Basketball players, coaches, and fans agree: Players are more likely to make a shot after they’ve successfully completed one or multiple consecutive shots than after they’ve had a miss. Players therefore know to feed the teammate who’s “hot.” Coaches know to bench the one who’s not. This understanding is dittoed for the batter who’s on a hitting streak, the poker player who’s drawing strong hands and the stock picker who has a run of soaring successes. In life, as in sports, it pays to go with the hot hand.
But as psychologists Thomas Gilovich, Robert Vallone and Amos Tversky revealed in a seminal 1985 report, the basketball hot hand is one of those universally shared beliefs that, alas, just isn’t so. When they studied detailed individual shooting records from the National Basketball Association (NBA) and university teams, the hot hand was nowhere to be found. Players were as likely to score after a miss as after a make.
When told Gilovich’s team’s cold facts about the hot hand in a July 27 interview, Stephen “Steph” Curry, an all-time NBA three-point shooter, looked incredulous. “They don’t know what they’re talking about at all,” he replied. “It’s literally a tangible, physical sensation of "all I need to do is get this ball off my fingertips, and it’s gonna go in....” There are times you catch the ball, and you’ve maybe made one or two in a row—and ... the rim feels like the ocean. And it’s one of the most rewarding feelings.”
Sports fans concur with Curry. In an article published on the same day, sports writer Jack Winter counseled, “Don’t be fooled by numbers-driven naysayers. The next time you’re feeling it at your local pickup game, don’t hesitate to indulge the temptation for even the most brazen of heat checks. Why? Stephen Curry, the truest expert on the matter, knows the hot hand is real.”
The scientific story did not, however, end in 1985 with Gilovich and his colleagues. Their analyses stimulated a host of follow-up studies of streaks in free-throw shooting, as well as in baseball, golf and tennis. Occasional examples of a slight hot hand have appeared, as in NBA three-point shooting contests—but nothing like the 25 percent increase in shots made following a make that was estimated by Philadelphia 76er players surveyed in Gilovich’s team’s study.
In a January 2022 study, operations researcher Wayne Winston of Indiana University Bloomington and computer scientist Konstantinos Pelechrinis of the University of Pittsburgh analyzed some 400,000 shot sequences across all NBA players over the 2013 –2014 and 2014–2015 seasons. Their results showed the slight opposite of a hot hand: after making one or two field goals, the average player became slightly less likely to make the next shot. (This replicated an earlier study that analyzed 12 NBA seasons between 2004 and 2016: 45 percent of field goal attempts were successful after a make, and 46 percent were successful after....)
Nevertheless, some players analyzed in Winston and Pelechrinis’s January 2022 study were, to a varying extent, more likely to make a shot after making one or more. So I wondered, “Was Curry among them?”
In their data, Curry “did not exhibit the hot hand phenomenon,” Pelechrinis wrote in an e-mail to me. The computer scientist elaborated further:
“After a single make his FG% [field goal percentage] was almost identical to the one expected based on the shot quality.”
“After two consecutive makes his FG% was slightly below expected (2.5 percentage units).”
“After three consecutive makes his FG% was 7.5 percentage units below expectation.”
I can hear you protesting, “Are Gilovich and the stats geeks denying the reality of amazing hot and cold streaks in sports and in other life realms?”
Actually, they are saying quite the opposite: Streaks do occur. Indeed, random data are streakier than folks suppose. And when streaks happen, our pattern-seeking mind finds and seeks to explain them.
Given enough data—from sports statistics, stock market fluctuations or death rates—some really weird clusters are sure to appear. Buried in the essentially random digits of pi, you can find your eight-digit birthdate. (Is that a wink from God or just a lot of digits?)
To demonstrate the streaks in random data, I flipped a coin 51 times, with these results (“H” and “T” represent heads and tails.):
HTTTHHHTTTTHHTTHTTHHTTHTTTHTHTTTTTTHTTHTHHHHTHHTTTT
Looking over the sequence, patterns jump out. For example, on the 30th to 38th tosses, set in boldface above, I had a “cold hand,” with only one head in nine tosses. But then my fortunes reversed with a “hot hand”: six heads out of seven tosses. Did I mentally snap out of my tails funk and get in a heads groove? No, these are the sorts of streaks found in any random sequence. When I compared each toss outcome with the next, 24 of the 50 comparisons yielded a changed result—just the sort of nearly 50 percent alternation we would expect from coin tossing.
Can you see a similar hot hand in one of the basketball shot sequences shown below? Both show a player making 11 successful shots out of 21 attempts. Which one has outcomes that approximate a random sequence?
Player B’s outcomes look more random to most people. (Do they look that way to you, too?) But Player B has fewer streaks than expected. For a 50 percent shooter, chance shooting, like chance coin tossing, should produce a changed outcome about half the time. But Player B’s outcome changes in successive shots 70 percent of the time (that is, in 14 out of 20 shots). Player A, despite a six-of-seven hot streak followed by a one-of-six cold streak, scores in a pattern that is more like what we would expect from a 50 percent shooter: Player A’s next outcome changes 10 times out of 20 shots.
So, like his fans, coaches and commentators, Curry is right to perceive hot and cold streaks. Basketball shooting, like so much of life, is streaky. We just misinterpret the inevitable streaks. After the fact, we describe the “hot” player as “in a zone.”
The phenomenon is ubiquitous. Maternity ward staff notice streaks of births of boys or girls—such as when 12 consecutive female babies were born in one New York State hospital in 1997—and sometimes these events are attributed to the phases of the moon during conception or to other mysterious forces. Cancer or leukemia cases may cluster in neighborhoods, sometimes provoking a fruitless search for a toxin. My then 93-year-old father once called me from his Seattle retirement home, where about 25 people died each year. He wondered about a curious phenomenon. “The deaths seem to come in bunches,” he said. “Why is that? A contagion?” How odd that folks should pass en masse!
The streaks are real; the invented explanations are not.
Nevertheless, forced to choose between data science and personal observation, between the statistics and their lying eyes, players and fans prefer the latter, so the hot hand hype lives on. After hearing the late CBS basketball commentator Billy Packer admonish college coaches to recognize the hot hand phenomenon, a friend of mine sent him my textbook summary of Gilovich’s team’s facts of life. Packer replied: “There is and should be a pattern of who shoots, when he shoots, and how often he shoots, and that can and should vary by game-to-game situations. Please tell the stat man to get a life.”
I smiled. So did my colleague Thomas Gilovich when I shared Steph Curry’s response to his work:.“Steph is one of my favorite players (how unusual is that!),” Gilovich wrote, “so to hear him say that we don’t know what we’re talking about is precious.”
Moreover, we can understand the science of serendipitous streaks and still marvel at the fact that Curry made 105 consecutive three-point practice shots. We can realize the realities of randomness and yet find pleasure in life’s weird streaks and coincidences. As countless things happen, we can savor the happenstances—such as three of the first five U.S. presidents dying on July 4 or someone winning the lottery twice or discovering a mutual friend on meeting a stranger overseas. In 2007 the late psychologist Albert Bandura recalled a book editor who came to Bandura’s lecture on the “Psychology of Chance Encounters and Life Paths" and ended up marrying the woman he happened to sit next to.
As statisticians Persi Diaconis and Frederick Mosteller observed in a 1989 paper, “With a large enough sample, any outrageous thing is likely to happen.” And what fun when it does!
This essay appeared earlier at ScientificAmerican.com as “Your Brain Looks for ‘Winning Streaks’ Everywhere—Here's Why.” David Myers, a Hope College social psychologist, authors psychology textbooks and trade books, including his recent essay collection, How Do We Know Ourselves: Curiosities and Marvels of the Human Mind.
Photo permission: jeffmilner/Getty Images
