Are Scoring Runs Real? The Math Behind the Hot Hand

Jai Pandey
Apr 24
5 min read

Updated: May 3

Picture this: a basketball player has just hit ten free throws in a row. The crowd is going electric. His teammates are feeding him the ball every chance they get. Everyone in the arena knows he's "on fire."

But is he actually? Or is the whole thing a story we're telling ourselves?

This question has driven statisticians, psychologists, and sports fans absolutely crazy for decades, and the answer is way more complicated than you'd expect.

We Are Wired to See Streaks

The belief in hot streaks goes way beyond basketball. Roulette players bet on more numbers after a win than after a loss. Stores that sell a winning lottery ticket see a spike in ticket sales. Investors assume a rising stock will keep rising. NBA legend Walt Frazier wrote in his 1974 memoir that if a teammate had a hot hand, he would constantly feed him the ball.

The problem is that humans are genuinely not great at distinguishing real patterns from random noise, especially when we're emotionally invested.

The Coin Flip Problem

Here is the core question statisticians ask about streaks: are a player's performances actually connected to each other, or is each game essentially independent, like a coin flip?

Take a baseball player with a 75 percent chance of getting a hit in any given game. He has gotten a hit in ten straight games. Does he still have a 75 percent chance of getting a hit in game eleven? Most statisticians would say yes, full stop. Each game is its own coin flip.

To test this, researcher Trent McCotter and mathematician Dr. Peter Mucha from Dartmouth took batting records from every player between 1957 and 2006 and randomly reshuffled each player's game by game results 10,000 times. The logic: if hitting streaks are just random variation, reshuffling the order shouldn't change how many long streaks appear.

The numbers didn't match. In real life, there were 19 single-season hitting streaks of 30 or more games between 1957 and 2006. The simulations produced an average of just 7.07. Real life had nearly three times as many long streaks as pure chance would predict. The real life total was 13.5 standard deviations away from the expected mean, odds of roughly one in 150 duodecillion.

Something beyond randomness is going on.

So Why Do Streaks Happen?

There are a couple of compelling explanations, and they are not mutually exclusive.

Behavior changes. When a player has a long streak going, they start playing differently to protect it, swinging at more pitches, seeking fewer walks, doing whatever it takes to stay in the batting order. McCotter found that the gap between real streaks and expected streaks widens dramatically as streaks get longer. There were about 7 percent more 10-game hitting streaks than expected, but 80 percent more 25-game streaks. That spike is hard to explain unless players are actively responding to their streak.

The hot hand might actually be real. In 2011, Yale researchers analyzed over 300,000 NBA free throws and found genuine statistical support for the hot hand at the individual level, players were meaningfully more likely to make a second free throw after making the first. A 2021 study of 34 years of NBA Three-Point Contest data found similar evidence of hot hand shooting. And Stanford researchers found that when accounting for the fact that hot players take harder shots and face tighter defense, the effect was real, raising shooting probability by 1.2 to 2.4 percent.

That being said, the original 1985 study by Thomas Gilovich and Amos Tversky found no predictive power in streaks whatsoever, concluding the hot hand was an illusion caused by "a general misconception of chance". In 2015, researchers found a statistical flaw in that original methodology, but even with the correction, the effect appears small and limited to certain players. The debate is very much still open.

The Ancient Brain Behind the Bias

Whether or not the hot hand is statistically real, our belief in it almost certainly is, and it runs much deeper than sports.

Psychologist Benjamin Hayden found that monkeys display hot hand thinking too, suggesting the bias goes back at least 25 million years. Researcher Dr. Wilke argues it traces back to how our ancestors foraged. Animals and plants cluster together in nature, so if you found one berry, looking nearby for more was genuinely smart. Our brains evolved to chase streaks because in the wild, streaks were real. The hot hand isn't a bug in human thinking. It might be a very old feature.

Creative Hot Streaks Are a Different Story

Here is the twist: outside of sports, hot streaks appear to be very real.

Researcher Dahun Wang from the Kellogg School of Management studied the careers of 3,480 artists, 6,233 film directors, and 20,040 scientists. What he found was striking: 91 percent of artists, 82 percent of film directors, and 90 percent of scientists experienced at least one distinct hot streak, a cluster of their highest impact work occurring in sequence, lasting about four to five years. The work wasn't just more frequent. It was genuinely better.

Wang suggests confidence building on itself, collaborators flocking to successful people, or a creator landing on a rich idea that fuels multiple strong works. But none of these fully explains the pattern alone. What it does suggest is that in creative fields, momentum is measurable, consistent, and very hard to fake.

The Verdict

So are scoring runs real? Sometimes, in some forms, for some people, and our brains are going to believe they exist either way.

The math shows long hitting streaks happen far more often than pure randomness predicts. The research shows creative hot streaks are nearly universal among high achievers. And the neuroscience shows the belief in streaks is baked into our evolutionary wiring going back millions of years.

What the math cannot fully resolve is where randomness ends and genuine momentum begins. Scientists are still arguing about it.

Which, honestly, is what makes sports worth watching in the first place.

Enjoyed this post? Numbers in the Wild is all about the math hiding inside the moments you thought were pure instinct, from a batter's hot streak to a scientist's creative peak. More posts coming soon.

Braithwaite, Phoebe. "Science Is Trying to Understand the Secrets of Creative Hot Streaks." Wired, 13 July 2018, www.wired.com/story/creative-hot-streaks-science-film-music-art/.

McCotter, Trent. "Hitting Streaks Don't Obey Your Rules: Evidence That Hitting Streaks Aren't Just By-Products of Random Variation." Society for American Baseball Research, 2008, sabr.org/journal/article/hitting-streaks-dont-obey-your-rules-evidence-that-hitting-streaks-arent-just-by-products-of-random-variation/.

Miller, Joshua B., and Adam Sanjurjo. "Is It a Fallacy to Believe in the Hot Hand in the NBA Three-Point Contest?" European Economic Review, vol. 138, 2021, www.sciencedirect.com/science/article/abs/pii/S0014292121001240.

Peart, Karen N. "Athletes' Winning Streaks May Not Be All in Our -- or Their -- Heads." Yale News, 6 Oct. 2011, news.yale.edu/2011/10/06/athletes-winning-streaks-may-not-be-all-our-or-their-heads.

Stanford Graduate School of Business. "Jeffrey Zwiebel: Why the Hot Hand May Be Real After All." Stanford GSB, www.gsb.stanford.edu/insights/jeffrey-zwiebel-why-hot-hand-may-be-real-after-all.

Zimmer, Carl. "That's So Random: Why We Persist in Seeing Streaks." The New York Times, 26 June 2014, www.nytimes.com/2014/06/26/science/the-science-of-hot-hand.html.