Chess Elo – How Elo-rating system works

How the Elo-rating system works in chess

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The Expected Result for a tournament or chess event is calculated individually as the sum of all expected results with each opponent. The FIDE rule of 350 points has impact on the Expected Result. Before, FIDE calculated Expected Result in another way, not individually.

Example 1 (the FIDE rule of 350 points not applied): Player A rated 2200, played 2 games against Player B rated 2300 and Player C rated 1950. The Expected Result for player A is therefore calculated as this:
Expected Result 1 (rating difference is 100, Player A is weaker) = 0.36
Expected Result 2 (rating difference is 250, Player A is stronger) = 0.81
Expected Result for Player A = 0.36 + 0.81 = 1.17

Example 2 (the FIDE rule of 350 points applied): Player A rated 2200, played 2 games against Player B rated 2600 and Player C rated 1950. The Expected Result for player A is therefore calculated as this:
Expected Result 1 (rating difference is more than 350 (400), Player A is weaker) = 0.11
Expected Result 2 (rating difference is 250, Player A is stronger) = 0.81
Expected Result for Player A = 0.11 + 0.81 = 0.92

Example 3 (the FIDE rule of 350 points applied): Player A rated 2200, played 2 games against Player B rated 2300 and Player C rated 1600. The Expected Result for player A is therefore calculated as this:
Expected Result 1 (rating difference is 100, Player A is weaker) = 0.36
Expected Result 2 (rating difference is more than 350 (600), Player A is stronger) = 0.89
Expected Result for Player A = 0.36 + 0.89 = 1.25

Calculating New Rating and K-factor

New Rating = Old Rating + Rating Change … or …
New Rating = Old Rating + K-factor * (Result – Expected Result)

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:

• 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;
• The K-factor is 15 for players with a rating under 2400;
• The K-factor is 10 once the player has reached 2400 and been registered for at least 30 games. Thereafter it remains permanently at 10, even if the player’s rating is under 2400 at a later stage.

Calculating Rating Increase/Decrease

Rating Increase/Decrease is very important for your Rating Change. If your Rating Increase is 0.15 and your K-factor 20, then your Rating Change will be 3. If your Rating Decrease is – 0.20 and your K-factor 10, then your Rating Change will be – 2.

Rating Increase/Decrease is actually not called like this. Officially, it is called in the FIDE Players’ Database as “change”. But let’s name it Rating Increase/Decrease for better understanding. It is an absolute value which can be plus, minus, or zero and is calculated as this:

Rating Increase/Decrease = Result – Expected Result

Example 1: Player A in a 9-game chess tournament scored 5.5 and his Expected Result was 4.0. The Rating Increase/Decrease for player A is therefore calculated as this:
Rating Increase = 5.5 – 4.0 = 1.5

Example 2: Player A in a 5-game chess event scored 1.5 and his Expected Result was 3.5. The Rating Increase/Decrease for player A is therefore calculated as this:
Rating Decrease = 1.5 – 3.5 = – 2.0

Example 3: Player A in a 9-game chess tournament scored 4.5 and his Expected Result was 4.5. The Rating Increase/Decrease for player A is therefore calculated as this:
Rating Increase/Decrease = 4.5 – 4.5 = 0

Calculating Performance Rating

Performance Rating = Opponents’ Average + Performance Change

Performance Change is based on the Performance Ratio. If a player scored 9 in 9 games, his or her Performance Ratio is 1.00 and Performance Change + 677. If he scores 4.5 in 9 games, it is correspondingly 0.50 and Performance Change will be 0. The needed value is taken from the Table of Performance Change.

Please notice that your Performance Rating does not depend on your own rating but does depend on your Opponents’ Average and “how you performed” (Performance Change). Performance Rating is very important for getting the Grandmaster and International Master Norms.

In some Chess Organizations, the Performance Rating is calculated with “the algorithm of 400”: If you win, add 400 to the opponent’s rating; if lose, subtract 400, if you make a draw, no change. Then find the average.

Calculating Grandmaster and International Master Norms

The Grandmaster or International Master Norm is the minimum score at which the player may get the norm. The Grandmaster or International Master Norm is possible under the following 2(two) conditions:

1. The player must meet the FIDE norm requirements.
2. The player’s score must provide, at least, the minimum Performance Rating needed for the norm.

The following is some of the FIDE norm requirements:
• At minimum, 9 games played;
• At least 50% of the opponents must be titled;
• For a GM norm, at least 3 of the opponents must be GMs;
• Maximum 22% of the opponents can be unrated.

The following minimum Performance Rating is needed:
• 2601 for the Grandmaster Norm;
• 2451 for the International Master Norm;
• 2401 for the Woman Grandmaster Norm;
• 2251 for the Woman International Master Norm.

You can get the International Master Title if you have 3(three) 9-game-tournament’s International Master Norms, and if FIDE recalculated your current rating at 2400 even once. You can get the Grandmaster Title if you have 3(three) 9-game-tournament’s Grandmaster Norms, and if FIDE recalculated your current rating at 2500 even once.

Calculating Opponents’ Average

There is no need to explain Opponents’ Average; it is quite understandable. The only thing you must remember is that the FIDE rule of 350 points in rating difference has impact on Opponents’ Average too as shown below.

If you are rated 2350, and 2 your opponents 1800 each, the FIDE average of your opponents will be 2000, but not 1800 as expected. If you are rated 2150, and 2 your opponents 2600 each, the FIDE average of your opponents will be 2500, but not 2600 as expected.

Conclusion

Elo rating is often used to mean a player’s chess rating as calculated by FIDE. However, other Chess Organizations, National Federations, Internet Servers, and so one have adopted Elo’s and Harkness’ general ideas, but added their own rules to them.

Some Chess Federations have their own rating scale categories for the chess players. Please click on the following link for reference on the FIDE Rating Scale Categories.

Elegant and beautiful, this is the Elo-rating system which was named after its creator Arpad Emrick Elo who had improved the original Harkness’ rating system…

On the next page, you can find the Internet links which will direct you to the FIDE Players’ Database, Tables, Norm requirements, more detailed information on the FIDE rating system. You can also find the link to Elo Calculator for FIDE chess players.

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© 2008 Bohdan Vovk

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