The hot hand was debunked and then the debunking was corrected

The original finding and why it was so persuasive

Players, coaches and spectators believe strongly that performers get hot — that a run of successes raises the chance of the next one. A well-known analysis of shooting records examined whether a success actually followed a success more often than it followed a failure, and reported that it did not, within the precision available. The conclusion drawn was that the hot hand is a perceptual error: people see patterns in sequences that are statistically indistinguishable from independent trials.

It became a standard teaching example, and for good reason. Human beings genuinely are poor at judging what a random sequence looks like, expecting runs to be shorter and alternations more frequent than chance produces. That underlying point is solid and independently supported, which lent the specific conclusion more credibility than it had earned on its own.

The correction, which took decades to arrive

In the 2010s, researchers identified a genuine flaw in the standard way this question had been analysed. If you take a finite sequence of trials, find the moments that follow a streak of successes, and average the outcomes at those moments, the resulting estimate is biased downward — not because of anything about the performer, but because of how conditioning on a streak within a finite sequence changes what you are averaging.

The bias is small in large samples and substantial in the sample sizes actually used, and it goes in exactly the direction needed to hide a modest real effect. Once the correction is applied to the original data and to newer datasets, the evidence points to a small hot-hand effect existing in at least some settings, rather than to nothing at all. The reversal is not total, and specialists continue to argue about magnitude and generality.

What the episode actually demonstrates

It is tempting to file this as a story about experts being wrong, which misses the useful part. The original analysis was competent, published, replicated in method by others, and widely taught, and it was undone by a subtle property of a statistic that nobody had examined. Nothing about it looked shaky from outside.

The transferable lesson is that a null result depends on the measure being unbiased just as much as a positive result does, and that measures get inherited rather than checked. When a finding is repeated for thirty years using the same analytic approach, the repetitions do not test the approach — they inherit it. That is a different failure from the ones usually discussed under the heading of replication, and it is harder to detect.

The gambler’s fallacy is a separate mistake

It is worth keeping these apart, since they are often mentioned together and point in opposite directions. The gambler’s fallacy expects independent events to compensate for each other — that a run of one outcome makes the other due. For genuinely independent trials, such as a fair coin, this is simply false, and no amount of previous history changes the next result.

The hot hand question is different because the trials may not be independent. A person shooting is a physical system with a state, and there is no principled reason why success should be independent of what just happened. Whether it is, and how much, is an empirical question, which is exactly why it required data and a correct statistic rather than an appeal to how randomness works.

Where this leaves streak perception

Two things can be true at once. People do over-detect patterns in sequences, expecting less clustering than chance actually produces, and this is well supported. And genuine dependence between consecutive attempts can also exist in some performances, at a magnitude far smaller than observers believe.

So the practical position is neither the folk belief nor its confident rejection. A run of successes is weak evidence of a small change in the underlying rate, drowned in noise, and a spectator’s strong impression that somebody cannot miss is not tracking that small effect. The belief is roughly the right shape and wildly the wrong size, which is a more accurate and much less quotable summary than either camp offered.

Reading claims about randomness after this

When somebody asserts that an apparent pattern is just randomness, the claim requires the same scrutiny as the assertion that it is real. What test was used, does that test have known properties in samples of this size, and has anybody checked it recently. Scepticism is not automatically the safe direction; it is a claim with its own statistical commitments.

That is the durable takeaway, and it applies well beyond sport. Declaring a pattern illusory feels rigorous and can be just as wrong as declaring it real, particularly when the declaration has been repeated so often that nobody rechecks the arithmetic underneath it.