Chess rating system

A chess rating system is a system used in chess to calculate an estimate of the strength of the player, based on his or her performance versus other players. They are used by organizations such as FIDE, the US Chess Federation (USCF), International Correspondence Chess Federation, and the English Chess Federation. Most of the systems are used to recalculate ratings after a tournament or match but some are used to recalculate ratings after individual games. In almost all systems a higher number indicates a stronger player. In general, players' ratings go up if they perform better than expected and down if they perform worse than expected. The magnitude of the change depends on the rating of their opponents. The Elo rating system is currently the most widely used.

The first modern rating system was used by the Correspondence Chess League of America in 1939. Soviet player Andrey Khachatoruv proposed a similar system in 1946. The first one that made an impact on international chess was the Ingo system in 1948. The USCF adopted the Harkness system in 1950. Shortly after, the British Chess Federation started using a system devised by Richard W. B. Clarke. The USCF switched to the Elo rating system in 1960, which was adopted by FIDE in 1970 (Hooper & Whyld 1992:332).

Ingo system

The Ingo system was designed by Anton Hoesslinger and published in 1948. It was used by the West German Chess Federation from 1948 until 1992, when it was replaced by an Elo-based system, Deutsche Wertungszahl. It influenced some other rating systems. This is a simple system where players' new ratings are the average rating of their competition minus one point for each percentage point above 50 obtained in the tournament. Unlike most other systems, lower numbers indicate better performance (Harkness 1967:205–6).

Harkness system

The Harkness System was invented by Kenneth Harkness, who published it in 1956. It was used by the USCF from 1950 to 1960 and by some other organizations.

When players compete in a tournament, the average rating of their competition is calculated. If a player scores 50%, they receive the average competition rating as their performance rating. If they score more than 50%, their new rating is the competition average plus 10 points for each percentage point above 50. If they score less than 50%, their new rating is the competition average minus 10 points for each percentage point below 50 (Harkness 1967:185–88).

Harkness rating categories
CategoryRating range
Grandmaster2600 and up
Senior master2400–2599
Master2200–2399
Expert2000–2199
Class A1800–1999
Class B1600–1799
Class Cunder 1600

Example

A player with a rating of 1600 plays in an eleven-round tournament and scores 2½–8½ (22.7%) against competition with an average rating of 1850. This is 27.3% below 50%, so their new rating is 1850 – (10 × 27.3) = 1577 (Harkness 1967:187).

English Chess Federation system

Main article: ECF grading system

The English Chess Federation (formerly British Chess Federation) Grading System was devised by Richard W. B. Clarke and first published in 1958. Points are scored for every game played in a registered competition (generally, English congresses, local and county leagues, and other team events). A player's grade is calculated by taking the opponent's grade and adding 50 points for a win, subtracting 50 points for a loss, and taking the opponent's grade as it stands for a draw. For grading purposes it is assumed that the opponent's grade is never more than 40 points above or below one's own. The ECF grades approximately 200,000 games a year. The grading season runs from 1 June to 31 May. An ECF grade can be approximated to an Elo rating by multiplying by 7.5 and adding 700. An ECF grade of 100 is approximately 1450 Elo, while 200 ECF equals 2200 Elo.

Elo rating system

Main article: Elo rating system

The Elo system was invented by Arpad Elo and is the most common system. It is used by FIDE and other organizations.

FIDE classifies tournaments into categories according to the average rating of the players. Each category is 25 rating points wide. Category 1 is for an average rating of 2251 to 2275, category 2 is 2276 to 2300, etc. For women's tournaments, the categories are 200 rating points lower, so a Category 1 is an average rating of 2051 to 2075, etc.[1]

Elo scales, 1978[2]
Rating rangeCategory
2600+World Championship contenders
2400–2600most Grandmasters (GM) and International Masters (IM)
2300–2400FIDE Masters (FM)
2200–2300FIDE Candidate Masters (CM), most national masters
2000–2200candidate masters, experts (USA)
1800–2000Class A, category 1
1600–1800Class B, category 2
1400–1600Class C, category 3
1200–1400Class D, category 4
below 1200novices

The USCF uses a modification of the Elo system, where the K factor varies and there are bonus points for superior performance in a tournament. The USCF classifies players according to their rating (Just & Burg 2003:259–73). USCF ratings are generally 50 to 100 points higher than the FIDE equivalents (Just & Burg 2003:112).

USCF rating categories
CategoryRating range
Senior master2400 and up
National master2200–2399
Expert2000–2199
Class A1800–1999
Class B1600–1799
Class C1400–1599
Class D1200–1399
Class E1000–1199
Class F800–999
Class G600–799
Class H400–599
Class I200–399
Class J100–199

Example

Elo gives an example of calculating the rating of Lajos Portisch, a 2635-rated player, in an actual tournament of 16 players, and scored 10½ points. First the difference in rating is calculated for each other player, subtracting the other player's rating from Portisch's rating. Then the expected score against each player is determined from a table, based on this rating difference. For instance, one opponent was Vlastimil Hort, who was rated at 2600. The rating difference of 35 gave Portish an expected score of 0.55. The expected score is summed for each opponent, giving Portisch 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.

Portisch's new rating (Elo 1978:37) is 2635+10×(10.5–9.66)=2643.4.

Linear approximation

Elo devised a linear approximation to his full system. With that method, a player's new rating is

R_{ new } = R_{ old } + \frac{ K }{ 2 } \left( W - L + \frac{ 1 }{ 2 } \frac{ \sum_i D_i }{ C } \right )

where Rnew and Rold are the player's new and old rating respectively, Di is the opponent's rating minus the player's rating, W is the number of wins, L is the number of losses, C = 200 and K = 32. (Elo 1978:28–29)

The example of Portisch with K = 10, with the sum of the rating differences being 1620 is:[3] (Elo 1978:39)

2635 + \frac{ 10} { 2 } \left( 10.5 - 4.5 - \frac{ 1 }{ 2 } \frac{ 1620 }{ 200 } \right) = 2644.75

The USCF used a modification of this system to calculate ratings after individual games of correspondence chess, with a K = 32 and C = 200.[4]

Glicko rating system

Main article: Glicko rating system

The Glicko system was invented by Mark E. Glickman as an improvement of the Elo system. The Glicko-2 system is a refinement and is used by the Australian Chess Federation and some online playing sites.

USA ICCF system

The ICCF U.S.A. used its own system in the 1970s. Now it uses the Elo system.

Deutsche Wertungszahl

Main article: Deutsche Wertungszahl

The Deutsche Wertungszahl system replaced the Ingo system in Germany.

Chessmetrics

Main article: Chessmetrics

The Chessmetrics system was invented by Jeff Sonas. It is based on computer analysis of a large database of games and is intended to be more accurate than the Elo system.

Chronology

See also

Notes

  1. ↑ FIDE Handbook, Section B.0.0, FIDE web site
  2. ↑ Elo, 1978, p. 18
  3. ↑ Elo's book has the incorrect 2645.75. This calculation also uses K = 10.
  4. ↑ USCF CC
  5. ↑ Glickman website
  6. ↑ Chessmetrics website

References

External links