The "hot hand" is the widespread belief that a basketball player who has made several shots in a row is more likely to make the next one — that success streaks reflect a real, temporary state of heightened performance. Rigorous statistical analysis of actual shot sequences has repeatedly failed to find evidence for this: streaks in real basketball data occur about as often as you'd expect from pure chance, no more and no less.
What makes this such a durable illusion is that truly random sequences don't look random to human intuition — they contain streaks and clusters as a basic mathematical property, but our pattern-detecting minds interpret those clusters as meaningful rather than as the ordinary texture of randomness. Believing in the hot hand isn't a sign of poor basketball knowledge; it's a sign of a very normal, very human misunderstanding of what randomness actually looks like when you're inside it.