macrocephalopod

1/ The funny thing about the Hot Hand Fallacy is that there actually is a Hot Hand effect in basketball. A small thread on a surprising statistical mistake.

2/ Brief history: basketball coaches and players historically felt that there was a Hot Hand effect, i.e shooting performance is autocorrelated. Behavioural economists did some statistics and found out that there was no Hot Hand, so it became known as the Hot Hand fallacy.

3/ “You fools! You fell victim to one of the classic blunders – ascribing patterns to random chance!” they said. Well it turns out that all of these researchers made a mistake – once corrected for, there is indeed a Hot Hand effect in basketball.

4/ How does this work? Consider a sequence of fair coin flips. Each flip is independent, so regardless of the previous number of consecutive heads, the next flip should come up heads 50% of the time.

5/ Being an evidence-based researcher, I decide to test this by flipping a fair coin 1000 times, then computing the empirical frequency of heads conditioned on the previous coin being a head.

7/ Intuitively, the problem here is that we are “cutting off” potential streaks by fixing the sample size. This introduces a downward bias in our estimate of the streakiness.