Here\u2019s a statistical challenge worthy of a grandmaster: How do you create an accurate ranking system when the best players usually don\u2019t win?<\/p>\n
This is the conundrum of elite chess. The stronger the players, the greater the odds of the match ending in a draw.<\/p>\n
\u201cWhat ended up happening,\u201d said Mark Glickman<\/a>, senior lecturer in the Department of Statistics and longtime chess enthusiast, \u201cis that these top players were not having their ratings change very much, just because the games would be drawn all the time.\u201d<\/p>\n Now Glickman has devised a solution: the first-ever ranking system that takes account of player strength when estimating the probability of a tie.<\/p>\n Chess may be the quintessential game of skill, but oftentimes top-ranked competitors cancel each other out and prevent a decisive outcome. Among elite chess grandmasters, more than 70 percent of competitions end in ties. And that is just conventional \u201cover the board\u201d chess; in the growing realm of online competition known as \u201ccorrespondence chess,\u201d some 95 percent of matches end without a winner.<\/p>\n Even epic matchups have ended indecisively. In the 2018 world chess championships between Magnus Carlsen\u00a0and Fabiano Caruana, all 12 games ended in draws \u2014 for the first time in history. One analyst asked, \u201cIs Classical Chess Dead From Draws?\u201d<\/a><\/p>\n Not only chess faces this deadlock dilemma. In simpler games such as checkers or tic-tac-toe, a match is guaranteed to end without a winner if neither player makes a mistake. Likewise, ties are common in sports such as soccer or cricket.<\/p>\n So Glickman decided it was time for a new statistical approach to rankings.<\/p>\n \u201cThese top players were not having their ratings change very much, just because the games would be drawn all the time.\u201d<\/p>\n As a child in New Jersey, he started playing chess around age 5, entered U.S. Chess Federation tournaments by age 11, and eventually attained the ranking of chess master. As an undergraduate at Princeton, he was appointed to the ratings committee of the U.S. Chess Federation and a few years later became chair of the committee while a Ph.D. student at Harvard.<\/p>\n Paired comparison models are widely used to measure relative strengths of competitors in games and sports. These systems are important not only for ranking-obsessed fans and players, but also for establishing betting odds or organizing tournament brackets.<\/p>\n In chess, most existing rating systems accounted only for win-loss outcomes and treated ties as half a win and half a loss. They did not explicitly model the probability of a draw \u2014 even though it was the most common outcome among top competitors.<\/p>\n \u201cAs a result, these systems may produce stagnant ratings,\u201d observed Glickman, \u201cespecially for elite players.\u201d<\/p>\n To address that shortcoming, Glickman built a new system. He adapted a widely used paired comparison model but replaced the fixed tie parameters with ones that incorporated measures of player strength. The new version, he says, yields a \u201cricher and more realistic representation of competitive outcomes.\u201d<\/p>\n Glickman presented his new model in two recent papers in the Journal of Data Science<\/a> and Statistical Modeling<\/a>.<\/p>\n \u201cMy innovation basically allows you to come up with much more accurate probabilities of wins, losses, and draws \u2014 draws in particular,\u201d said Glickman. \u201cBefore this, the probability of a draw would just simply not depend on how strong the players were. Now, if I have two strong players, my model allows me to predict that the probability of a draw is actually quite large. We would not have been able to do that before.\u201d<\/p>\n Glickman began working on the new model several years ago and in 2021 the International Correspondence Chess Federation (ICCF) commissioned him to develop a revised rating system. Two years later, the organization adopted his model for its player rankings.<\/p>\n Austin Lockwood, the ICCF services director, said the organization turned to Glickman because its old rating system from the 1980s had become outdated. In recent years, online chess competitors have relied more and more on computer engines to help them plan moves. \u201cIt is increasingly difficult for strong players to find wins, even against a relatively weaker player,\u201d he said. \u201cThe effect of this has been that nearly all games between highly rated players are now draws.\u201d<\/p>\n He said the adoption of the Glickman system had gone smoothly for the ICCF.<\/p>\n \u201cIt does seem to be performing well so far,\u201d Lockwood said. \u201cPlayers (especially correspondence chess players) take a while to get used to change, but we haven\u2019t had many complaints, which suggests that is has been well-received.\u201d<\/p>\n Glickman believes that the ICCF is the first major organization to implement a rating algorithm that models the probability of a tie as a strength-dependent outcome.<\/p>\n He suggests the framework also might be useful in soccer, boxing, or cricket. (Ties also used to be more frequent in professional hockey until 2005, when the NHL introduced shootouts at the end of overtime.)<\/p>\n Glickman, who also serves as co-director of graduate studies in the Department of Statistics, often has applied his expertise beyond the University. Last year, he won the American Statistical Association\u2019s\u00a0Founders Award for his longtime service to the organization, and he currently chairs the ASA Committee on Data Science and AI.<\/p>\n When he appears at public events, odds are high that he will inject a little fun. He performs magic tricks and sings stat geek parody songs such as \u201cBayesian Believer\u201d (a takeoff on \u201cDaydream Believer\u201d) and \u201cValencia Wood\u201d (after \u201cNorwegian Wood\u201d).<\/p>\n But there\u2019s one hobby he doesn\u2019t have much time for these days: chess.<\/p>\n \u201cI still play, but not competitively because of the amount of time it takes to remain competitive,\u201d Glickman said, gesturing at shelves of chess books behind his desk. \u201cI would have to be studying hours per day.\u201d<\/p>\n","protected":false},"excerpt":{"rendered":"Here\u2019s a statistical challenge worthy of a grandmaster: How do you create an accurate ranking system when the…\n","protected":false},"author":2,"featured_media":453332,"comment_status":"","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2],"tags":[4,450,3048,1978,451,3,1728,452,453],"class_list":["post-453331","post","type-post","status-publish","format-standard","has-post-thumbnail","category-breaking-news","tag-breaking-news","tag-breakingnews","tag-computers","tag-games","tag-headlines","tag-news","tag-research","tag-top-stories","tag-topstories"],"_links":{"self":[{"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/posts\/453331","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/comments?post=453331"}],"version-history":[{"count":0,"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/posts\/453331\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/media\/453332"}],"wp:attachment":[{"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/media?parent=453331"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/categories?post=453331"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/tags?post=453331"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}