To simplify computation even further, Elo proposed a straightforward method of estimating the variables in his model (i.e., the true skill of each player). And while he thought it was likely that players might have different standard deviations to their performances, he made a simplifying assumption to the contrary. Actually, there is a probability of a draw that is dependent on the performance differential, so this latter is more of a confidence interval than any deterministic frontier. If the game is a draw, the two players are assumed to have performed at nearly the same level.Įlo did not specify exactly how close two performances ought to be to result in a draw as opposed to a win or loss. Conversely, if the player loses, they are assumed to have performed at a lower level. Therefore, if a player wins a game, they are assumed to have performed at a higher level than their opponent for that game. Performance can only be inferred from wins, draws and losses. One cannot look at a sequence of moves and derive a number to represent that player's skill.

Elo thought of a player's true skill as the mean of that player's performance random variable.Ī further assumption is necessary because chess performance in the above sense is still not measurable. Although a player might perform significantly better or worse from one game to the next, Elo assumed that the mean value of the performances of any given player changes only slowly over time. For example, winning an important golf tournament might be worth an arbitrarily chosen five times as many points as winning a lesser tournament.Ī statistical endeavor, by contrast, uses a model that relates the game results to underlying variables representing the ability of each player.Įlo's central assumption was that the chess performance of each player in each game is a normally distributed random variable. Rating systems for many sports award points in accordance with subjective evaluations of the 'greatness' of certain achievements. Įlo's system replaced earlier systems of competitive rewards with a system based on statistical estimation. At about the same time, György Karoly and Roger Cook independently developed a system based on the same principles for the New South Wales Chess Association. On behalf of the USCF, Elo devised a new system with a more sound statistical basis.

The Harkness system was reasonably fair, but in some circumstances gave rise to ratings which many observers considered inaccurate. The USCF used a numerical ratings system, devised by Kenneth Harkness, to allow members to track their individual progress in terms other than tournament wins and losses. 4.1 Game activity versus protecting one's ratingĪrpad Elo was a master-level chess player and an active participant in the United States Chess Federation (USCF) from its founding in 1939.2.3 United States Chess Federation ratings.Players whose ratings are too low or too high should, in the long run, do better or worse correspondingly than the rating system predicts and thus gain or lose rating points until the ratings reflect their true playing strength.Įlo ratings are comparative only, and are valid only within the rating pool in which they were calculated, rather than being an absolute measure of a player's strength. This means that this rating system is self-correcting. The lower-rated player will also gain a few points from the higher rated player in the event of a draw. However, if the lower-rated player scores an upset win, many rating points will be transferred. If the higher-rated player wins, then only a few rating points will be taken from the lower-rated player.

The difference between the ratings of the winner and loser determines the total number of points gained or lost after a game. After every game, the winning player takes points from the losing one. A player whose rating is 100 points greater than their opponent's is expected to score 64% if the difference is 200 points, then the expected score for the stronger player is 76%.Ī player's Elo rating is represented by a number which may change depending on the outcome of rated games played. Two players with equal ratings who play against each other are expected to score an equal number of wins. The difference in the ratings between two players serves as a predictor of the outcome of a match. The Elo system was originally invented as an improved chess-rating system over the previously used Harkness system, but is also used as a rating system in association football, American football, baseball, basketball, pool, table tennis, and various board games and esports.

It is named after its creator Arpad Elo, a Hungarian-American physics professor. The Elo rating system is a method for calculating the relative skill levels of players in zero-sum games such as chess. Arpad Elo, the inventor of the Elo rating system

Factor form to standard calculator