Letter #43 -  2010

Sub:    ELO calculation
Date:   10/22/10  12:58:37 AM EDT
From:  Mateo Bernal
To:      service@Chess-poster.com

Greetings.

I would like to know what is the mathematic formula used to calculate an ELO rating.

Thank you very much.

Dear viewer,

The ELO system is based on the rating of the player and rating of the opponents, and that the rating is adjusted based on how the player's actual result compares with the expected result.

A "K-factor" (K-coefficient) is a constant used to make the adjustment. If, on the basis of the ratings, a player is expected to score 5 points out of 10, but only scores 3, then the player would lose 2 times the K-factor. If the player scored 7, then the player would gain 2 times the K-factor. Now, if the player scores 5 points, no change would take place.

The K-factor is assigned, and it may range from 10 to 45 for different Chess organizations. FIDE uses the following rules to the K-factor:

1. The K-factor is 25 for players new to the rating list, until they have completed events with a total of at least 30 games.

2. The K-factor is 15 for players with a rating under 2400.

3. The K-factor is 10 once the player has reached 2400 and been registered for at least 30 games.

4. Thereafter, the K-factor remains permanently at 10, even if the player’s rating is under 2400 at a later stage.

Next, an example of calculating the rating of player X, a 2635 rated player, in a tournament of 16 players, and scoring 10½ points.

First, the difference in rating is calculated for each other player, subtracting the other player's rating from Player X rating. Then the expected score against each player is determined from a table, based on this rating difference.

Now, an opponent was player Y, who was rated at 2600; the rating difference of 35 gave player X an expected score of 0.55. The expected score is summed for each opponent, giving player X a total expected score of 9.66.

Then the formula is:

new_rating= old_rating+K×(W-We), (where K=10, W= actual_score, and We= expected_score.)

or,

2635+10×(10.5-9.66)= 2643.4 (the new ELO rating for player X.)

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