In basketball, fans often say a player has a "hot hand" after a few good shots in a row. In 1985, a famous study said the hot hand was not real. For more than 30 years, many people believed this.

But in 2018, two researchers found a small math problem in the old study. When they fixed it, they found some evidence that the hot hand is real after all.

Basketball fans often talk about the "hot hand." A player who has made several shots in a row seems more likely to make the next one. In 1985, psychologists compared players' success rates right after a hit and right after a miss, and they found almost no difference.

So they decided the hot hand was an illusion. Textbooks used it as an example of how people misread random patterns. Then, in 2018, two economists found a hidden bias in the 1985 method.

Even with a fair coin, the method makes the success rate after a hit look lower than it really is. Experts still argue about how big the effect is. But after correcting for the bias, the economists found that players really did shoot better after a streak.

Flip a fair coin four times and note how often a head is followed by another head. Repeat this over many rounds and average the results, and you get about 40 percent, not the 50 percent most people expect. That small puzzle overturned one of psychology's favorite examples of human error.

In 1985, Gilovich, Vallone and Tversky analyzed professional game records and a shooting experiment with college players. They compared success rates just after hits and just after misses, found almost no difference, and concluded that the "hot hand" was an illusion, born of our habit of seeing meaning in random sequences. For decades, textbooks agreed. In 2018, the economists Joshua Miller and Adam Sanjurjo pointed out the coin problem.

The same selection bias affects any limited record of shots, so the method underestimates success after a hit. A measured difference of zero therefore hides a positive effect. When they corrected for the bias, a meaningful hot hand appeared in the original experimental data. Its size in real games is harder to pin down, because a player on a streak faces tighter defense and may attempt harder shots. A real effect also does not mean that fans judge it accurately.