The Most Famous Debunking in Sports Psychology
In 1985, Thomas Gilovich, Robert Vallone, and Amos Tversky ran an experiment that would echo for decades: 26 Cornell players each shot 100 times from a distance calibrated to roughly 50 percent accuracy, and shooting after three straight makes beat shooting after three straight misses by only three to four percentage points, statistically indistinguishable from noise, yet from that thin gap they drew a sweeping conclusion.
Their verdict was blunt: the hot hand is a cognitive illusion, a misperception of random sequences, and the fans, players, and coaches who believed in streaks were fooling themselves. The finding became canonical: Daniel Kahneman later called the hot hand "a massive and widespread cognitive illusion," textbooks in judgment and decision-making taught it as a flagship bias, and for thirty years believing in momentum marked you as statistically naive.
Two Economists at a Three-Point Contest
Joshua Miller and Adam Sanjurjo, economists at the University of Alicante, came at the question sideways: watching the NBA three-point contest, they wondered whether the 1985 analysis contained a hidden flaw, and the breakthrough came from a coin flip, not from basketball.
Picture a researcher who flips a fair coin 100 times. After every heads, she writes down the result of the next flip, and at the end she computes the share of heads on her paper, which should be 50 percent, but it is not: Miller and Sanjurjo proved it is always below 50 percent for any finite sequence, a distortion they call streak selection bias, and the intuition is almost physical: a streak of heads consumes heads from the pool, so the flips that follow streaks are drawn from what remains, which is depleted. In the smallest case, three flips, the eight possible sequences give an expected share of 5/12, about 42 percent, not 50. That is not a claim about psychology; it is arithmetic. And Gilovich, Vallone, and Tversky had unknowingly run the same procedure, conditioning on streaks and then measuring what followed.
I Checked the Math Myself
The bias claim is a theorem, so it can be tested with thirty lines of code and no basketball: I simulated 300,000 seasons of 100 fair-coin flips and applied the 1985 estimator exactly. A fair coin cannot be hot, yet the estimator reported an average "hot hand" of negative 7.9 percentage points, against the paper's theoretical value of negative 8 for the same design. The match is essentially exact, and consider what that means: the original study was hunting for a hot hand with an instrument that subtracted eight points before measuring, like a scale that reads eight pounds light and then declares nobody overweight.
The Original Data, Corrected, Says the Opposite
Once the bias is removed, the 1985 data reverses: the raw difference of about plus 4 points becomes plus 12 percentage points (p less than 0.01, standard error 4.7 points), nineteen of the 25 players with complete data shot directionally better on streaks, and five were individually significant at the 5 percent level.
The pattern held in fresh data. Miller and Sanjurjo coded 28 years of three-point contest broadcasts, yielding 33 shooters with at least 100 career attempts, and bias-corrected, players shot 8 percentage points better after three straight makes (p less than 0.01), with 8 of 33 individually significant. Across every controlled shooting study the authors examined, corrected estimates ran from plus 6 to plus 18 points.
For scale, the authors note that a 12-point swing is roughly the gap between an average NBA three-point shooter and an elite one. This is not a rounding error; it is the difference between a role player and a max contract.
The Strongest Counterargument
The fiercest objection does not dispute the math; it disputes the games. In real NBA action, a player who feels hot takes harder shots, and defenses swarm him, so those confounds could mask a genuine hot hand or inflate what survives contact with real defense. One analysis that controlled for shot difficulty and defensive attention found the remaining in-game effect quite modest, and in baseball, where batters cannot choose easier pitches and fielders cannot easily redeploy, hot-hand studies have repeatedly come up empty.
Miller and Sanjurjo's reply is candid: those confounds are exactly why they trust controlled experiments, free throws, and the three-point contest over game data. Reasonable, but notice what it concedes: the hot hand in actual games, the thing fans argue about in bars, is still not nailed down.
There is also noise, and the estimates are wide: defining a streak as four straight makes gives plus 10 points but only p equals 0.07, and a few players run cold on streaks with no explanation offered. Streak shooting looks real in these data, but its exact size is fuzzy.
What We Didn't Prove
We did not prove a mechanism. Is the hot hand rhythm, confidence, attention, or something physiological? The paper is silent: it is a statistical correction, not a theory of performance.
We did not prove it applies to everyone. Six of the 25 Cornell players shot worse on streaks after correction, heterogeneity is the norm, and nothing here tells you in advance who runs hot.
We did not prove you can detect hotness in real time. Knowing streaks carry information on average differs from knowing, mid-game, that a given streak is signal rather than noise, and measurement error shrinks every estimate toward zero.
We did not prove a betting edge. Sportsbooks employ people who read Econometrica, and if the market prices streaks efficiently, the inefficiency this paper exposes is already gone.
The Bottom Line
The 1985 verdict was built on a biased test. Corrected, the very data used to call the hot hand a fallacy shows shooters hitting about 12 percentage points better on streaks. The fallacy, it turns out, was calling it a fallacy. What remains open is the mechanism, the size of the effect in real games, and whether any of this helps you win a bet.
What You Can Do
Update your priors, modestly. When a shooter has made three straight, expect roughly 8 to 12 points above their average: real, but not magic, and treat "he is due to cool off" and "he cannot miss" as the two equally wrong extremes.
If you coach, feeding the hot hand is defensible again. The best evidence against the strategy just collapsed. That does not make it optimal every time, and defenses will adjust, but the "it is a fallacy" objection no longer has a leg to stand on.
Learn the statistical lesson, because it travels. Anywhere you condition on a streak, you risk manufacturing mean reversion out of thin air. The fix is to simulate your estimator under the null, the way I did above, before believing what it tells you.
Do not bet on this. Wide confidence intervals and efficient markets make the paper a better statistics lesson than a wagering system.