Plain-language answer
Truly random sequences are lumpier than people expect. Flip a fair coin 100 times and you should expect to see a run of 5 or more heads (or tails) in a row somewhere in the sequence — that’s not a sign anything unusual is happening, it’s what randomness typically looks like. Human intuition, asked to invent a “random-looking” sequence, systematically under-produces long runs and over-produces alternation, because alternation looks more “fair” to us even though it is actually less representative of real randomness.
Why it matters
This gap between how randomness actually behaves and how people imagine it behaving cuts both ways in coincidence stories. Sometimes it makes a genuinely random cluster (a run of good luck, a series of similar events close together in time) look like it needs a causal explanation, when clustering is exactly what unremarkable randomness produces on a long enough timeline. Other times, it makes a real, non-random pattern (an actual streak with a cause) look implausible, because it violates the “smoother,” more alternating pattern people expect from chance.
Worked example: the hot hand controversy
The clearest documented case is basketball’s “hot hand.” A widely cited 1985 study examined shooting records and concluded that players’ hit-and-miss sequences looked statistically indistinguishable from independent coin flips — no detectable tendency for a make to be followed by another make more often than chance would predict. The authors concluded that the common belief in streak-shooting (“hot hands”) was a cognitive illusion: people were seeing meaningful clusters in a process that was actually closer to random.(Gilovich, Vallone & Tversky, 1985)
That conclusion stood as the standard account for over three decades — until a 2018 econometric reanalysis identified a subtle selection bias in the original method itself. Measuring “the probability of a hit after a streak of hits” from a finite sequence systematically underestimates the true underlying probability, because in short random sequences, the positions right after a hit streak are slightly less likely to be followed by another hit just from how sampling without replacement works — a bias that has nothing to do with basketball. Correcting for it reversed the finding: the original data, reanalyzed properly, showed evidence for a real, modest hot hand after all.(Miller & Sanjurjo, 2018)
Common misconception
“Someone showed the hot hand is a myth, so all streak-perception is illusion” overstates a genuinely contested case as settled. The accurate summary is that a famous demonstration of a cognitive bias about randomness was later shown to contain a different statistical error, and that correcting it partly restored the phenomenon it was meant to debunk. Evaluating this history carefully — not repeating either the original finding or its reversal as unquestioned fact — is itself a case study in how easy it is to misjudge streaks and clusters, including in the professional research literature.
Limits and open questions
The 2018 reanalysis addresses the specific statistical method used in the 1985 study; it does not establish the size or practical significance of any real hot-hand effect in basketball, nor does it settle every subsequent methodological debate on the topic. The safest general lesson is not “hot hands are real” or “hot hands are fake,” but that judging whether a run in a short, finite sequence is unusual requires care that both casual intuition and, on this occasion, expert statistical practice got wrong on a first pass.
Related
- The law of large numbers explains why short-run streaks are not corrected by subsequent trials, only diluted by them over a much longer run.
- Multiple opportunities and selection effects covers a related way that noticing “the longest streak in the data” after the fact inflates how surprising it looks.
Key takeaways
- Genuinely random sequences contain more, and longer, streaks and clusters than intuition expects — clustering is not, by itself, evidence of a non-random cause.
- The most famous study concluding that streak-belief was purely illusory has itself been shown to rest on a subtle statistical bias, and a corrected reanalysis found evidence for a real (if modest) effect.
- Treat both “streaks always need an explanation” and “streaks never need an explanation” as oversimplifications; the honest position on any specific case requires checking the actual sequence and method involved.