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Ideas

The ‘hot hand’ might be real after all

Is that ballplayer ‘in the zone,’ or just lucky? A new challenge to statisticians’ skepticism

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In the zone. In a groove. En fuego. Sports broadcasters—and fans—have coined any number of terrible clichés to describe an athlete, especially a basketball or a baseball player, on a hot streak. The idea that a player might have the “hot hand”—a greater chance of draining his next shot or driving his next pitch—is, to many people, a fact as undeniable as the numbers on the scoreboard itself.

To researchers, it’s something else: a problem to be solved. Do players really get hot—quantifiably? Or are we just seeing inevitable patterns in an ultimately random world?

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It sounds like a minor question, but over the past 30 years, “hot hand studies” have become something of a subfield among behavioral economists, psychologists, and statisticians—in part because they like sports, yes. But it’s more than just that. As amateur athletes, playing golf on weekends or competing in over-30 basketball leagues, they’ve felt the hot hand at times. And they want to know: Is it real?

Boston Red Sox relief pitcher Koji Uehara.

AP Photo/Tim Donnelly

Boston Red Sox relief pitcher Koji Uehara.

“It’s something that people who play sports can experience and relate to very intimately. That feeling—I’m on a roll,” said John Ezekowitz, a recent Harvard University graduate and the coauthor of a new hot hand paper. “The hot hand ties into a lot of things that we romanticize about sports. It fits into narrative structure that we love.”

Sadly for sports romantics, it’s also a narrative that has been largely debunked. Hot hand research has found little evidence that players can experience true streakiness. Where we see athletes on fire, researchers see something closer to happenstance. If you throw up enough shots at a backboard, or take enough cuts at the plate, the research argues, you’re bound to see a streak of hits every once in awhile.

Now, however, at least two new papers suggest it may be more complicated than that. A working paper by two finance professors documents the existence of hot hand in baseball. And Ezekowitz’s research—coauthored by fellow Harvard graduates Carolyn Stein and Andrew Bocskocsky—shows that the hot hand may exist in basketball, too.

What’s at stake is, to some extent, a question of greatest interest to sports fans. But John Huizinga, a professor of economics at the Booth School of Business at the University of Chicago, believes the implications are much larger. Hot hand studies can offer insight into what impact recent success has on future performance—on and off the court—and what role randomness plays in our lives.

“People overestimate streakiness. And because of that, they frequently mistake what is, in fact, luck for skill,” said Huizinga, who’s conducted his own hot hand studies. “This distinction between ascertaining skill and luck shows up all the time,” he added. “Who do you give your money to for investing? How much do you pay a certain employee? It’s everywhere. It isn’t just about sports. It’s about life.”

***

If a hot hand exists, it works like this: When a player gets hot, he’s more likely than normal to make his next shot. If it doesn’t exist, that doesn’t mean there’s no such thing as a streak. It just means these streaks are most likely random, not much different from flipping a coin over and over. Sometimes you just keep getting heads.

In the early 1980s, Tom Gilovich, then a graduate student at Stanford University, began to wonder which effect we were seeing in basketball when a player suddenly began scoring a lot of points: true hot hand or just random streakiness. “I had always played basketball,” said Gilovich, now a professor of psychology at Cornell University. “So sports were on my mind.”

And so was human judgment. As a student under the great psychological theorist Amos Tversky, Gilovich had learned how people tend to misinterpret random sequences.

“Chance,” he said, “is lumpier than we expect.” Maybe they’d find the same thing if they analyzed an entire season of Philadelphia 76er shooting statistics. Gilovich figured our notion of a hot hand was exaggerated. But Tversky, Gilovich recalled, believed they wouldn’t find any evidence of it whatsoever. “And he turned out to be right.”

Their study—conducted along with a third researcher, Robert Vallone—reported that people believed in the existence of a hot hand. Ninety-one percent of basketball fans surveyed for the study agreed that a player who had just made his last two or three shots had a better chance of making the next shot than the player who had missed his last few. And the 76ers themselves agreed. Six of the eight players interviewed by Gilovich’s team said that, on occasion, after having made a few shots in a row, they “know” they’re going to make their next shot—that they “almost can’t miss.”

But the results showed that their previous shots had no effect on future shots—not even in free throws, with no defender in the way, or in a controlled shooting experiment involving 26 college basketball players. The stat line from future Hall of Famer Julius Erving, a member of that 76ers team that Gilovich studied, seemed to say it all. After missing three shots, he shot 52 percent from the floor on his next shot. And after making three, he shot 48 percent on his next attempt—four percentage points lower. “Evidently,” the study concluded, “people tend to perceive chance shooting as streak shooting.”

Since then, there have been countless other hot hand analyses across the sports world—with evidence of true streakiness typically only showing up in sports like bowling, darts, and horseshoes, where the conditions are controlled and the athlete’s actions are repeated in rapid time.

The two new studies, however, are poking holes in the long accepted findings. First, there is one conducted by two finance professors, focusing on baseball. The authors—Brett Green, at the Haas School of Business at the University of California Berkeley, and Jeffrey Zwiebel, at the Stanford University Graduate School of Business—analyzed a mountain of data for their study: 12 major league baseball seasons, or roughly 2 million at-bats. They controlled for variables, like the abilities of the batter and the pitcher, the stadium in which the at-bats took place, and even matchups like lefty versus lefty. And their findings, laid out in a working paper, show that a baseball player on a hot streak is batting 15 to 20 points higher than a teammate who is cold. Home run rates also went up while strikeouts fell—and pitchers enjoyed similar advantages on the mound.

“Think of all the clichés that managers give for why they’re playing one guy today,” Zwiebel said. “It’s always, ‘He’s seeing the ball well. He’s swinging the bat well.’ And we hear exactly the opposite, too. ‘I’m going to sit him down for a few days. He’s not swinging the bat well.’” The findings suggest that such notions might actually mean something. “These things really do matter,” Zwiebel said. “I think those clichés are probably right.”

Just why they’re seeing the effect is harder to explain. “I can’t tell you whether this is because guys wake up on the right side of the bed,” Green said, “or they just have a higher level of confidence.” Maybe they’ve overcome an injury and are hitting better as a result, or maybe they’ve tweaked their swing. “My best guess,” Green said, “is it’s some combination of these, and perhaps many other, factors.”

Ezekowitz and his coauthors, on the other hand, can say exactly why they’ve been able to identify a hot hand effect in their new basketball study: modern technology. They analyzed 83,000 shots from the 2012-13 NBA season, with the help of cameras that NBA teams had installed at 15 arenas to, according to the study, “provide precise three-dimensional image tracking of the players, referees, and ball every 1/25th of a second.”

With the Harvard graduates able to know the position of the players on the court, they could see that players with recent success in shooting were more likely to be taking shots from further away, facing tighter defenses, and throwing up more difficult shots. “They were more likely to just jack it up,” Ezekowitz said. “Shoot more often.”

So the researchers controlled for these variables—and found what players and fans have long believed: The hot hand does exist. At least a little. According to the new research, players enjoying the hot hand are 1.2 to 2.4 percentage points more likely to make the next shot. Not exactly en fuego, but still.

“It is significant,” said Stein, one of the study’s coauthors, given the history of the research in this area. “But people are wrong when they think of the hot hand as being this big effect—like you heat up and you can’t miss.”

***

The Harvard graduates didn’t intend their study to be a rebuke of the seminal Gilovich research. “We view it more as an update,” Ezekowitz said. But it was exciting, they admitted, to take on things accepted as fact and offer a different point of view. They titled their paper, “The Hot Hand: A New Approach to an Old ‘Fallacy.’” And they’re getting an audience. The researchers will be presenting their work in a few weeks at the MIT Sloan Sports Analytics Conference in Boston.

Gilovich said he appreciates the new approach—and the technology that made it possible. “Being able to know where the shots were taken,” he said, “that’s a great thing.” But he and others aren’t ready to throw out decades of studies questioning the existence of hot streaks just yet. At most, said Alan Reifman, author of the book “Hot Hand: The Statistics Behind Sports’ Greatest Streaks,” there’s a small effect at play here. “It’s consistent with some other studies,” said Reifman, a professor of human development and family studies at Texas Tech University. “With super huge data sets in the hundreds of thousands or millions, you can find maybe a 1 or 2 percent rise in performance.” Or, as Reifman called it, “a tiny hot hand.”

In the meantime, the debate will surely rage on. Nearly 30 years removed from the publication of his study, Gilovich said he still gets phone calls all the time from people who want to talk about it. “Anytime Kobe Bryant scores 80 points,” he said, “I’m going to get a call from someone. It’s a story that never dies.”

On the phone, with these strangers, he’ll lay out his case, discussing the results of his study that showed “a complete absence of streakiness.” And some will believe him. “I’ve convinced lots of statisticians and gamblers,” he said.

But it’s a little harder to persuade anyone who’s ever played basketball—and the new research might make it even more difficult now. Even Gilovich will admit it: There’s just something magical about the hot hand. People want to believe.

“If you watch basketball, or play, it’s the most compelling phenomenon you can experience,” he said. “It just feels like the game gets easy when you’re hot.”

Freelance writer Keith O’Brien is a former staff writer for the Globe and the author of the book “Outside Shot,” chronicling one town’s lonely quest for basketball greatness. E-mail him at kob.story@gmail.com.
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