Streaks in sports can be the stuff of legend or infamy.
In 1941, the New York Yankee’s star outfielder, Joe DiMaggio, recorded at least one hit in 56 consecutive games, setting a record untarnished in 84 years and unlikely to be broken.
On the other hand, in the early 2000s, Los Angeles Dodger’s pitcher, Éric Gagné, set the record for the most consecutive saves with, coincidentally, 84; however, Gagné later admitted to using human growth hormone, a performance enhancing substance prohibited by Major League Baseball.
Not that baseball has a monopoly on either streaks or controversies about them.
In 2024, Chess.com asked Jeffrey Rosenthal, a professor of probability and statistical computing in the Faculty of Arts & Sciences’ Department of Statistical Sciences, to investigate allegations that the winning streaks of grandmaster and five-time U.S. chess champion Hikaru Nakamura — who goes by the player name Hikaru — could only be achieved by cheating.
“When Chess.com asked me to look into it, I was happy to,” says Rosenthal. “It's the sort of opportunity I like because it involves some genuine statistical probability issues. And it was something that was of genuine importance — not just to a small number of statistical scientists — but to large numbers of people around the world.”
The games in question were played on the online platform Chess.com, a popular website which hosts some ten million matches every day. Because it’s an online platform, there is greater potential for cheating than in face-to-face games — for example, by players using chess-playing software.
In particular, former world chess champion Vladimir Kramnik suggested Hikaru’s streaks were suspicious and worth investigating, pointing to a streak of 46 matches in which Hikaru won 45 and tied one. The controversy made international headlines, including coverage in The New York Times.
It wasn’t the first time Rosenthal had been asked to look into claims of cheating. In 2006, CBC journalists asked for his expert help in their investigation into retailers who were winning a seemingly disproportionate number of lottery draws in Ontario. Rosenthal’s analysis showed retailers were indeed winning far more than the odds predicted. The revelations ultimately led to criminal charges, jail terms, the firing of Ontario Lottery and Gaming Corporation’s CEO, and the introduction of many safeguards in place today.
Rosenthal analyzed data supplied by Chess.com and in an August 2024 report, publicized by Chess.com, he concluded that Hikaru’s streaks were well within statistical expectations. In other words, it was unlikely he’d cheated.
Kramnik responded with a video in which he was critical of the report. Rosenthal responded to Kramnik’s concerns, with another report in September 2024 and, in April 2025, a paper titled, An Investigation Into Probabilities of Streaks in Online Chess, published in the Harvard Data Science Review.
Throughout his analysis, Rosenthal points to two reasons why the streaks aren’t necessarily signs of malfeasance.
Just because something is striking and dramatic doesn't necessarily mean that it has statistical significance. In order to truly understand what’s going on, you have to stop and think. You have to do the work to figure out the probabilities of something like that happening. It’s how we understand what is and isn’t true.
Firstly, Rosenthal quantified the fact that Hikaru’s opponents were measurably less skilled than him. For example, Hikaru’s own player rating during a particular 116-game streak averaged 3,017 — a very high score. Meanwhile, his opponents in those matches averaged just 1,526.
In other words, because Hikaru was significantly more skilled than his opponents, the chances of long winning streaks was higher than if he’d played more skilled players.
Rosenthal also showed that the likelihood of winning streaks increased because Hikaru played so many games.
As he points out in his April 2025 paper, if you flip a coin twelve times, your chances of tossing twelve heads in a row are extremely small. However, if you tossed that same coin ten thousand times, there is a much higher likelihood you’ll toss twelve consecutive heads.
Rosenthal demonstrated this by running what statistical scientists call a Monte Carlo simulation: a computer program that in this case flips a virtual coin ten thousand times. The simulation — which was run one thousand times for statistical rigour — demonstrated that with so many coin tosses, there was a nearly 70 per cent chance of hitting a streak of twelve heads, a far from unlikely occurrence.
As Rosenthal explains, both factors answer one of Kramnik’s questions: Why does Hikaru have so many more long winning streaks, 21, than a top player like Magnus Carlsen, the Norwegian grandmaster and multiple world champion who in the same period had only one streak? Plus, how could Hikaru have several streaks of more than 100 games, while Carlsen’s longest was just 32?
Rosenthal’s answer? Hikaru played 57,421 games compared to just 5,104 for Carlsen; and Hikaru’s opponents were rated much lower than Carlsen’s.
“Just because something is striking and dramatic doesn't necessarily mean that it has statistical significance,” says Rosenthal.
“In order to truly understand what’s going on, you have to stop and think. You have to do the work to figure out the probabilities of something like that happening. It’s how we understand what is and isn’t true.”