If you’ve played a competitive game in order to improve your rating, it’s likely you’ve come across the Elo rating system. Named after the physicist and chess player Arpad Elo, the mathematical rating system is used to calculate the relative skill of players.
Arpad E. Elo was a Hungarian-American chess master and professor of physics based in Milwaukee, Wisconsin in the 20th century. Today he lends his name to a mathematical formula familiar to players of games from chess to Age of Empires.
Who was Arpad Elo?
Professor Arpad Emrick Elo was a physicist and astronomer. He was born near Papa, Hungary on 25 August, 1903 and moved with his family to Cleveland, Ohio in the United States in 1913. He was the founder of the United States Chess Federation, prior to which he served as the president of the American Chess Federation between 1935 and 1937.
In Milwaukee, Wisconsin, he formed a chess program for children that served as a model for children’s chess programmes across the United States. He died at age 89, on 5 November 1992 from a heart attack. His obituary in the New York Times remarked that Elo enjoyed grinding his own telescope lenses for stargazing.
A chess master
Professor Elo was a master-level chess player. He was a nine-time champion or co-champion of Wisconsin between 1935 and 1961, making him the strongest player in the chess city of Milwaukee. He taught himself chess using the Encyclopaedia Britannica in his high school library.
Though he played chess competitively over several decades, and played against Bobby Fischer in 1957, he retired to focus more on his academic career. He was a professor of physics and astronomy at Marquette University, and then lectured at the University of Wisconsin. As a chess administrator, he saw the widespread adoption of the Elo rating system.
What is the Elo rating system?
The Elo system uses four-digit ratings to measure the relative skill of each player in a game. It’s based on pairwise comparisons, which means it always compares entities in pairs. Originally designed to be used in chess and adopted by the World Chess Federation as a standard rating system, it is used throughout sports and esports.
The ratings are based on the results of matches and are weighted according to the strength of opponents. As a measurement of players’ relative skill, it can serve as a predictor of the outcome of a match.
How does the Elo rating system work?
After every game, a winning player takes points from the losing player. The total points equals the difference between the ratings of the winner and the loser. A lower-rated player risks few points if they lose to a higher-rated player, but the higher-rated player stands to lose many points in the event of an upset victory.
Essentially, the more games you win, the higher your Elo gets. Instead of arriving at an absolute figure for a player’s strength, the Elo rating system measures players’ relative skill. This means that it’s a comparative rating and is only meaningful inside one rating pool.
It also only works in a competitive zero-sum game like chess (or Age of Empires). A zero-sum game is one in which the total gains of a player equals the total losses of their competitor. In other words, if one player wins, the other must lose.
A measuring tool
Elo described the Elo rating system as “a measuring tool, not a device of reward or punishment […] It is a means to compare performances, assess relative strength, not a carrot waved before a rabbit, or a piece of candy given to a child for good behavior.”
Nevertheless, Elo ratings acquire prestige that can encourage players to avoid play in order to protect their rating. It can be exploited if players can select their own opponents, and there are also discussions about how ratings inflation and deflation can make comparing players over different periods problematic.
History of the Elo rating system
Elo designed his rating system as a superior alternative to the Harkness rating system, which was developed in 1950 by Kenneth Harkness. Elo regarded its arbitrary weighting based on the reputation of certain competitions as unsatisfactory, and intended the Elo rating system to be more objective.
The statistical Elo rating system was designed to model a player’s true skill by linking it to the mean of a random variable that attends each of their matches. The system assumes that this mean value of performance, inferred from wins, draws and losses, changes slowly over time.
The Elo system was adopted in 1960 by the US Chess Federation in Saint Louis. The International Chess Federation (FIDE) adopted it in 1970. Elo himself made the calculations for rated players into the 1980s, when there were fewer than 2000 players rated by FIDE.
Elo also produced standardised works, titled The Ratings of Chess Players, Past & Present, and “Age Changes in Master Chess Performance”. At the time of his death in 1992, the chess player with the highest-rated Elo was the Russian grandmaster Gary Kasparov, with a rating of 2790. He had recently surpassed Bobby Fischer’s high watermark rating of 2780, set 20 years earlier.
Age of Elo
Thanks to the Elo system being a fairly simple way of rating competitors, its use has expanded far beyond the rank and file of the chessboard. It is used, generally in a modified form, throughout sports and esports competitions from table tennis to Counter Strike: Global Offensive.
Ratings are comparative and meaningful only within specific rating pools. So while the tournament Elo of the number one Age of Empires II player TheViper is 2354, this is on the low end for a chess grandmaster.