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.
Gilovich, Vallone, and Tversky analyzed thousands of actual shot sequences from professional basketball players and found no statistical evidence that players or teams go on genuine hot streaks beyond what pure chance would produce on its own. Despite the rigor and clarity of the finding, belief in the hot hand remained (and remains) close to universal across players, coaches, and fans — Kahneman notes this is one of the clearest examples in the book of a well-established statistical finding that completely fails to change deeply held intuitive belief, even among people whose profession depends on understanding the game.