Where it sits
The honest position: the old proof was broken. That is not the same as the belief being correct.
Tell it apart
| Aspect | Hot hand | Gambler's fallacy |
|---|---|---|
| Domain | Human performance | Independent events |
| Independence holds | No | Yes |
| Still a fallacy? | Contested | Yes |
| Key year | 2018 | 1913 / 1971 |
Long taught as twin errors, they have parted company. The gambler's fallacy remains a genuine error because roulette spins are independent by design. A basketball player is not a roulette wheel, shots are not independent draws, and the analysis that declared the belief false has since been shown to be biased. Treating the two as equivalent is now itself the mistake.
What it doesn't mean
This is the most important correction on this page. The 1985 result was a mathematical problem, not a data problem: the standard streak-conditional measure is biased downward by construction, so even a genuinely random sequence produces an apparent anti-streak signal. Re-analysed with the bias corrected, the canonical study's conclusions reverse and evidence consistent with a real hot hand appears.
That overcorrects. What was established is that the evidence *against* the hot hand was invalid — not that streaks are a forecasting tool. Effects vary by sport and task, and may reflect players having genuinely better and worse periods rather than success breeding success. Where they have been measured most carefully — Miller and Sanjurjo's re-analysis of the 1985 shooting experiment — the bias-corrected gap is about +13 percentage points, which they call moderate to large.
What it really means
For thirty years the hot hand was the showpiece example of human irrationality. Gilovich, Vallone and Tversky examined basketball shooting data in 1985, found that a made shot didn't raise the odds of the next one, and concluded that a belief held by every player, coach and fan alive was a “powerful and widely shared cognitive illusion.” It went into every textbook.
In 2018 Joshua Miller and Adam Sanjurjo showed that the measure used to reach that conclusion is biased by construction. Here is the version you can check yourself. Write out every possible sequence of three fair coin flips. In each sequence, find the flips that came immediately after a head, and record what fraction of those were heads. Average across all sequences. You get a number below 50% — from a coin that is provably fair. The way the conditioning selects which flips get counted builds the shortfall in.
That is exactly the conditioning the 1985 analysis applied to shooting data. Which means 'no hot hand' was the expected output whether or not a hot hand existed. Corrected, the canonical study's conclusions reverse.
The honest position now is neither of the two confident ones. The old proof was broken — that is not the same as the belief being right. Real streak effects vary by sport, and may reflect players simply having better and worse days rather than success feeding success — but where they have been measured carefully they are not small: about 13 percentage points in the corrected 1985 data. What's genuinely settled is smaller and more interesting: a finding taught as certainty for thirty-three years was never established at all.
Where it comes from
gambling and sporting slang for a run of success
The term now outlives the finding that justified calling it a fallacy.
- 1985
Gilovich, Vallone and Tversky analyse basketball shooting data, find no evidence that made shots raise the chance of the next one, and conclude the widespread belief in the hot hand is 'a powerful and widely shared cognitive illusion'.
- 2018
Miller and Sanjurjo prove in Econometrica that the standard measure used to test for streak dependence carries a built-in downward distortion — 'streak selection bias'. Correcting it, the canonical study's conclusions reverse.
In real life
- A basketball player sinks four shots in a row and teammates start passing her the ball. For years this was the textbook example of the fallacy; since 2018 it has looked more like a reasonable guess.
- A darts player who's in the zone may really be having a better evening than usual. Whether one hit makes the next more likely is a separate, harder question.
- Where the original label still fits: a roulette player who believes a hot table will keep paying. On a fair wheel there is no streak to ride, whatever the last ten spins did.
Questions
Q01So should I pass to the player who's hit four in a row?
The evidence no longer says that's irrational, but it doesn't hand you a rule either. Corrected analyses find real streak effects that are not small — about +13 percentage points in the 1985 experiment once the bias is removed — but defences adjust — the hot shooter draws coverage, which can lower their next shot's quality even if their touch is genuinely better.
Q02What exactly was wrong with the original analysis?
A selection artefact, easiest to see in miniature. Take every three-flip sequence of a fair coin, work out within each sequence the share of heads among the flips that followed a head, then average those shares: the result comes out below 50% even though the coin is fair, purely because of how the conditioning selects which flips get counted. The 1985 study used that same conditioning on shooting data — so 'no hot hand' was the expected reading even if a hot hand existed.
Q03Do textbooks still teach the 1985 version?
Many do, and that lag is the useful lesson. The hot hand was one of the most cited examples of human irrationality for over thirty years. When you meet it cited as proof of a cognitive illusion, check whether the source postdates 2018.
Sources
- Miller & Sanjurjo, 'Surprised by the Hot Hand Fallacy? A Truth in the Law of Small Numbers', Econometrica (2018) — arXiv.
- The Hot (Invisible?) Hand (PLOS ONE) — PMC.