Are Scoring Runs Real? The Math Behind the Hot Hand
- Jai Pandey
- Apr 24
- 5 min read
Picture this: a basketball player has just hit ten free throws in a row. The crowd is losing it. His teammates are feeding him the ball every chance they get. Everyone in the arena knows he's on fire.
But is he actually?
This question has driven statisticians, psychologists, and sports fans absolutely crazy for decades, and the answer is way more complicated than anyone would 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 right after. Investors assume a rising stock will keep rising and prefer to buy that one. NBA legend Walt Frazier wrote in his 1974 memoir that whenever a teammate had a hot hand, he would constantly feed him the ball.
None of these people think they are being irrational. Humans are genuinely not great at separating real patterns from random noise, and we get significantly worse at it when we are emotionally invested in the outcome.
The Coin Flip Problem
Here is the question at the heart of all of this: are a player's performances actually connected to each other, or is each game basically independent, like flipping a coin?
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 in game eleven, or is something else going on? Most statisticians would say 75 percent. Techinically, each game is its own coin flip, and the last ten don't change the next one.
To actually test this, researcher Trent McCotter and mathematician Dr. Peter Mucha from the University of 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 is that if hitting streaks are just random variation, shuffling the order of games around shouldn't change how many long streaks show up. The numbers should match.
However, the researchers found that the numbers did not match at all.
In real life, there were 19 single season hitting streaks of 30 or more games between 1957 and 2006. The 10,000 simulations produced an average of 7.07. Real life had nearly three times as many long streaks as pure chance predicted. The real life total sat 13.5 standard deviations away from the expected mean. The odds of that happening by chance alone are about one in 150 duodecillion, a number so large it almost means nothing.
Clearly, something beyond randomness is going on. The question is what.
So Why Do Streaks Happen?
Nobody has pinned it down to one thing, and honestly it might not be just one thing.
The first is that behavior changes. When a player has a long streak going, they start playing differently to protect it. More pitch swinging, fewer walks, whatever it takes to stay in the batting order and keep getting plate appearances. McCotter found that the gap between real streaks and expected streaks gets dramatically wider as streaks get longer. About 7 percent more 10 game hitting streaks than expected. But 80 percent more 25 game streaks. That kind of spike is very hard to explain, given that players are not actively responding to their own streak and adjusting how they play.
The second is that the hot hand might be real. In 2011, Yale researchers analyzed over 300,000 NBA free throws across five seasons and found statistical support for the hot hand at the individual level. Players were on average more likely to make a second free throw right after making the first. A 2021 study covering 34 years of the NBA Three Point Contest data found similar evidence. Stanford researchers found that once you account for the fact that hot players take harder shots and face tighter defense, the effect was real, bumping shooting probability up by 1.2 to 2.4 percent.
Still, the original 1985 study by Thomas Gilovich and Amos Tversky found no predictive power in streaks at all, concluding the hot hand was an illusion due to a general misconception of chance. In 2015, researchers discovered a mistake in that original methodology that had gone unnoticed for 30 years. But even corrected, the effect seems small and limited to certain players, displaying that the debate is genuinely still open, and has been for 40 years now.
The Ancient Brain Behind the Bias
Here is the part that reframes the whole argument.
Whether or not the hot hand is statistically real, our belief in it almost certainly is, and it goes a lot deeper than sports. Psychologist Benjamin Hayden found that monkeys display hot hand thinking too, which puts the bias at least 25 million years old. Researcher Dr. Wilke argues it traces all the way back to how our ancestors foraged for food. Animals and plants cluster together in nature. If you found one berry, looking nearby for more was thought to be the smart move. Our brains evolved to chase streaks because in the wild, streaks were real and ignoring them could mean starvation.
So, The hot hand isn't a mistake in the human brain, but might be one of the oldest and most useful features we have.
Creative Hot Streaks Are a Different Story
Outside of sports, hot streaks appear to be very real and very consistent. Researcher Dahun Wang from the Kellogg School of Management studied the careers of 3,480 artists, 6,233 film directors, and 20,040 scientists, tracking the impact of their work over time. The results showed that 91 percent of artists, 82 percent of film directors, and 90 percent of scientists went through at least one distinct hot streak during their career, a cluster of their highest impact work hitting in sequence, typically lasting four to five years. And the work during these periods wasn't just more common but even better.
Wang has a few theories. Maybe success builds confidence which builds more success. Maybe people just want to work with someone who is winning. Maybe a creator stumbles onto a genuinely rich idea and rides it across several projects. Probably some combination of all three. What is clear is that in creative fields, momentum is real, it shows up across wildly different disciplines, and it is not something you can manufacture.
The Verdict
So are scoring runs real? The answer is sometimes, in some forms, for some people, and our brains are going to believe in them regardless.
The math shows long hitting streaks happen far more often than pure randomness would ever predict. The research shows creative hot streaks are nearly universal among high achievers. Furthermore, the neuroscience shows the belief in streaks is wired into us going back millions of years before basketball was invented.
What the math still cannot tell us is exactly where randomness ends and where the momentum begins. That line is blurry, it shifts from player to player and sport to sport, and scientists have been arguing about it for four decades without a clean resolution.
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.