The hot hand fallacy fallacy fallacy

The hot hand fallacy: Gilovich, Vallone and Tversky (1985) convinced the world that basketball players don’t get hot — people just see patterns in randomness.

The hot hand fallacy fallacy: Miller and Sanjurjo discovered a statistical bias in the original analysis. If you observe sequences of finite length and condition on a make, the average of subsequent shooting percentages is biased downward. Re-analysing the same data with the correction shows that the hot hand is real — a 50% shooter who appears to remain at 50% after a make is actually shooting hot, because the conditional baseline is 40%, not 50%.

The hot hand fallacy fallacy fallacy: Drew at Albert Bridge Capital points out that how you calculate the baseline matters. If you take the average of sequence-level percentages (Miller & Sanjurjo’s approach), yes, the conditional baseline is 40%. But if you pool all shots across all sequences and calculate the overall percentage after a make, a 50% shooter is still 50%. So whether the “fallacy fallacy” holds depends on which averaging procedure the original study used — and if it used the pooled approach, the hot-hand fallacy fallacy is itself a fallacy.

Gelman adds another layer: the “constant probability” null model was never a sensible default anyway. Player skill varies over years and months — why wouldn’t it vary over minutes? He also quotes Jason Collins’s observation that behavioural economists readily accepted that “words associated with old people can slow you down” but dismissed the idea that making a few shots could affect your next shot.

Then there’s a fourth layer buried in the Albert Bridge Capital comments: depending on how you count remaining shots in the sequence, even the pooled approach yields 47% rather than 50%, which would still support a hot hand — making the whole chain a “hot hand fallacy fallacy fallacy fallacy.”

Albert Bridge Capital — UNSW seminar — Gelman blog — r/badeconomics