Elo Calculator for FIDE at chesselo.com
 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 Elo system in simple and show you its beauty.
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Elo Rating System: General Description
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 is 2450 and you have met the International Master norm requirements, you will get the IM Norm. If your Performance is 2600 and you have met the Grandmaster norm requirements, you will get the GM Norm.
If you have 3 Grandmaster Norms and you hit anytime the current rating 2500 (once is enough, only once, then the current rating may go down or up, does not matter before the norm or after), you will become a Grandmaster.
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 Kfactor or Kcoefficient. The possible values of Kcoefficient in FIDE are 10, 20, and 40. The second most commonly used Kfactor value combination is 16, 24, and 32 in some other systems...
Important. Please be informed that the new Kfactors 10, 20, and 40 were introduced from 1 July 2014 instead of the old ones 10, 15, and 30. The old ones 10, 15, and 30 were in force from 1 November 2011 until 1 July 2014.
Note. Before 1 November 2011 the values of Kfactor were 10, 15, 25.
Calculating Expected Result and Rating Change
The current Elo rating of the chess player changes after each game. The onegame Rating Change depends on: • The player’s Kfactor (10, 20, or 40 the possible Kfactors 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 0.92 to 0.08 in the FIDE system, though many National Federations run it from 1.00 to 0.00).
Note. According to the FIDE rules, the Kfactor 10, 20, or 40 is used for rating calculations in all standard chess tournaments. In rapid and blitz chess tournaments, the only Kfactor 20 is used for all chess players.
Please notice that the FIDE range for the player’s expected result is 0.92 to 0.08 while many National Federations run it from 1.00 to 0.00. It is because FIDE has been using the rule of 400 points in rating difference since 1 July 2009.
The rule of 400 points goes, "A difference in rating of more than 400 points shall be counted for rating purposes as though it were a difference of 400 points". If the rating difference between 2 chess players is less than 400 points, the rule of 400 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 2000 and Player B rated 1900 have to officially play a 100game chess tournament between themselves.
Before this long chess event starts, please remember that the rating difference between Player A and Player B is 100 (2000  1900), 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 playing as strong as 2000 and Player B as 1900, 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 onegame 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 onegame Rating Change for Player A if he win, loss, or make a draw playing with Player B?
Example 1 with Kfactor of 10: Player A rated 2000, played against Player B rated 1900 and defeated him. The Rating Change for player A is therefore calculated as this (Result is 1, Expected Result 0.64): Rating Change = Kfactor * ( Result – Expected Result ) Rating Change = 10 * ( 1 – 0.64) = 10 * 0.36 = 3.6
Example 2 with Kfactor of 10: Player A rated 2000, played against Player B rated 1900 and lost. The result for player A is therefore calculated as this (Result is 0, Expected Result 0.64): Rating Change = Kfactor * ( Result – Expected Result ) Rating Change = 10 * ( 0 – 0.64) = 10 * ( 0.64) =  6.4
Example 3 with Kfactor of 10: Player A rated 2000, played against Player B rated 1900 and made a draw. The result for player A is therefore calculated as this (Result is 0.5, Expected Result 0.64): Rating Change = Kfactor * ( Result – Expected Result ) Rating Change = 10 * ( 0.5 – 0.64) = 10 * ( 0.14) =  1.4
If Player B were rated 1400, FIDE would calculate onegame Expected Result for Player A as 0.92 (rating difference is more than 400, Player A is stronger). If Player B were rated 2450, FIDE would calculate onegame Expected Result for Player A as 0.08 (rating difference is more than 400, Player A is weaker).
Please remember the FIDE rule of 400 points in simple: If the rating difference between 2 players is more than 400, then there are only 2 possible values for the Expected Result. For one game, it is 0.92 for the stronger player and 0.08 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 the Expected Result is calculated for a multigame 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...
On the next page, we will discuss Expected Result, New Rating and Kfactor, Rating Increase/Decrease, Performance Rating, Grandmaster and International Master Norms, Opponents' Average...
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