In 1985, three researchers set out to kill a belief that nearly every basketball player, coach, and fan on earth holds: that a shooter who has just made a few shots in a row has a “hot hand,” and is more likely to make the next one. They pulled field goal data from the Philadelphia 76ers, free throw data from the Boston Celtics, and ran a controlled shooting experiment with twenty-six Cornell players who each took a hundred shots. The shots came back independent. A hit did not make the next hit any more likely. The belief, they concluded, was a cognitive illusion, and for thirty-three years the hot hand was the standard textbook proof that human beings cannot read randomness.
🧠 The Study That Killed the Streak
The paper was The Hot Hand in Basketball: On the Misperception of Random Sequences (Gilovich, Vallone & Tversky, 1985). One of those authors was Amos Tversky, half of the Tversky-and-Kahneman pair who built the modern study of human misjudgment. If Tversky said the hot hand was a myth, it was a myth. Kahneman later called the belief a “massive and widespread cognitive illusion.”
The players disagreed. They always disagreed. Coaches who watched shooters every night kept insisting the streak was real, and they were the ones being told they simply couldn’t count.
⚙️ How the Test Was Built, and Where the Trap Was
To test the hot hand you need one comparison: how often does a player score after making a few shots, versus after missing a few?
The standard method has three steps. Label every shot by what came before it, tagging it as either “after k hits” or “after k misses.” Throw out any shot whose previous few attempts fall in neither bucket. Then compute the shooting percentage inside each bucket and compare.
That looks airtight. The trouble lives in the word percentage.
Each player’s number is a ratio: makes divided by shots that qualified. The average of a bunch of ratios is not the same as the ratio of the totals. When the bottom of that fraction is small, the fraction swings wildly, and it does not swing evenly. It swings downward.
Here is the smallest possible version. Take a fair coin, flip it four times, and keep only the flips that came right after a head. Ask what fraction of those were heads. Do it for all sixteen possible sequences and average the results. You get 0.405, not 0.50. A perfectly fair coin, scored this way, looks like it is punishing streaks.
The reason is structural. In the six sequences where only one flip qualified, five of them score zero. They only had one qualifying flip because heads were scarce to begin with. When the lone head sits near the start, the flip right after it is forced to land inside a stretch of tails. Scarcity of qualifying shots and bad luck are the same fact, described twice, and those thin, forced zeros drag the average down.
Longer sequences shrink the bias. Longer streaks enlarge it. GVT’s players had a hundred shots each.
🤔 The Number That Reversed Everything
In 2018, two economists, Joshua Miller and Adam Sanjurjo, ran that bias through the math and found it worth −8 percentage points for a perfectly consistent 50% shooter taking 100 shots. I re-ran it in simulation: 46.0% after three hits, 54.0% after three misses. Minus 7.9 points, matching their figure.
So a shooter with no hot hand at all would still appear to shoot 46% after a streak and 54% after a cold patch. The measuring stick was tilted, and it was tilted against the exact thing it was built to measure.
GVT’s own Cornell data showed +4 percentage points. Correct for the eight-point tilt and you land at +12. Miller and Sanjurjo redid the original 1985 data with the correction: nineteen of twenty-five players now leaned toward the hot hand (p < .01), five of them significantly, with an average difference of thirteen percentage points (p < .01). For scale, the gap between a median and an elite three-point shooter in the 2015–16 NBA season was twelve points.
The honest ending is narrower than “the hot hand is real.” The effect is small, it shows up in some players and not others, and it survives mainly when shots repeat from the same spot: free throws, three-point contests. In live game action, with defenders adjusting and shooters moving, it stays hard to find. What is dead is the older, cleaner claim, that the 1985 study proved the streak was an illusion.
There is a stranger consequence. The same bias means that in short sequences, streaks genuinely do break more often than the underlying odds say they should. That is precisely what a gambler believes when he thinks red is due. His intuition was not pure superstition. It got drawn, unfairly, from a finite sample.
🔗 Why This One Follows You Around
Short sequences manufacture streaks, and then we read meaning into them. Watch a few sessions with an AI companion land well and it starts to feel like it is “in form” tonight. The same thin sample, doing the same kind of work. Build a product that treats a user’s run of good reactions as a signal, boosting the tone and queueing the next thing, and you are pulling a lever attached to a biased meter. The first question worth asking is how long the sequence actually was.
It travels further. A fund manager with three good years and a hot sector: skill, or a hundred-shot sample? The methodology cuts both ways, which is the harder part. Don’t crown a streak as talent, and don’t wave it off as noise. Fix the bias first, then look at the effect size and how much it varies from person to person.
🎲 The Coin You Can Try Tonight
Flip a fair coin four times. Record only the flips that came right after a head, and ask how often they were heads. Do it a few dozen rounds and average. You will land near 0.40. Your coin is fair. Your ruler is not.