The Hot Hand Had a Bug

Two claims, both from careful people, both about the same thing.

The first: when a shooter sinks four in a row and the arena starts chanting that he’s hot, the arena is fooling itself. A make tells you nothing about the next shot. Believing in the streak is a textbook error, the mind inventing a pattern where only chance is at work.

The second: that famous conclusion rests on a counting mistake, and once you correct it, the same numbers say the hot hand is real.

Both cannot be the right reading of the evidence. For three decades the first one won, and it won by a mile.

Start with its case, because it was strong. In 1985 three psychologists went hunting for the hot hand and came back empty. They had the Philadelphia 76ers’ shot records. They ran clean experiments with Cornell players calling their own odds. They asked the direct question: after a make, is the next shot more likely to fall? The answer kept coming back no. A hit after a hit landed about as often as a hit after a miss.

One of the three was Amos Tversky, who with Daniel Kahneman had already rebuilt how we think about human judgment. The finding fit their bigger theme. People see faces in clouds and momentum in noise, then bet real money on the story. The hot hand became one of the most cited results in the field, the go-to classroom proof of a brain fooled by randomness.

And it stayed there, taught and quoted, for thirty years.

The trouble hid in the arithmetic, and it is easy to miss. Flip a fair coin a few dozen times. Now go back, find every flip that landed right after a heads, and ask how often those flips are heads too. The obvious answer is half. The obvious answer is wrong. In a short sequence it comes out below half, closer to forty-odd percent than fifty.

Coins have no memory. Nothing mystical is happening. It falls out of how you chose which flips to count. In a limited run, the act of selecting the flips that come after a heads tilts the sample downward. Nobody feels the tilt. It sits in the math regardless.

Now put that next to the 1985 method. The researchers compared shooting after makes with shooting after misses, and treated an even, fifty-fifty split as the fingerprint of “no hot hand.” But for a truly streaky player, the honest no-effect baseline sits below fifty. So a player who genuinely ran hot would show up in their test looking merely ordinary. Ordinary was the signal. They read it as silence.

Two researchers, Joshua Miller and Adam Sanjurjo, spotted this and reran the old data with the correction applied. The hot hand didn’t just creep back into significance. It came back large, several percentage points, bigger than most fans would have dared to claim.

Before anyone spikes the ball, the crowd doesn’t get to be right about everything. People still badly overrate streaks. They pull starters, feed the hot man every possession, and remortgage a game plan on a run of three. The size of the real effect is modest, and the betting-market version of the hot hand is mostly the old illusion in a jersey. On that, the 1985 team were onto something true about us.

But notice what actually happened to their headline. It wasn’t a small footnote adjusted. The central result flipped. And the flaw that flipped it was not exotic. It was a subtle bias in a simple count, the kind a sharp undergraduate can follow once it’s pointed out.

So here is where I land, and it isn’t really about basketball. The hot hand exists. That part is now clear enough. The part I can’t get past is how a wrong answer lived for thirty years inside one of the most scrutinized findings in social science.

It survived, I think, partly because of who signed it. Tversky’s name made the result feel finished. A finished result gets cited, not checked. Every citation was another vote that someone else must have already done the auditing, so no one did. Prestige, which is supposed to mark reliability, worked here as a sedative.

Ask yourself how many other “well-established” numbers you carry around got their last real inspection decades ago, back when a name on the paper was enough to close the question. That is the uncomfortable part. Not that a screaming arena was fooled by a streak. That the experts who caught the arena were fooled by a smaller streak of their own, and it took a coin, thirty years, and two people willing to recount, before anyone looked again.