In his 2013 New York Times best-seller, "Thinking, Fast and Slow," Nobel Prize-winning economist Daniel Kahneman wrote: "The hot hand is a massive and widespread cognitive illusion." No less an authority than Michael Lewis, author of "Moneyball," has declared: "The streaks observed by fans and announcers and the players themselves [are] illusions."
For 30 years, the consensus in the statistical and scientific community has been resounding: Our eyes are deceiving us. The hot hand is little more than a mirage.
But what if they were all wrong?
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And so the Fallacy of The Hot Hand was born. For 30 years, GVT's findings would be held sacred in the scientific community. In the basketball community, not so much. Tversky once said: "I've been in a thousand arguments over this topic. I've won them all, and I've convinced no one." When asked about the hot-hand fallacy, Red Auerbach wasn't too keen on Tversky's study, "Who is this guy? So he makes a study. I couldn't care less." The legendary Bobby Knight wasn't a fan of the so-called fallacy, either.
Nonetheless, lessons gleaned from the 1985 "Hot Hand in Basketball" paper were repeated from lecture halls to business conferences to casinos across the globe. Beware the stockbroker who has beaten the S&P five years in a row. Don't be tricked by the roulette table that seems to be running "hot" on red. And more recently, Don't buy into Klay Thompson's hot hand.
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if you study the fourth shots that follow three makes in a row, the probability that those fourth shots are makes is ... lower. In fact, he says, it's 46 percent, in the case of 100 shots, for example.
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Let's say that in analyzing the results of 100 coin flips you see a string of three heads (HHH_) and "_" is, say, Flip 42 in the sequence -- which was selected because it was preceded by HHH. What is the _ in the sequence? Of course, you don't know which kind of sequence you are in. it could be HHHT or it could be HHHH. You think it's a 50-50 chance that Flip 42 is H (or T).
But here's where it changes, and it is sneaky. In sequence HHHH, you could have selected Flip 43 because it continues a run of three heads, and you haven't excluded Flip 44 or 45, like you would have in sequence HHHT (it ends the run of heads). The excluded flips in the HHHT world mean it is more likely that Flip 42 will turn up T rather than H, given the condition that the flip was selected because it was preceded by three heads in a row. The choice has been restricted.
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The implication is huge: If Curry is statistically less likely to make a shot after a string of makes (46 percent), then even shooting 50 percent is evidence of the hot hand.
Interesting indeed. This coin-flip discovery, upon its publishing in 2015, flipped the statistical community upside down. One prominent statistician called it "the zeitgeist jackpot." In a world of people who study probabilities, the unlikeliest of things had happened.
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"In contrast with previous studies, we find substantial evidence of hot-hand shooting in the NBA Three-Point Contest. This leaves little doubt that the hot hand not only exists, but actually occurs regularly."
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"People with tremendous math skills are all over the map on this one," Gilovich says over the phone. "I simply say that because the mathematicians I talk to are befuddled about the proper statistical analysis. Time will have to tell on that one."
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"It uses the most elementary of arguments from probability theory, yet seems to shed new light on a well-studied, much-argued problem. This achievement is wonderful, and gives me hope that there are still simple insights out there, simple insights that we all have missed -- yet insights that could dramatically change the way we look at some of our most important open problems."
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