January 22, 2015. Klay Thompson, in the third quarter against the Sacramento Kings, scores 37 points in twelve minutes. He makes nine consecutive shots, hits thirteen total in the quarter on thirteen attempts, and finishes the period with the most points any player has ever scored in a single twelve-minute period of NBA basketball. The Oracle Arena crowd is on its feet. The Warriors’ bench is on its feet. Steve Kerr, watching from the sideline, is doing the universal coaching gesture for “this is real, keep feeding him.” For the next decade, the third quarter against Sacramento becomes the most-cited piece of evidence in arguments for the existence of the hot hand. The math, sitting unmentioned in academic journals and a handful of analytics blogs, says something more complicated. The math also says, since 2014, that the academic consensus had been wrong about the hot hand for thirty years, and that Thompson’s twelve minutes were, in fact, statistically distinguishable from pure chance.
The hot-hand fallacy is one of the most-studied and most-rewritten questions in sports analytics. From the original Gilovich-Vallone-Tversky paper in 1985, which famously claimed that there was no statistical evidence for the hot hand in basketball shooting, through a decades-long period in which “the hot hand is a fallacy” became received wisdom, to the 2014-2016 papers by Joshua Miller and Adam Sanjurjo that identified a systematic error in the original analysis and showed that the hot hand does, in fact, exist — the academic and analytical conversation has been one of the cleaner case studies in how a high-status finding can dominate a field for decades, then quietly invert when the math is redone correctly. The reversal has not, in 2026, fully reached the public conversation. Most sports coverage still treats “hot hand” as a popular delusion that smart analytical writing should debunk. The current academic literature suggests the popular intuition was largely correct, and the analytical writing has been catching up unevenly.
I have been writing about basketball analytics since 2014, which means I have, professionally, lived through the entire arc of this argument, and the question I find myself most often re-explaining to readers is the one this article is about. The hot-hand fallacy — what the original research claimed, what the corrected research shows, where the question still has uncertainty, and how to write about streaks without falling into either of the trap interpretations, is the subject of this article.
The origin: where the hot-hand fallacy came from
The original paper that became the foundational text for “the hot hand is a fallacy” was published in 1985 by Thomas Gilovich, Robert Vallone, and Amos Tversky (yes, that Tversky — the Nobel laureate behavioral economist) in the journal Cognitive Psychology. The paper, titled “The Hot Hand in Basketball: On the Misperception of Random Sequences,” analyzed shooting data from the 1980-81 Philadelphia 76ers, conducted shooting experiments with the Cornell University men’s and women’s basketball teams, and concluded that the perception of “streakiness” in shooting was a cognitive illusion. The actual sequences of made and missed shots, the authors argued, were not significantly different from random.
The paper had outsized influence. Tversky’s stature in behavioral economics gave it intellectual weight. The conclusion fit nicely into the broader popular-science narrative about cognitive biases. Sports analytics writing throughout the 2000s and early 2010s frequently cited the paper as definitive: people think they see hot hands, but the math proves they don’t. Daniel Kahneman’s book Thinking, Fast and Slow (2011) treated the hot-hand fallacy as one of the canonical examples of pattern-imposition bias.
The reversal began with a 2015 working paper (later published in 2018) by Joshua Miller and Adam Sanjurjo, two economists working on probability theory. Miller and Sanjurjo identified a subtle but important statistical bias in the original Gilovich analysis: when you condition on a player having just made a shot and then look at their next shot, the probability calculation has a small but systematic downward bias due to the way the conditional sequences are constructed. The bias, when corrected for, completely changed the empirical conclusion. The shooting data the original authors had analyzed actually showed evidence of streakiness — modest but real — once the correct probability framework was applied.
The Miller-Sanjurjo correction has been replicated and extended by multiple subsequent researchers. The modern academic consensus, as of 2026, is that the hot hand exists as a measurable phenomenon in basketball shooting. The original 1985 paper was, on the empirical question, wrong. The popular intuition was, on the empirical question, largely right.
How hot-hand math works: in plain language
The basic question is straightforward. After a player makes a shot, is their next shot more likely to go in than their baseline rate would suggest? After a player misses, is their next shot more likely to miss? If the answer to both is yes, there is evidence for a hot hand. If both probabilities are statistically indistinguishable from the baseline rate, there is no evidence.
The original Gilovich analysis took a player’s full sequence of shots, identified all the post-make and post-miss sub-sequences, and calculated the make rates in each. The numbers came back showing post-make and post-miss rates were nearly identical to the overall rate. Conclusion: no hot hand.
The Miller-Sanjurjo correction involved noticing that when you take a fixed sequence of made and missed shots and conditioned on “this shot was a make,” you are systematically more likely to be looking at sequences where the previous run included some makes — which produces a small downward bias in the apparent post-make rate. The bias is subtle in casual analysis and shows up clearly only when you simulate the right null hypothesis. Once corrected for, the empirical data from the same Cornell experiments and Philadelphia 76ers games showed measurable positive autocorrelation in shooting sequences. The effect size is not huge — usually 3-5 percentage points of lift after a make — but it is real and statistically significant.
The deeper version of the question involves not just consecutive shots but longer streaks. Does a player who has made his last four shots have an elevated probability of making his fifth? The data, with the Miller-Sanjurjo correction applied, supports a meaningful effect: yes, but smaller than the popular perception. After a long streak of makes, the player’s expected next-shot make rate is probably 4-6 percentage points above his baseline. After a long streak of misses, it’s probably 3-5 points below. These are real effects, not random noise.
The critical component: bias correction in conditional probability
The single most important technical insight in the modern hot-hand literature is the Miller-Sanjurjo bias correction. The bias is subtle enough that it took thirty years of academic literature to identify, and it requires careful probability work to fully grasp. The intuition: when you conditionally sample from a sequence of binary outcomes, the probability of “what comes next” is not the same as the unconditional rate, even in fully random sequences.
The illustration that has become standard in the literature uses the example of a coin flip. Take a fair coin flipped 100 times. Identify all the post-heads outcomes and calculate their rate. Naïvely, you’d expect 50%. But when you condition on “this flip was heads” and look at the next flip, you’re slightly more likely to be looking at a flip in the middle of a heads-run, where the random structure of the sequence has a small downward bias for the next flip. The expected post-heads rate, in a fair coin flipped 100 times, is actually about 48.5% — not 50%. The bias is small but compounds in shooting data, where the effect of interest is also small.
Hot-hand theory vs the alternative interpretations: a comparison
The major positions in the modern hot-hand debate:
| Position | What it claims | Status in 2026 literature |
|---|---|---|
| Original “no hot hand” (Gilovich et al. 1985) | Streaks in shooting are random | Effectively refuted by Miller-Sanjurjo correction |
| Corrected “hot hand exists” (Miller-Sanjurjo 2018+) | Small but real positive autocorrelation in shooting | Current academic consensus |
| Strong-form “you can ride the hot hand” (popular) | Hot hands are large effects you can bet on | Partially supported but effect sizes smaller than popular perception |
| Defense-adjusted “no hot hand” | Apparent streaks reflect opposing defense’s adjustments, not shooter skill | Plausible secondary effect; not the full explanation |
| Shot-quality “endogenous hot hand” | Players take harder shots after makes, easier after misses | Real effect; partial confound on raw autocorrelation analysis |
The careful position is some combination of the corrected mainstream view and the defense/shot-quality caveats. The hot hand exists. The effect is smaller than popular perception suggests. It’s also partially confounded by player behavior (taking harder shots after makes) and opposing defense (closing harder after multiple makes). The net effect, after controlling for these confounds, is still positive — but the size of the corrected effect is closer to 2-4 percentage points than the 10-15 points popular intuition might suggest.
What the data needs: inputs
Hot-hand analysis requires shot-by-shot data with sequence information, shot location and difficulty data, and defensive context. The minimum input is the per-shot sequence for each player, which Basketball-Reference and NBA.com/stats provide for the full play-by-play era.
The deeper analysis requires shot-quality measurements — was the shot taken from an easier or harder location than the player’s average? This data, available through NBA tracking and PFF Sports’ college basketball coverage, lets analysts distinguish “the player made harder shots because he was hot” from “the player made easier shots because the defense relaxed.”
The most sophisticated work also incorporates defender data: was the player closely defended, lightly defended, or open? The post-make-defense interaction is where some of the most interesting recent hot-hand work has been done. The data is mostly inside Second Spectrum’s NBA tracking system; the public versions are limited.
Building the analysis: a working framework
The practical workflow for hot-hand-related writing:
- Be cautious about single-game extrapolation. A player going 9-of-12 in a quarter is, structurally, consistent with hot hand evidence but also consistent with normal variance for an elite shooter.
- Look at career-long streak data. Some players show measurable hot-hand effects in their career data; others don’t. The variation across players is itself an analytical finding.
- Account for shot-quality drift. A player who shoots harder shots when hot — Klay Thompson is the canonical case — is generating real streak performance, but the apparent shooting-rate elevation is partially because the shot diet shifts.
- Distinguish hot-hand from hot-team. A team that’s collectively shooting well is, in part, a function of the shot diet the offense is generating. Individual hot-hand effects are smaller than the team-level shooting variance.
- Be precise about effect size. The honest analytical claim is “the hot hand exists, but the effect size is roughly 2-4 percentage points after correction for confounds.” That’s a useful claim. “The hot hand is huge” or “the hot hand is a myth” are both inaccurate.
Where this gets weird: common mistakes
The reversal-reflex. Some analytics writers, having absorbed the original “hot hand is a fallacy” frame, are slow to update on the Miller-Sanjurjo correction. The “popular delusion that smart analysts debunk” framing is still occasionally circulated as if it were current research. The current research says the opposite.
The over-correction. Some writing has swung too far the other way: “the hot hand is real, so we should trust streaks.” The effect sizes are modest. A player on a hot streak is, in expectation, slightly more likely to make their next shot than baseline. They are not certain to make it. The cognitive bias that the 1985 paper was trying to address — that people overestimate how much streaks predict future outcomes — is still real, even after we accept that some autocorrelation exists.
Single-streak narrative inflation. A player making nine straight shots becomes a 1000-word column. The math says one streak is, well, one streak. Career-long streak data is much more informative.
Conflating shooting hot hand with other forms. The Miller-Sanjurjo analysis is about shooting specifically. The same correction applied to other activities (free throws, three-point contests, basketball-related events) produces somewhat different results. Generalizing “hot hands exist” to all forms of athletic performance is overreach.
The defense interaction. A shooter who has made his last three shots is, by 2026, much more likely to face an aggressive double-team or face-guard on the fourth attempt. The post-make defense effect is real and partially offsets the hot-hand effect. Analyses that don’t control for this can over- or underestimate.
When hot-hand thinking shines: use cases
End-of-game shot selection. A team with a player who has been shooting well in the last few minutes is justified in feeding them the ball. The hot-hand effect, in the context of a closing run, is real enough to influence decision-making. Not blindly — the player should still take reasonable shots — but enough to tilt borderline decisions toward the streaking player.
Lineup construction. A coach who has identified that a particular player runs hot for extended stretches can build rotation patterns around catching those stretches. The analytical work on which players show the strongest career hot-hand patterns is, in my opinion, the most useful applied output of the corrected literature.
Player evaluation. A player whose efficiency is partially driven by his hot-hand profile (long streaks with elevated rates) is a different asset than one whose efficiency is uniform across all shooting situations. The two profiles have different playoff translation properties and different team-fit implications.
Betting markets. The corrected hot-hand math has produced small but measurable edges in in-game prop betting markets, particularly for player-prop totals where the prior shots’ results aren’t fully priced into the line.
A working example: Klay Thompson’s 2014-15 season
Klay Thompson’s 2014-15 NBA season — the year of the 37-point quarter, plus several other extended hot stretches — is one of the cleanest hot-hand case studies in the modern era. Thompson’s career-long shooting data, run through the Miller-Sanjurjo-corrected framework, shows a measurable positive autocorrelation of approximately 4-6 percentage points after consecutive makes. The effect is larger than the league average but not historically anomalous.
What made Thompson’s case study interesting was the shot-quality drift. When Thompson got hot, his shot diet visibly shifted — more pull-up threes, more deep attempts, fewer easy catch-and-shoot looks. The naïve hot-hand analysis would have reported his shooting rate elevation as larger than it was; the shot-quality-adjusted analysis showed a smaller but real effect. The “hot hand” was real. The size of the effect, properly measured, was about half of what the raw shooting splits suggested.
The 37-point quarter against Sacramento was extreme even by Thompson’s standards. By every probability model, the run was rare enough to be considered an outlier. But it was consistent with a player who had measurable hot-hand performance plus elite baseline shooting ability plus an unusually permissive defensive matchup. The Sacramento defense that night was, by Synergy charting, the second-most-permissive matchup Thompson had faced that season. The streak was real. The streak also benefited from the right opponent on the right night. Both are true.
The limits: what hot-hand analysis cannot tell you
Hot-hand analysis cannot tell you which specific shot will go in. The math gives probability estimates. Individual outcomes are dominated by variance.
Hot-hand analysis cannot fully separate shooter ability from coaching design. A team whose offense generates higher-quality shots when momentum is building will appear to have stronger hot-hand effects than they actually have at the player level. The systems-vs-skill confound is real.
Hot-hand analysis cannot resolve the cognitive question. Even with the Miller-Sanjurjo correction, the gap between “the hot hand is real” and “the popular perception of the hot hand is calibrated to the actual effect size” is large. People still overestimate how much a streak predicts the next shot. The bias that the 1985 paper identified is real even though their specific empirical analysis was wrong.
Hot-hand analysis cannot replace film study. A shooter who is rhythmically synced into the game flow looks different on film than one who is forcing shots. The numbers can show the streak; the film tells you whether the shooter’s mechanics, decision-making, and rhythm are actually elevated or whether the streak is variance riding on baseline ability.
One additional limit: the conversation about hot hands has been so dominated, for thirty years, by the original “fallacy” framing that the corrected literature is taking time to penetrate public coverage. A piece written in 2026 that updates the reader on the current state of the research — rather than recycling the older framing — is doing useful work. Most pieces still don’t.
Frequently asked questions
Is the hot hand real?
Yes, by the current academic literature. The Miller-Sanjurjo bias correction, applied to the original Gilovich-Vallone-Tversky data and to subsequent shooting datasets, finds measurable positive autocorrelation in shooting performance after made shots. The effect size is small — usually 2-4 percentage points of lift, sometimes larger for specific players — but it is real and statistically significant.
How big is the hot-hand effect?
After correction for the statistical bias and for confounds like shot-quality drift and defense response, the typical effect size is in the 2-4 percentage point range. Some players show larger effects (5-7 points) and some show effectively zero. The popular perception, which often treats hot hands as 10-15 point shifts, is overstated relative to the data.
Should I bet on hot streaks?
Cautiously and at the margins. The corrected hot-hand math suggests that in-game prop betting markets sometimes mis-price the elevated probability of a continued hot stretch. The edge is small. The variance is large. The honest answer is that there’s a real but modest pricing inefficiency for the carefully calibrated bettor, and an easy way to lose money for everyone else.
What about Klay Thompson’s 37-point quarter?
It was extreme even by hot-hand standards but consistent with a high-variance combination of elite baseline shooting, measurable hot-hand effects, and a favorable defensive matchup. The math doesn’t say the streak was certain or even likely. The math says it was substantially more probable than pure random chance would suggest.
Sources and further reading
- Miller & Sanjurjo 2014/2018 — “Surprised by the Hot Hand Fallacy?” — the foundational corrected analysis that restored the hot hand to the empirical literature.
- Gilovich, Vallone & Tversky 1985 — original paper — the canonical “no hot hand” study, now considered superseded by the corrected work.
- FiveThirtyEight coverage of the hot-hand reversal — accessible writing on the academic shift.
- Cleaning the Glass — Ben Falk’s site with related shooting-variance analysis.
- Journal of the American Statistical Association archive — the technical journal where much of the formal hot-hand work has been published.
The Thompson quarter that opened this article — nine straight, thirteen-of-thirteen, the most points anyone has ever scored in twelve minutes — was the kind of moment that, for thirty years, the hot-hand fallacy literature would have explained away as cognitive illusion. The corrected literature, in 2026, says the moment was real. Streaks exist. The effect is smaller than fans believe and larger than zero. The careful analytical writing in the next decade is the work of holding both halves of that finding without flattening into either of the trap interpretations. For the broader frame on reading NBA shooting variance carefully, our guide to pace and space is the natural companion piece.
