Chess Elo Page 2 [for mobile]

Expected Result and Rating Change

The current chess rating of the chess player changes after each game. The one-game Rating Change depends on:
• The player’s K-factor (10, 15 or 30 the possible K-factors in FIDE);

• 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).

Rating Change is calculated with this formula:
Rating Change = K-factor * (Result – Expected Result)
At the bottom of this page you will see 3 calculation examples. But before we must understand some details…

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.

If it is 50, the stronger player has the winning probability 0.57 while the weaker 0.43. If it is 150, the stronger player has the winning probability 0.70 while the weaker 0.30. If it is 200, the stronger player has the winning probability 0.76 while the weaker 0.24. If 300, it is 0.89 and 0.11.

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 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 (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 one-game Rating Change, let’s meet again Player A and Player B. Just 3 possibilities for a chess 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 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 = 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 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 = 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 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 = K-factor * ( Result – Expected Result )
Rating Change = 10 * ( 0.5 – 0.64) = 10 * (- 0.14) = – 1.4

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