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Friday, April 24, 2009

Rating Regulations in chess - The K-Factor

Effective July 1st,2009 the new FIDE Rating system comes into effect. An important consideration for the rating of chess players in the world is the K-factor or K-coefficient.The "K" factor represents an estimate of player rating volatility. The higher the value the more uncertain the prior rating is assumed to be, and therefore how rapidly a player's rating may change. Its value is determined from number of prior games, number of games played in the current event, and prior rating.

The Elo System

The system for rating chess players is named after Dr. Arpad Elo who improved the original one developed by Kenneth Harkness. It has been in use in the USA since 1960 and was taken on by FIDE in 1970. The system is twofold:
1. It shows how strong the player is: Player A rated 2400 is stronger than Player B rated 2300.
2. The system also calculates the results of a game, tournament, or chess event as numerical Elo results.
Originally designed as a chess rating system, nowadays it is also being used in a number of other sports.

The Main Elo Idea

Each chess player has chance to win a game. The stronger player, the more chances to win. FIDE uses a special winning probability table for a game which is based on the rating difference between the two opponents.
If the rating difference between the two is 0, each player has equal chances to win, and his or her winning probability is 0.50. If the rating difference is 100, the stronger player has the winning probability 0.64 while the weaker 0.36. Please remember 100, 0.64, and 0.36.

Let's imagine that Player A rated 2400 and Player B rated 2300 are to officially play 100 games. The rating difference being 100, the expected result for Player A is therefore 0.64 and for Player B 0.36. And now the main Elo idea follows...
If Player A is really playing as strong as 2400 and Player B as 2300, at the end of the event Player A will score 64 and Player B 36 for sure. If Player A scores only 55 (but not expected 64) and Player B 45 (more than expected 36), the Elo system will change their new ratings.

The K-factor

The Elo rating system uses the K-factor which is necessary for Elo calculation. The K-factor is assigned to the chess player, and its possible values in FIDE are 10, 15, and 25 as follows:
* 25 for players new to the rating list, until they have completed events with a total of at least 30 games.
* 15 for players with a rating under 2400.
* 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 the Rating Change

The current rating of the chess player changes after each game. The one-game Rating Change depends on:
* The player's K-factor.
* The player's score (1, 0.5, or 0).
* The player's Expected Result for a game.

Example 1. With the K-factor 10, Player A rated 2400 defeated Player B rated 2300. The Rating Change for Player A is therefore calculated as this:
Rating Change = K-factor x (Result - Expected Result)
Rating Change = 10 x (1 - 0.64) = 10 x 0.36 = 3.6

Example 2. With the K-factor 10, Player A rated 2400 lost to Player B rated 2300. In this case, the Rating Change for Player A is calculated as this:
Rating Change = K-factor x (Result - Expected Result)
Rating Change = 10 x ( 0 - 0.64) = 10 x (- 0.64) = - 6.4

Example 3. With the K-factor 10, Player A rated 2400 made a draw with Player B rated 2300. The Rating Change for Player A is now calculated as this:
Rating Change = K-factor x (Result - Expected Result)
Rating Change = 10 x (0.5 - 0.64) = 10 x (- 0.14) = - 1.4

Conclusion

The new rating of the chess player is calculated based on the rating change. Updated, the FIDE rating list is available online on 1 January, 1 April, 1 July, and 1 October. (source:http://www.abcarticledirectory.com/)

According to the new rating regulations:

The K-factor 10 disregarded, effective from 1 July 2009.
• The K-factor 15 disregarded, effective from 1 July 2009.
• The K-factor 25 disregarded, effective from 1 July 2009.

Instead:

• The New K-factor 20 introduced, effective from 1 July 2009.
• The New K-factor 30 introduced, effective from 1 July 2009.

2. The New K-factor Assignment

The New K-factor 30:
• As long as a player's rating remains under 2400.

The New K-factor 20:
• Once a player's published rating has reached 2400 and remains at that level subsequently, even if the rating drops below 2400.



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.


The K-factor is important to chess players who have FIDE chess ratings because of the fact that:


A player's
New Rating = Old Rating + Rating Change ... or ...
New Rating = Old Rating + K-factor * (Result - Expected Result)


Rating lists will be published every two months, the k-factor will change accordingly, the rating floor has been decreased from 1400 to 1200 and it will be more difficult to score norms. These are some of the important decisions that were taken during the FIDE Congress that was held during the Olympiad in Dresden.

According to GM Bartlomiej Macieja:
"publishing more frequently rating lists leads to an effective decrease of the development coefficient. To understand this effect it is enough to imagine a player rated 2500 playing one tournament a month. With 2 rating lists published yearly, if he wins 10 points in every tournament, his rating after half a year will be 2500+6*10=2560. If rating lists are published 4 times a year, after 3 months his rating becomes 2500+3*10=2530 so it gets more difficult for him to gain more rating points. After 3 more tournaments the player reaches the final rating only about 2500+3*10+3*6=2548. With 6 rating lists published yearly, the final rating of the player is only about 2500+2*10+2*7+2*5=2544. Obviously it is only an approximation, the exact values may slightly differ, however the effect is clear. It looks like FIDE officials “forgot” to increase the K-factor some years ago to compensate the effect of more frequent rating lists. Or they were not fully aware they should have changed the K-factor in order not to change the whole system. The increase of the K-factor is essential not for the reason to make the system more dynamic, but for the reason not to make the system less dynamic! Eventually, it has been decided to increase the value of the K-factor to K=20 + K=30. (source:http://www.chess-players.org/eng/news/viewarticle.html?id=735)

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