Calibration Certificate No. hot-hand-fallacy
Hot-Hand Fallacy
The hot-hand fallacy is the belief that a streak of successes raises the probability of further success — that a person or process is "hot" — beyond what the evidence supports.
documented offset from the normative answer
The original GVT 'no hot hand' result was treated as robust for 30 years, but Miller and Sanjurjo (2018, Econometrica) proved a streak-selection bias in the standard estimator that, once corrected, reverses GVT's own data into a sizeable positive effect (~+13 pp). Independent studies controlling for shot difficulty (Bocskocsky, Ezekowitz & Stein 2014: 1.2–2.4 pp) and in volleyball (Raab, Gula & Gigerenzer 2012) also find small real hot hands. The behavioral claim that people sometimes over-believe in streaks survives, but the strong claim that the hot hand is a pure illusion does not. Earlier meta-analytic support (Czienskowski et al.) inherits the same bias and is therefore discounted.
Calibration record
Source of systematic error
GVT attributed the supposed fallacy to misperception of randomness: people expect short random sequences to be more alternating than they really are (a consequence of Tversky and Kahneman's 'belief in the law of small numbers' and the representativeness heuristic), so genuinely chance streaks look meaningful and are read as evidence of being 'hot'. Memory bias reinforces this — vivid streaks are recalled more readily. The Miller–Sanjurjo correction, however, shows the deeper issue is statistical, not purely psychological: the standard streak-conditioned estimator is itself biased toward finding no hot hand, so part of what GVT diagnosed as a human error was an error in their own measure.
(1) Pure-illusion account (GVT 1985): belief in continuation is a cognitive bias with no real signal. (2) Statistical-artifact account (Miller & Sanjurjo 2018): the apparent absence of a hot hand was largely a selection-bias artifact; modest hot hands are real, so the 'fallacy' may be overstated. (3) Ecological/adaptive account (Raab et al. 2012): detecting streaks can be a rational, useful cue in settings where the hot hand genuinely exists. The mechanism debate is unresolved and partly definitional — whether 'the fallacy' means believing in any continuation vs. over-estimating its size.
Recalibration procedure
State the base rate and sample size first, then ask what a purely random process of that length would produce before attributing a streak to 'heat.' For any decision that conditions on a streak (bet more, allocate to the hot fund, keep feeding the hot shooter), check for streak-selection bias — the naive 'success rate after a streak' is downward-biased, so neither a high nor a low number should be taken at face value without the Miller–Sanjurjo correction or a permutation test.
Miller & Sanjurjo (2018) show the standard streak-conditioned estimator is biased by roughly -8 percentage points for a 100-trial sequence (k=3), large enough to flip GVT's headline conclusion; correcting it recovers a ~+13-point effect, demonstrating that the cure for the fallacy is explicit statistical correction, not intuition.
Cross-calibrated against
- Gambler's FallacysiblingThe mirror image: after a streak, expecting a reversal ('due' for the opposite) rather than continuation. Both stem from the law of small numbers; people apply the gambler's fallacy to processes they see as mechanical (roulette) and the hot hand to processes they see as skill-driven (shooting).
- Law of Small NumbersparentTversky & Kahneman's idea that people expect small samples to mirror the population, treating short chance streaks as meaningful. GVT cited this as the engine of the hot-hand illusion.
- Representativeness HeuristicparentJudging probability by resemblance to a prototype of randomness; makes genuinely random streaks look non-random and patterned.
- Clustering Illusionmechanistically-linkedSeeing meaningful clusters in random data; the perceptual basis for reading shooting or stock streaks as signals.
- Momentum / performance-chasingeasily-confusedIn finance, real return momentum can coexist with investors over-attributing 'hot' streaks to skill; distinguishing a true effect from the fallacy requires controlling for the underlying process, exactly the issue Miller–Sanjurjo raised.