Elo Rating System
The Elo rating sysem is a method for calculating the relative skill levels of players in two-player games such as Chess.
"Elo" is often written in capital letters (ELO), but it is not an acronymn. It is the family name of the system's creator, Arpad Elo (1903-1992), a Hungarian-born American physics professor.
Elo's central assumption was that the chess performance of each player in each game is a normally distributed random variable. 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. Elo thought of a player's true skill as the mean of that player's performance random variable.
A further assumption is necessary, because chess performance in the above sense is still not measurable. One cannot look at a sequence of moves and say, "That performance is 2039." Performance can only be inferred from wins, draws and losses. Therefore, if a player wins a game, he is assumed to have performed at a higher level than his opponent for that game. Conversely if he loses, he is assumed to have performed at a lower level. If the game is a draw, the two players are assumed to have performed at nearly the same level.
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). One could calculate relatively easily, from tables, how many games a player is expected to win based on a comparison of his rating to the ratings of his opponents. If a player won more games than he was expected to win, his rating would be adjusted upward, while if he won fewer games than expected his rating would be adjusted downward. Moreover, that adjustment was to be in exact linear proportion to the number of wins by which the player had exceeded or fallen short of his expected number of wins.
Implementing Elo's scheme
The USCF (United States Chess Federation) implemented Elo's suggestions in 1960, and the system quickly gained recognition as being both fairer and more accurate than the older Harkness system. Elo's system was adopted by FIDE in 1970, and by the WCU in 1972.
A batch consists of 25 games. However, a batch does not end during a tournament.
Inserting a late result can set off a lot of changes. Please ensure I receive results promptly.
You begin the season with your E1 rating. This is the one published in the WCU Yearbook. Use this all year for Tournament entry etc.
E2, E3, E4 ratings etc
Each batch has a different rating, E1, E2, E3 and so on.
You shall be rated against your opponent's current batch rating, and not necessarily against their E1 rating.
Your K factor determines how quickly your rating changes.
Performance can't be measured absolutely; it can only be inferred from wins and losses. Ratings therefore have meaning only relative to other ratings. Therefore, both the average and the spread of ratings can be arbitrarily chosen. Elo suggested scaling ratings so that a difference of 200 rating points in chess would mean that the stronger player has an expected score of approximately 0.75.
For each game you have an expected score.
To calculate the expected score from the 2 players ratings, use a normal distribution with standard deviation of 200 multiplied by the square root of 2.
You should score 36% against players rated 100 points higher than you.
Your expectancy is 0.36. If you win you have performed 0.64 better than expected.
This is multiplied by your K Factor. So, your rating increases by 20.48 for K=32, 15.36 for K=24 or 10.24 for K=16.