRisk yet? Start the free 15-day trial and run all 40,000 replays yourself.
Is the hot hand the same as the gambler's fallacy? They are opposites. The gambler's fallacy is expecting a streak to reverse (“red is due”), and the hot hand is expecting it to continue. The same measurement bias affects both, because in a short sequence the outcomes after a streak lean towards the opposite result. That can make a real hot hand look absent, and it can make random data seem to confirm the gambler's intuition.
Does the bias disappear with more data? It shrinks as sequences get longer: about −8 points at 100 shots, −4 at 200 and under −1 at 1,000 in our simulations. More players do not help. Averaging many short sequences keeps the bias at full strength, and that was exactly the 1985 design.
Who corrected the original study? Joshua Miller and Adam Sanjurjo, in “Surprised by the Hot Hand Fallacy? A Truth in the Law of Small Numbers”, Econometrica 86(6), 2018, pp. 2019–2047. The original study is Gilovich, Vallone and Tversky, “The hot hand in basketball: On the misperception of random sequences”, Cognitive Psychology 17(3), 1985, pp. 295–314.
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