In the ever-evolving world of online chess, the role of statistics is becoming increasingly critical.
When the CEO of Chess.com, one of the largest online chess platforms, reached out to Professor Jeffrey Rosenthal, a renowned statistician from the University of Toronto, they sought answers to an intriguing problem: Are some players' long winning streaks indicative of cheating?
The Problem of Long Streaks
Professor Rosenthal was tasked with analyzing data from Chess.com to investigate claims that some players were winning so many games in a row that it seemed statistically improbable without the aid of external help, such as computer assistance. The concern arose when even former world chess champions suggested that these streaks might be too good to be true.
One particularly controversial case involved the top-level player Hikaru Nakamura, who had achieved an impressive streak of 46 high-level games, winning 45 and tying one. With such streaks raising suspicions, Rosenthal was called upon to determine whether these results could be explained by natural statistical variability or if they were indeed outliers suggesting foul play.
The Statistical Approach
Using a simple model to calculate the probability of winning or tying a chess game based on the players' ratings, Professor Rosenthal dug into the data. He examined the likelihood of certain streaks occurring naturally versus through potential cheating. His analysis focused not only on individual streaks but also on the broader context of the player's entire history on the platform.
Rosenthal employed the Elo rating system, which predicts the expected score (win, tie, or loss) based on the rating difference between players. He adjusted this model to account for factors like the slight advantage of playing White and the lower likelihood of draws in online blitz chess. His method involved calculating the probability of each streak and comparing these probabilities across the player's extensive game history.
What the Numbers Revealed
Initially, some streaks seemed highly improbable—one chance in 830 for a particular streak. However, Rosenthal expanded the scope of his analysis by considering the player’s extensive history on the platform, spanning over a decade with more than 57,000 games played. When factoring in the sheer volume of games, the likelihood of such streaks occurring naturally was much higher than initially assumed.
Through his calculations and computer simulations, Rosenthal determined that the streaks, while rare, were not beyond the realm of possibility. The probability of achieving such streaks naturally was as high as 43% when considering the entire dataset. His simulations also showed that it was not uncommon to find streaks with seemingly low probabilities when looking at many games. For instance, the controversial streak of 46 games had about a one in 830 chance but considering the numerous opportunities to achieve such a streak across thousands of games, its occurrence was not particularly surprising.
Rosenthal also examined whether these streaks could be attributed to a "hot hand" effect, where a player's performance might improve temporarily due to factors like concentration or motivation. His analysis showed no significant autocorrelation in the player's scores, indicating that the streaks were not the result of a persistent "hot hand."
Final Verdict: The Role of Statistics in Fair Play
Professor Rosenthal's analysis provides a fascinating insight into how statistical methods can be used to assess fairness in online gaming. His findings suggest that, in this case, the long winning streaks were within the realm of statistical expectation, meaning that there was no solid evidence pointing toward cheating.
In a world where online activities are under constant scrutiny, the role of statisticians like Professor Rosenthal is crucial in ensuring fair play and maintaining trust in digital platforms. The application of rigorous mathematical analysis helps in distinguishing between genuine skill and foul play, contributing to the integrity of the gaming community.
Read the original publication by Professor Rosenthal, or visit probability.ca for more.