The Hot Hand Fallacy: The "Cognitive Bias" That Two Statisticians Reversed In 2018

For thirty years, every behavioral economics textbook taught the “hot hand fallacy” --- basketball players never have streaky shooting, fans only think they do. In 2015, two statisticians found a subtle methodological bias in the original 1985 paper that, once corrected, reversed the finding. Players were right. Academics were wrong. A case study in how canonical “cognitive biases” can themselves be statistical illusions.

Walk into any sports bar in March and you will hear it. “He’s on fire.” “Feed the hot hand.” “Don’t take him out, he can’t miss.” Coaches design plays around it. Commentators spend halftimes diagramming it. Fans bet on it. The intuition that a basketball player can get into a rhythm where the shots just keep falling --- and that a smart team should ride that rhythm while it lasts --- is one of the most universally shared beliefs in sports.

For thirty years, academic behavioral economics told everyone that this universally shared belief was wrong. Not “partially wrong” or “overstated” but flatly, demonstrably, foundationally wrong. The hot hand was a textbook example --- literally, in every introductory behavioral economics textbook --- of the human mind’s tendency to hallucinate patterns in randomness. People saw streaks because people are bad at randomness. The streaks were not really there. The data proved it. The proof was so clean that Daniel Kahneman, in Thinking, Fast and Slow, called the hot hand “a massive and widespread cognitive illusion.”

Then, in 2015, two relatively unknown researchers --- one at Bocconi University in Milan, the other at the University of Alicante --- noticed something the original analysis had missed. The methodology had a subtle statistical bias built into it. The bias was small enough that nobody had caught it for three decades. It was large enough to flip the result.

After correcting for the bias, the original 1985 dataset --- the data that had launched the “hot hand fallacy” into the behavioral economics canon --- actually supported a real hot-hand effect. Players genuinely did get hot. The shooting streaks were not a hallucination. The fans, the coaches, and the players were right. The academic “debunking” of the hot hand was itself based on a statistical illusion.

This is the story of one of the cleanest reversals in the modern behavioral sciences. It is also a story about what calibration looks like when a discipline you trust for its rigor tells you, with great confidence, that ordinary people are systematically wrong about something --- and then turns out to have been wrong itself.

What Gilovich, Vallone & Tversky 1985 Actually Claimed

The foundational paper is Gilovich, T., Vallone, R., & Tversky, A. (1985), “The Hot Hand in Basketball: On the Misperception of Random Sequences,” Cognitive Psychology 17(3), 295—314 (DOI 10.1016/0010-0285(85)90010-6). It is one of the most-cited papers in behavioral economics, and for thirty years it was treated as a closed case.

The paper used three datasets. The first was a survey of basketball fans, who were asked whether they believed a player was more likely to make a shot after a recent streak of made shots than after a streak of misses. Roughly nine out of ten respondents said yes. The “hot hand belief” was, in other words, a real and pervasive belief among people who watched basketball.

The second dataset was field-shooting data from the Philadelphia 76ers’ 1980-81 home season. The authors went through the play-by-play of forty-eight home games and computed, for each player, the conditional probability of making a shot after one, two, or three consecutive makes, and the conditional probability after one, two, or three consecutive misses. If the hot hand existed --- if making a shot really did temporarily raise a player’s hit rate --- the probability after a streak of makes should be meaningfully higher than the probability after a streak of misses. The authors found no such difference. For most players, the conditional probabilities were essentially flat. For a handful of players, the post-make probability was actually slightly lower than the post-miss probability, the opposite of what the hot-hand belief predicts.

The third dataset was free-throw data from the Boston Celtics. Free throws are an unusually clean test because every shot is from the same distance, under the same conditions, with no defender. If a player got “hot,” the conditional probability of making free throw N+1 given a make on free throw N should exceed the unconditional rate. It did not, in the Celtics data. The conditional probabilities were statistically indistinguishable from the unconditional ones.

The fourth piece was a controlled experiment with Cornell varsity and intercollegiate players, shooting from a fixed distance under standardized conditions. Same result. The runs of made shots were no longer than would be expected from independent Bernoulli trials at the player’s baseline shooting percentage.

The authors’ conclusion was direct. The pattern of conditional probabilities was statistically consistent with each shot being an independent trial, and the runs of made shots were no longer than chance would produce. The shooting outcomes were “essentially independent.” The widespread belief in streak shooting was therefore “a cognitive illusion.” The mechanism, the authors suggested, was that people are bad at recognizing random sequences --- they expect more alternation than random sequences actually produce, so genuine random sequences look “streaky” to observers, and observers attribute the streakiness to a causal hot hand that does not exist.

The paper was clean. Multiple datasets, multiple methodologies, converging on a single conclusion. The data appeared to be unambiguous. And the conclusion lined up beautifully with the broader Kahneman-Tversky program of demonstrating that intuitive judgments of probability are systematically biased by failures of statistical reasoning. The “hot hand fallacy” became one of the load-bearing examples of that program.

How It Became Canonical Behavioral Economics

What happened next is what gives this reversal its weight. The Gilovich-Vallone-Tversky finding did not just enter the academic literature. It became, very quickly, one of the defining examples of behavioral economics in the public mind.

The popularization began almost immediately. The paper was cited approvingly in Tversky’s later work on representativeness. Stephen Jay Gould wrote about it for a general audience in his 1989 essay “The Streak of Streaks,” using the Gilovich finding to argue that Joe DiMaggio’s 56-game hitting streak was the only true anomaly in a baseball record otherwise consistent with randomness. Throughout the 1990s the finding appeared in every undergraduate textbook on judgment and decision-making, every popular treatment of behavioral economics, every survey article on heuristics and biases.

By the time Daniel Kahneman wrote Thinking, Fast and Slow in 2011, the hot hand fallacy was treated as a settled fact. Kahneman discussed it in the context of System 1’s tendency to manufacture narratives from random sequences. The relevant passage is direct: “The hot hand is entirely in the eye of the beholders, who are consistently too quick to perceive order and causality in randomness. The hot hand is a massive and widespread cognitive illusion.” For millions of readers, Thinking, Fast and Slow was their introduction to behavioral economics, and the hot hand was one of the first concrete examples they encountered.

The same framing showed up in Michael Lewis’s The Undoing Project, in Richard Thaler and Cass Sunstein’s Nudge, in Dan Ariely’s books, in Phil Rosenzweig’s The Halo Effect, in essentially every popular behavioral economics treatment of the past three decades. The hot hand was the canonical example of how observers see patterns in randomness that are not really there. Anyone who pushed back --- coaches, players, fans --- was treated as a case study in why intuition was unreliable.

The finding even seeped out of behavioral economics into adjacent fields. Financial commentators used it to argue against momentum trading. Sports analytics writers cited it to argue against “trusting the hot hand” in lineup decisions. Self-help authors used it to argue that streaks of success in business or relationships were also illusions. The cultural reach of the original 1985 paper, by the early 2010s, was enormous. It was almost certainly the most-cited example of a “cognitive bias” in the entire popular behavioral economics canon.

Which made what came next all the more striking.

Miller & Sanjurjo 2015/2018 --- Discovering The Methodological Bias

The reversal began with a working paper. In June 2015, Joshua Miller (then at Bocconi, now at the University of Melbourne) and Adam Sanjurjo (University of Alicante) posted a paper to SSRN titled “Surprised by the Gambler’s and Hot Hand Fallacies? A Truth in the Law of Small Numbers.” The paper went through several revisions, became an IGIER Working Paper, and was eventually published as Miller, J. B., & Sanjurjo, A. (2018), “Surprised by the Hot Hand Fallacy? A Truth in the Law of Small Numbers,” Econometrica 86(6), 2019—2047 (DOI 10.3982/ECTA14943).

The headline finding of the paper is a proof that the standard methodology for testing the hot-hand hypothesis --- the methodology Gilovich, Vallone, and Tversky used in 1985, and that essentially every replication of their work used in the three decades since --- contains a subtle but substantial bias against finding a hot hand. The bias is mathematical, not empirical. It is built into the procedure of conditioning on a streak in a finite sequence.

To see the bias, you have to think carefully about what the analysis actually does. The Gilovich-Vallone-Tversky procedure takes a finite sequence of shot outcomes, identifies the positions immediately following a streak of made shots, and computes the proportion of those positions that are themselves made shots. It then compares this conditional proportion to the unconditional shooting percentage. If the conditional proportion exceeds the unconditional rate, that is evidence for the hot hand. If it does not, that is evidence against.

The subtle problem is that for a finite sequence of independent random outcomes --- the kind of sequence the null hypothesis says shooting data is --- the expected value of that conditional proportion is not equal to the unconditional probability. It is systematically lower. The conditioning procedure introduces a downward bias. When you compute the conditional proportion in any finite Bernoulli sequence and average across all possible realizations, you get something below the underlying coin’s probability of heads.

The procedure is therefore biased against finding a hot hand even when one is present. A real, modest hot-hand effect can be hidden inside a conditional-proportion estimate that comes out near or below the unconditional rate. The 1985 finding of “essentially flat” conditional probabilities, in other words, was consistent both with the null (no hot hand) and with a non-trivial positive hot-hand effect being canceled by the bias.

The bias is named the “streak selection bias” in the Miller-Sanjurjo paper. It is small for very long sequences --- it asymptotically vanishes as sequence length goes to infinity --- but for the sequence lengths typical of basketball shooting data (a player taking ten or twenty or thirty shots in a game) it is meaningfully large. Large enough, as it turns out, to fully account for the difference between the 1985 finding and what the corrected analysis shows.

The paper went through extensive peer review. The acceptance at Econometrica --- one of the most rigorous journals in economics, with a famously high mathematical bar --- is itself a signal that the underlying mathematics was checked carefully. There has been no published refutation of the streak selection bias result. The mathematics is now considered settled.

The Math, Explained

The cleanest way to see the bias is the three-flip example that Miller and Sanjurjo use to introduce the problem.

Imagine you flip a fair coin three times. There are eight equally likely sequences of outcomes: HHH, HHT, HTH, HTT, THH, THT, TTH, TTT. Now, for each sequence, look at the flips that come immediately after a heads, and compute the proportion of those that are also heads. This is the analog of “the proportion of shots made immediately after a made shot.”

Walk through it sequence by sequence.

HHH: there are two flips after a heads (position 2, which is H; position 3, which is H). Proportion of those that are heads: 2/2 = 1.

HHT: there are two flips after a heads (position 2, H; position 3, T). Proportion: 1/2.

HTH: there is one flip after a heads (position 2, T; position 3 is also after a heads in the sense that it follows the H at position 1, but wait --- the convention here is to look at the flip immediately following an H, so we look at position 2, which is T. Position 3 follows a T, so it does not count). Proportion: 0/1.

HTT: one flip after a heads (position 2, T). Proportion: 0/1.

THH: one flip after a heads (position 3, H). Proportion: 1/1.

THT: one flip after a heads (position 3, T). Proportion: 0/1.

TTH: zero flips after a heads in the sequence (the H is at the end, with nothing after it). This sequence does not contribute to the average --- it is dropped, because there is no conditional proportion to compute.

TTT: zero flips after a heads. Also dropped.

Now average the proportions across the six sequences that contribute: (1 + 1/2 + 0 + 0 + 1 + 0) / 6 = 2.5 / 6 ≈ 0.417.

The expected proportion of heads-after-heads in a fair-coin three-flip sequence is roughly 0.417, not 0.5. The bias is about 8 percentage points downward in this small case.

This is deeply counterintuitive. The coin is fair. Each flip is independent. The probability of heads on any given flip, including any flip following a heads, is 0.5. And yet the average proportion of heads-after-heads across all possible sequences is below 0.5.

The reason is selection. The conditional-proportion measure samples flips non-uniformly. Sequences with more heads-after-heads (like HHH) contribute more total flips to the calculation, but they also contribute more heads to the numerator and more denominators. Sequences with isolated heads (like HTH) have a small denominator with a single non-heads in it. The arithmetic of averaging across sequences with different numerators and denominators produces the downward bias. The intuition that “each individual flip is 50/50, so the average must be 50/50” is exactly the kind of mistake that the formal mathematics catches.

The bias shrinks as sequence length grows, but for the kinds of sequence lengths used in the 1985 basketball analysis --- a single player’s shots in a single game, often fewer than twenty --- the bias is in the range of three to seven percentage points, which is enormous relative to any plausible real hot-hand effect.

That is the entire mathematical content of the Miller-Sanjurjo result. The Gilovich-Vallone-Tversky procedure compares the conditional proportion of made-after-made to the unconditional shooting rate. The conditional proportion is biased downward by several percentage points relative to the unconditional rate, even under the null of independent trials. So a “flat” finding in that comparison is not evidence of no hot hand. It is evidence of a hot hand whose magnitude is approximately equal to the bias --- which is to say, a real, meaningful hot hand.

What Happens When You Correct The Bias

Miller and Sanjurjo did not stop at the mathematical demonstration. They went back to the original Gilovich-Vallone-Tversky data --- the Cornell controlled-shooting study, where the raw shot-by-shot data was preserved --- and redid the analysis with the bias correction applied.

The corrected analysis showed a meaningful hot-hand effect. After three consecutive made shots, the shooters’ subsequent shooting percentage was elevated by approximately ten to thirteen percentage points relative to the unconditional rate, depending on the specification. This is an enormous effect in basketball terms. It is large enough that a coach would absolutely be right to design plays around a player who has just made three in a row. It is large enough that the players’ and fans’ intuitions about hot hands turn out to be substantially correct.

The reversal applied to the Cornell data specifically. The Philadelphia 76ers field-shooting data and the Boston Celtics free-throw data are noisier and have additional complications (shot selection, defensive adjustments, fatigue), but the core methodological point applies to those analyses as well: any test that uses the standard conditional-proportion approach is biased against finding a hot hand by an amount large enough to mask a real, meaningful effect.

The Miller-Sanjurjo work was not the only post-2014 evidence pointing toward a real hot-hand effect. The Sloan Sports Analytics paper by Bocskocsky, A., Ezekowitz, J., & Stein, C. (2014), “The Hot Hand: A New Approach to an Old ‘Fallacy’” (Sloan Sports Analytics Conference; also available as SSRN Heat Check: New Evidence on the Hot Hand in Basketball) used optical tracking data from over 83,000 NBA shots in the 2012-13 season and a sophisticated shot-difficulty model to control for the fact that “hot” players tend to take harder shots. After accounting for shot difficulty, the authors found a hot-hand effect on the order of 1.2 to 2.4 percentage points --- smaller than the corrected Cornell effect, but real, and consistent with what the bias-corrected analysis of older data would predict for a setting with more confounders.

Earlier statistical work had hinted at the issue without identifying the specific bias. Stone, D. F. (2012), “Measurement Error and the Hot Hand,” The American Statistician 66(1), 61—66 (DOI 10.1080/00031305.2012.676469) argued that ordinary measurement error in shooting performance could bias the standard tests against finding a hot hand. The Stone result was a piece of the eventual picture --- the standard tests were biased in the direction of accepting the null --- but it was Miller and Sanjurjo who identified the specific mathematical mechanism and proved its magnitude.

The cumulative picture from the post-2014 work is clean. The hot hand exists. It is modest in size, comparable to other shot-level effects that NBA coaches and analysts now routinely account for. The widely-held intuition that basketball players go through streaks of elevated and depressed shooting is broadly correct. The 1985 “fallacy” was itself a statistical illusion produced by an undetected bias in the analysis.

How The Field Has Responded

The academic response has been substantial but uneven. The Miller-Sanjurjo result is now accepted by essentially everyone in the statistical and sports-analytics communities. The Econometrica publication settled any remaining debate about the mathematics. The bias is taught in graduate econometrics courses, discussed in Andrew Gelman’s blog, and routinely cited by sports statisticians. Within the relevant technical communities, the hot-hand fallacy is now widely understood to have been a methodological artifact, and the underlying hot-hand effect is treated as a real, modest, well-documented phenomenon.

The behavioral economics community has been slower. Several of the original authors and key figures have engaged with the result, though not always cleanly. Thomas Gilovich, the lead author of the 1985 paper, has acknowledged the Miller-Sanjurjo finding but has continued to argue that the size of the corrected hot-hand effect is small enough that the original paper’s broader claim about misperception of randomness is largely intact. This position has been contested in turn by Miller and Sanjurjo, who note that the corrected effect in the Cornell data is large by basketball standards even if it is smaller than the maximal version of the hot-hand intuition.

Daniel Kahneman, to the best of the public record, has not issued a formal acknowledgment or retraction of the “massive and widespread cognitive illusion” framing in Thinking, Fast and Slow. The 2011 framing remains in subsequent printings of the book. This is a meaningful gap in the historical record. Kahneman has, on other occasions, been admirably willing to publicly revise his views in response to new evidence --- the most famous example is his 2017 acknowledgment that the social-priming literature he had endorsed earlier in the book was unreliable. The hot-hand reversal has not received a comparable public statement, and the absence is something readers of Thinking, Fast and Slow should know about when they encounter the hot-hand passage.

Popular treatments of the hot hand have updated slowly. Most behavioral economics textbooks published before 2018 still cite the original Gilovich-Vallone-Tversky finding as established fact. Textbooks revised since 2018 vary widely in how they handle the reversal --- some add a footnote, some rewrite the section, and many continue to teach the old version with no update. Popular science journalism is similarly uneven. Articles from major outlets including the Nautilus piece on the hot-hand reversal have done good work reporting on the Miller-Sanjurjo finding, but the basic pop-behavioral-economics framing of “the hot hand is a famous example of how people see patterns in randomness” is still encountered routinely in business books, TED talks, and corporate training programs.

This uneven update pattern matters for the broader replication-crisis story. The hot-hand reversal is unusual in that the underlying mathematics is unambiguous --- the bias is provably real, the correction is straightforward, and the reversed finding is well-supported by independent NBA-data analyses. There is no genuine ambiguity left to debate. And yet the canonical framing has not been fully corrected, particularly in the popular treatments that most non-specialists encounter. The half-life of an entrenched behavioral economics claim, even one that has been mathematically refuted, is much longer than the half-life of the underlying evidence.

What’s Honest To Say About Hot Hands Now

The intellectually honest summary, as of 2026, is roughly this.

NBA shooting data shows a real hot-hand effect, modest in size, on the order of one to several percentage points of shooting accuracy elevation following a sequence of recent makes. The exact magnitude depends on the sport, the shooting context (free throws versus field goals), the player population, and the specific statistical methodology, but a wide range of post-2014 studies using both reanalyses of older data and new optical-tracking datasets converge on the conclusion that the effect is real and non-trivial.

The original Gilovich-Vallone-Tversky 1985 finding of “essentially no hot hand” is no longer the consensus position. The conditional-proportion methodology used in that paper, and in essentially every direct replication of that paper for thirty years, contains a downward bias that masks a real underlying effect. The bias is a mathematical artifact of conditioning on streaks in finite sequences. It is real, it is provable, and it has been formally established in the peer-reviewed economics literature.

The “hot hand fallacy” as it appears in introductory behavioral economics textbooks --- the claim that the universal belief in streaks is a perceptual illusion, that the data clearly shows shots to be independent, and that the failure to recognize this is a paradigmatic example of human statistical irrationality --- is wrong. Not partially wrong. Wrong. The belief is not an illusion. The data did not show what it was claimed to show. The original analysis was contaminated by a bias the authors did not catch.

This does not mean every popular intuition about streaks is correct. The cleanest evidence is for basketball shooting; the evidence for streaks in other domains (stock-picker performance, gambling outcomes, sports betting picks, sales-call success) is much weaker and in many domains is actively contrary to a streak hypothesis. The right honest framing is not “intuition was right all along everywhere” but rather “in the specific domain where the canonical ‘fallacy’ was demonstrated, the demonstration was wrong and the intuition was substantially right.”

For coaches and players, the practical update is that designing plays around a player who has just made several shots is a reasonable strategy --- not because the effect is huge, but because it is real and non-trivial, and the bias against using it in 1985-2014 was based on a flawed analysis. For commentators and writers, the update is that “the hot hand is a famous example of a cognitive illusion” should be removed from the standard pop-behavioral-economics vocabulary. For executives and consultants encountering behavioral economics claims more generally, the update is bigger, and it is the topic of the next section.

What This Case Tells Us About “Established” Cognitive Biases

The hot-hand reversal is, in a sense, the most embarrassing single result in the modern history of behavioral economics. It is more embarrassing than the failed power-pose replications, more embarrassing than the ego-depletion meta-analysis, more embarrassing than the Bem precognition paper, because the failure mode is different and arguably more serious.

In the typical replication failure, an original finding is undermined by subsequent studies that fail to reproduce the effect. The original authors can plausibly argue that the failure is due to subtle differences in the replication procedure, that the underlying effect is real but contextually sensitive, that the field needs better measurement, and so on. The original finding is weakened, but the methodology that produced it can usually be defended as a legitimate first pass.

The hot-hand reversal is different. The original finding was not undermined by subsequent failed replications. It was undermined by the discovery that the original analysis had a subtle mathematical bias that the authors did not catch, that the peer reviewers did not catch, that thirty years of subsequent researchers replicating the methodology did not catch, and that the entire popularization of the result --- in Kahneman’s book, in countless textbooks, in every survey paper on cognitive biases --- depended on a piece of statistical reasoning that was simply wrong.

This is a failure of the analytical methodology itself, not of the empirical world. And it persisted for three decades, in plain sight, in one of the most-cited papers in the field, despite being technically straightforward to identify once you knew what to look for.

The lesson for anyone evaluating an “established” cognitive bias is not “the bias is probably also wrong” --- that would be overreaction. The lesson is that even mathematically clean-looking original analyses, in well-respected papers, by well-respected authors, can contain subtle methodological errors that go undetected for decades. The canonical status of a finding is not, by itself, evidence that the finding is true. It is evidence that the finding is widely cited.

For the broader replication-crisis literature, the hot-hand case adds a specific failure mode to the catalog. We already knew that low-powered original studies could fail to replicate. We already knew that p-hacking and garden-of-forking-paths analyses could produce false positives. We already knew that fraud and data manipulation occurred. The hot-hand case adds: even careful, well-intentioned analyses of real data, with no fraud and no p-hacking, can contain subtle statistical biases that systematically push the result in one direction. And those biases can be invisible to a generation of researchers because the field assumes the methodology is sound and never checks.

This means the calibration update from the hot-hand reversal is not just about the hot-hand specifically. It is about the entire class of behavioral economics findings that depend on a particular statistical methodology being unbiased. There are other places where similar issues might exist. The Miller-Sanjurjo paper itself suggests that some claims about the gambler’s fallacy, for analogous reasons, might also be partially methodological artifacts. The general principle is that whenever a behavioral economics finding rests on conditional probabilities computed in short sequences, the analyst should be alert to the possibility of bias.

What This Means For Strategists Evaluating Behavioral-Bias Claims

For CEOs, consultants, and operators who encounter behavioral economics claims as a source of supposedly evidence-backed guidance, the hot-hand reversal carries a specific calibration update. It is not “ignore behavioral economics.” It is more specific than that.

When someone presents a behavioral economics claim of the form “people systematically believe X, but the data shows X is wrong” --- the basic structure of essentially every “cognitive bias” finding --- ask the following question. Is the evidence for “X is wrong” coming from a controlled experiment that explicitly tests for the effect, or is it coming from a statistical analysis of observational data that infers the absence of an effect from a flat conditional probability or a non-significant difference?

The first kind of evidence (controlled experiment) is harder to refute. It still has its own failure modes --- the subject pool may not generalize, the effect size may not survive in real-world conditions, the demand characteristics of the experiment may produce the result --- but the basic logical structure of “we manipulated X and observed Y” is robust to most statistical-methodology errors.

The second kind of evidence (observational, inferring absence-of-effect from null statistics) is much more fragile. It depends on the assumption that the analysis would have detected the effect if it existed, which depends in turn on the statistical methodology being unbiased. The hot-hand case shows that this assumption can fail in subtle ways that nobody catches for decades.

In the strategic context, this maps onto a specific kind of business claim. When a consultant tells you that “studies show your customers are not actually motivated by price, despite what they say in surveys,” or that “studies show employees do not actually respond to monetary incentives once a baseline is met,” or that “studies show A/B test conversion lifts are usually illusory,” or any other claim of the form “the data shows the popular intuition is wrong” --- the question to ask is what kind of evidence underlies it. If it is observational, with the conclusion drawn from a null statistical finding, the hot-hand precedent says: be substantially less confident than the consultant sounds.

The other piece of the calibration update is about the people on the ground. The basketball players and coaches and fans who insisted that the hot hand was real were right, and the academic establishment that told them they were hallucinating was wrong. This is not a generic argument for “always trust common sense over experts.” It is a specific argument that when the people closest to a phenomenon, with the strongest incentives to track it accurately, insist that something is real --- and the academic finding against it depends on a particular statistical methodology --- the academic finding deserves more scrutiny than its canonical status would suggest.

The honest position for an executive evaluating behavioral economics inputs is that behavioral economics is a real field with real findings, that some of those findings are robust and decision-useful, that others have not survived scrutiny, and that the canonical status of a finding within the field is a much weaker indicator of its truth than most readers of popular behavioral-economics books would assume. The hot hand was canonical for thirty years, and it was wrong.

That is the operating principle. Trust the methodology, not the citation count. And when the methodology depends on assumptions that have not been independently verified --- as the conditional-probability methodology in the original Gilovich-Vallone-Tversky paper did, for thirty years --- discount accordingly.

Sources

• Gilovich, T., Vallone, R., & Tversky, A. (1985). The hot hand in basketball: On the misperception of random sequences. Cognitive Psychology, 17(3), 295—314. DOI: 10.1016/0010-0285(85)90010-6.
• Miller, J. B., & Sanjurjo, A. (2018). Surprised by the hot hand fallacy? A truth in the law of small numbers. Econometrica, 86(6), 2019—2047. DOI: 10.3982/ECTA14943. arXiv:1902.01265.
• Miller, J. B., & Sanjurjo, A. (2014, revised 2015). Surprised by the gambler’s and hot hand fallacies? A truth in the law of small numbers. IGIER Working Paper No. 552 (earlier version), SSRN abstract 2627354.
• Bocskocsky, A., Ezekowitz, J., & Stein, C. (2014). The hot hand: A new approach to an old “fallacy.” 8th annual MIT Sloan Sports Analytics Conference. Sloan Sports Analytics paper. Also available as Bocskocsky, Ezekowitz & Stein, “Heat Check: New Evidence on the Hot Hand in Basketball,” SSRN abstract 2481494.
• Stone, D. F. (2012). Measurement error and the hot hand. The American Statistician, 66(1), 61—66. DOI: 10.1080/00031305.2012.676469.
• Kahneman, D. (2011). Thinking, Fast and Slow. Farrar, Straus and Giroux.
• Gould, S. J. (1989). The streak of streaks. The New York Review of Books, August 18 issue.
• Nautilus (2017). The “hot hand” is not a myth. nautil.us/the-hot-hand-is-not-a-myth-643539.
• Page, L. (2024). The hot hand fallacy. Optimally Irrational. optimallyirrational.com/p/the-hot-hand-fallacy.

Related

• Replication Crisis Hub --- the broader project this article is part of.
• The Availability Heuristic --- a Tversky-Kahneman finding that did hold up under replication, as a counterpoint to this one.
• Confirmation Bias --- another canonical cognitive bias whose evidentiary status deserves scrutiny.
• The Dunning-Kruger Effect --- another case where a widely-cited “bias” turned out to be a statistical artifact.
• The Endowment Effect --- a behavioral economics finding that is real but more conditional than the popular treatments imply.

Frequently Asked Questions

Is the gambler’s fallacy also a methodological artifact?

The gambler’s fallacy --- the belief that after a streak of heads, tails is “due” --- is a related but distinct case. The Miller-Sanjurjo paper discusses how some demonstrations of gambler’s-fallacy reasoning may be partially affected by analogous selection biases in finite sequences, but the core phenomenon (people expecting reversals after streaks) does appear to be real in laboratory contexts. The cleanest summary is that for purely random sequences like fair coin flips, the gambler’s fallacy is genuinely a mistake --- but the basketball shooting case, where the underlying generating process is not random at all but is a human performance with real autocorrelation, is fundamentally different. The hot-hand reversal does not vindicate gambling-streak intuitions in casino games.

Should I bet on streaks in sports?

The hot-hand effect in NBA shooting is real but modest --- on the order of one to several percentage points of shooting accuracy elevation. This is large enough for coaches to factor into play design but is generally smaller than the bookmaker’s edge in sports betting. The hot-hand reversal does not provide a path to profitable sports betting on streaks. Betting markets have generally already priced in the relevant effects, and the modest size of the corrected hot-hand finding does not generate the kind of mispricing that would make a profitable strategy.

Did Kahneman publicly acknowledge the reversal?

To the best of the public record, no. Kahneman has not issued a formal statement or correction regarding the “massive and widespread cognitive illusion” framing in Thinking, Fast and Slow. Subsequent printings of the book retain the original passage. This is in contrast to his 2017 public acknowledgment that the social-priming literature he had endorsed earlier in the book was unreliable. The absence of a comparable hot-hand acknowledgment is itself meaningful information about how reliably the popular behavioral-economics literature updates in response to refutations.

Why did it take thirty years for the bias to be found?

The bias is mathematically subtle. It requires a careful enumeration of finite-sequence statistics that most analysts in the field were not in the habit of doing, because the standard assumption was that the conditional-proportion methodology was unbiased under the null. The field accepted the methodology as a given, and replications repeated it without questioning it. The Miller-Sanjurjo result required someone outside the standard behavioral economics training pipeline to look at the procedure with fresh eyes and notice that the conditional expectation was not what the standard analysis assumed.

What other “cognitive biases” might be wrong?

This is the right question to ask, but it does not have a clean answer. The hot-hand reversal does not imply that all behavioral economics is wrong, and the other foundational findings in the field --- the availability heuristic, anchoring, loss aversion --- have generally held up better under scrutiny. The honest update is that each major behavioral-economics claim should be evaluated on its own evidentiary base, and findings that depend on observational statistical analyses inferring absence-of-effect from null findings deserve particular scrutiny. The hub overall, of which this article is part, walks through this case-by-case for the most-cited claims in the field.

Was the original 1985 paper a case of fraud or p-hacking?

No. The hot-hand case is fundamentally different from the fraud and p-hacking cases elsewhere in this hub. Gilovich, Vallone, and Tversky appear to have analyzed their data carefully and honestly using the methodology that was standard in the field. The error was in the methodology itself --- a subtle mathematical bias that the field did not recognize. The case is closer to a generic methodological-pitfall story than to a misconduct story, and the original authors should be evaluated accordingly. They made an error that was not detected for thirty years because the field accepted the methodology as a given.

What does this mean for “evidence-based” decision-making?

The hot-hand case is a reminder that “evidence-based” is not a binary. Evidence comes in degrees of reliability, and the reliability depends on the methodology that generated the evidence, not just on whether the evidence is “from a study.” A canonical citation from a top journal in a major field can still be wrong, for subtle methodological reasons, for three decades. The right operating principle for evidence-based decision-making is to engage seriously with the methodology behind any claim, to discount appropriately when the methodology is fragile, and to update when new evidence overturns old findings --- even when the old finding has the weight of consensus behind it. The hot-hand reversal is an unusually clean example of why this kind of methodological engagement matters.

Where can I read more about the math?

The Miller-Sanjurjo 2018 Econometrica paper itself is the primary source; the arXiv version is freely accessible. For a more accessible treatment of the underlying bias, the Optimally Irrational write-up by Lionel Page is good. The Data Colada post 88 provides a concise explanation aimed at behavioral scientists. Andrew Gelman’s statistical modeling blog has a long-running thread on the result that captures the academic debate as it unfolded between 2015 and 2018.