The Day Steph Curry Made 105 3-Point Shots in a Row

(Bloomberg Businessweek) -- In 1985, Israeli psychologist Amos Tversky and two other researchers published a paper that rocked the world of sports. “The Hot Hand in Basketball: On the Misperception of Random Sequences,” which appeared in the journal Cognitive Psychology, said streaks and “hot hands” are illusions: Contrary to perception, hitting one shot doesn’t make a player any more likely to hit the next.

Players and fans who think they can spot a hot hand could be suffering from “memory bias,” where streaks are more memorable than on-and-off shooting even though not more likely, some researchers said. There was even a theory that the tendency to see patterns in what’s actually random behavior was a kind of apophenia, which according to Wikipedia was “coined by psychiatrist Klaus Conrad in his 1958 publication on the beginning stages of schizophrenia.”

Over the years some other researchers have claimed to have found flaws in the authors’ statistical analysis. But as recently as 2011, Daniel Kahneman, another Israeli-born psychologist who collaborated with Tversky before the latter’s death in 1996, wrote confidently in his bestselling book Thinking Fast and Slow, “The hot hand is a massive and widespread cognitive illusion.”

Somebody forgot to tell Steph Curry. One day in practice last month, the Golden State Warriors star hit 105 consecutive shots from beyond the 3-point arc. The last 102 of them are on video. Why is this significant? Because even for an excellent 3-point shooter like Curry, a streak of 105 made shots is phenomenally unlikely if each shot is unrelated to the others. The only way it could have happened is if the “hot hand” phenomenon really does exist—that is, if hitting each shot made Curry more likely to hit the next one. 

An article published on Jan. 4 on the website Mind Matters explains how crazy it is to make 105 straight 3-pointers, even without someone’s hand in your face. It’s by data scientist Jay Cordes and Gary Smith, a Pomona College professor of economics.

“Let’s suppose Curry has an unworldly 80% chance of making every 3-point shot he takes in practice. Even if he takes 500 consecutive 3-point shots, the chances of making 105 in a row is less than one in 200 million. Even if he has been taking 500 consecutive 3-point shots every day since he was 12 years old, the probability of a 105-shot streak is still only 0.000039. Even if 100 players with 80% accuracy have been taking 500 consecutive 3-point shots every day for 50 years, the probability of a 105-shot streak is still only 0.0049.” (That’s 1 in 204.) Unless, of course, Curry had a hot hand. Which he did.

The streak of 105 shots was such a clear example of the hot hand that it proved beyond dispute that the phenomenon is real. That’s what’s known as an existence proof. In other words, it’s fine to theorize that a hot hand might exist, but there’s nothing more persuasive than video evidence.

What does Curry’s streak tell us about hot hands in other fields such as investing or gambling? Not much. As Smith and Cordes write in a new book, The Phantom Pattern Problem, people tend to spot patterns where they don’t exist. In reality throws of the dice are purely random. As for stockpicking, some people are better at it than others (just as some people are better at shooting baskets), but having one good year in the stock market doesn’t cause you to do better in the future. In other words, Tversky and his co-authors, Thomas Gilovich and Robert Vallone, were mostly right. 

In sports, in contrast, the hot hand is real because athletes—some of them, anyway—get in a zone where success builds confidence and leads to more success. Anyone who’s watched a streaky athlete in action already knows that. As Cordes and Smith write: “Our conclusion is that it is very hard to explain Curry’s 105-shot streak as just another lucky day on the basketball court. He got gloriously red hot.”

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