This is a simple explanation of the Elo rating system in chess and Elo rating calculations with the examples. Mainly about FIDE, it is not meant to be complete, but to help you understand the system in simple and show you its elegance and beauty.
Page 1 and Page 2 are the main explanation on the Elo system, the next 2 Pages the additional. Page 3 is Chess Players Top List. Page 4 is valuable Chess FIDE Elo Links. To understand this chess site, you can click on the About link at the top right.
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Elo Rating System. General Description
First, please be informed that the introduction of the 1 July 2009 FIDE Rating System has been postponed until 1 July 2011 for taking a final decision… To understand the FIDE Rating System, effective now, read this page and the next one.
Then, you are recommended to find and click the Postponed 1 July 2009 FIDE Rating System link at the bottom of the next page within the Conclusion section. This will give you an idea of FIDE plans to change the rating calculations...
The Elo rating system is named after Dr.Arpad Elo, who improved the original chess rating system developed by Kenneth Harkness. It has been in use in the US since 1960 and was taken on by FIDE in 1970. It is twofold:
1. First. The Elo rating system shows how strong the player is. Chess Player A rated 2500 is stronger than Chess Player B rated 2000. But sometimes Player A loses Player B, and his or her Elo rating is going down while the weaker player's rating up...
2. Second. The Elo rating system calculates the results of a game, tournament, or chess event as numerical Elo results which are easy to read. For example, if your Performance Rating is 2570, you are performing like a strong International Master.
If your Performance Rating is 2451 and you have met the International Master norm requirements, you will get the International Master Norm. If your Performance Rating is 2601 and you have met the Grandmaster norm requirements, you will get the Grandmaster Norm.
If your Expected Result was 4.50 and you scored 4.5, your rating will no change. If your Expected Result was 7.28 and you scored 6, your rating will go down. If your Expected Result was 5.00 and you scored 5.5, your rating will go up...
The main Elo results in the Elo chess rating system are: Rating Increase/Decrease, Rating Change, New Rating, Performance Rating, Grandmaster/International Master Norm, Expected Result, Opponents' Average.
Please pay attention to the term "Elo chess rating system" in the above sentence. It is because the system is being used not only in chess, but in a number of other sports and computer games. But we will discuss here only chess.
The chess Elo rating system also uses K-factor or K-coefficient. The possible values of K-coefficient in FIDE are 10, 15, and 25. The second most commonly used K-factor value combination is 16, 24, and 32 in some systems. You will see what is K-factor or K-coefficient later...
Calculating Expected Result and Rating Change
The current Elo rating of the chess player changes after each game. The one-game Rating Change depends on:
• The player’s K-factor (10, 15, or 25 the possible K-factors in the FIDE system, but National Federations often use different values);
• The player’s score (1 for win, 0.5 for draw, or 0 for loss);
• The player’s expected result for the game (from 0.89 to 0.11 in the FIDE system, though many National Federations run it from 1.00 to 0.00).
Please notice that the FIDE range for the player’s expected result is 0.89 to 0.11 while many National Federations run it from 1.00 to 0.00. It is because FIDE has been using the rule of 350 points in rating difference since April 2006.
The rule of 350 points goes, " A difference in rating of more than 350 points shall be counted for rating purposes as though it were a difference of 350 points". If the rating difference between 2 chess players is less than 350 points, the rule of 350 points is not applied...
The expected result is the winning probability, as calculated based on the rating difference between the two players. If the rating difference is 0, each player has the winning probability 0.50. If it is 100, the stronger player has the winning probability 0.64 while the weaker 0.36.
The winning probability is calculated with a special formula which is not easy by itself. But let's take another approach and imagine the following. Player A rated 2400 and Player B rated 2300 have to play officially a 100-game chess tournament between themselves.
Before this long chess event starts, please remember that the rating difference between Player A and Player B is 100 (2400 - 2300), and Player A who is stronger has the winning probability 0.64, while player B who is weaker 0.36...
And now the main Elo idea. If Player A is as strong as 2400 and Player B as 2300, at the end of the chess tournament Player A will score 64 and Player B 36 for sure. If Player A scores only 55 and Player B manages to score 45, the Elo rating system will adjust their new ratings accordingly.
For Elo calculation of one-game Rating Change, let's meet again our friends Player A and Player B. Just 3 possibilities for a game for Player A: What will be one-game Rating Change for Player A if he win, loss, or make a draw playing with Player B?
Example 1 with K-factor of 10: Player A rated 2400, played against Player B rated 2300 and defeated him. The Rating Change for player A is therefore calculated as this (Result is 1, Expected Result 0.64):
Rating Change = K-factor * ( Result – Expected Result )
Rating Change = 10 * ( 1 – 0.64) = 10 * 0.36 = 3.6
Example 2 with K-factor of 10: Player A rated 2400, played against Player B rated 2300 and lost. The result for player A is therefore calculated as this (Result is 0, Expected Result 0.64):
Rating Change = K-factor * ( Result – Expected Result )
Rating Change = 10 * ( 0 – 0.64) = 10 * (- 0.64) = - 6.4
Example 3 with K-factor of 10: Player A rated 2400, played against Player B rated 2300 and made a draw. The result for player A is therefore calculated as this (Result is 0.5, Expected Result 0.64):
Rating Change = K-factor * ( Result – Expected Result )
Rating Change = 10 * ( 0.5 – 0.64) = 10 * (- 0.14) = - 1.4
If Player B were rated 2000, FIDE would calculate one-game Expected Result for Player A as 0.89 (rating difference is more than 350, Player A is stronger). If Player B were rated 2780, FIDE would calculate one-game Expected Result for Player A as 0.11 (rating difference is more than 350, Player A is weaker).
Please remember the FIDE rule of 350 points in simple: If the rating difference between 2 players is more than 350, then there are only 2 possible values for the Expected Result. For one game, it is 0.89 for the stronger player and 0.11 for the weaker player.
The Expected Result is very important for Elo calculation. It is the basis for calculating Rating Increase/Decrease, Rating Change, and New Rating. From the other hand, the Expected Result does not have any impact on the calculation of the Performance Rating, Grandmaster/International Master Norm, and Opponents' Average.
How is calculated the Expected Result for a multi-game tournament or chess event? Before, FIDE calculated it based on the simple rating difference between the player's own rating and his or her Opponents' Average. Some Chess Organizations may still use this method today. As for FIDE, it is a different picture now...
