Chess rating system

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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 or US Chess), 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. Popular online chess sites such as chess.com and Internet Chess Club also implement rating systems. 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 Khachaturov proposed a similar system in 1946 (Hooper & Whyld 1992:332). 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.

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 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.

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

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

The Elo system was invented by Arpad Elo and is the most common rating system. It is used by FIDE and other organizations. Elo once stated that the process of rating players was in any case rather approximate; he compared it to "the measurement of the position of a cork bobbing up and down on the surface of agitated water with a yard stick tied to a rope and which is swaying in the wind". Any attempt to consolidate all aspects of a player's strength into a single number inevitably misses some of the picture, so the Elo system is the "best" approximation available now. 

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.

Elo scales, 1978

Rating range	Category
2700+	WORLD CHAMPIONSHIP contenders
2500–2700	most Grandmasters (GM)
2400–2500	most International Masters (IM) and some Grandmasters (GM)
2300–2400	FIDE Masters (FM)
2200–2300	FIDE Candidate Masters (CM), most national masters
2000–2200	candidate masters, experts (USA)
1800–2000	Class A, category 1
1600–1800	Class B, category 2
1400–1600	Class C, category 3
1200–1400	Class D, category 4
below 1200	novices

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. USCF ratings are generally 50 to 100 points higher than the FIDE equivalents. 

USCF rating categories

Category	Rating range
Senior master	2400 and up
National master	2200–2399
Expert	2000–2199
Class A	1800–1999
Class B	1600–1799
Class C	1400–1599
Class D	1200–1399
Class E	1000–1199
Class F	800–999
Class G	600–799
Class H	400–599
Class I	200–399
Class J	100–199

Example

Elo gives an example of calculating the rating of Lajos Portisch, a 2635-rated player who scored 10½ points in an actual tournament of 16 players. 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 Portisch 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-W_e), where K=10,

W=actual score, and W_e=expected score.

Portisch's new rating 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 

${\displaystyle R_{new}=R_{old}+{\frac {K}{2}}\left(W-L+{\frac {1}{2}}{\frac {\sum _{i}D_{i}}{C}}\right)}$

where R_new and R_old are the player's new and old rating respectively, D_i 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.

The example of Portisch with K = 10, with the sum of the rating differences being 1620 is

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

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

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. It now uses the Elo system.

Deutsche Wertungszahl

The Deutsche Wertungszahl system replaced the Ingo system in Germany. 

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. 

Universal Rating System

The Universal Rating System was developed by Mark Glickman, Jeff Sonas, J. Isaac Miller and Maxime Rischard, with the support of the Grand Chess Tour, the Kasparov Chess Foundation, and the Chess Club and Scholastic Center of Saint Louis. 

Chronology

• 1933 – The Correspondence Chess League of America (now ICCF U.S.A.) is the first national organization to use a numerical rating system. It chooses the Short system which clubs on the west coast of the US had used. In 1934 the CCLA switched to the Walt James Percentage System but in 1940 returned to a point system designed by Kenneth Williams.
• 1942 – Chess Review uses the Harkness system, an improvement of the Williams system.
• 1944 – The CCLA changes to an improved version of the Williams system devised by William Wilcock. A slight change to the system was made in 1949.
• 1946 – The USSR Chess Federation uses a non-numerical system to classify players.
• 1948 – The Ingo system is published and used by the West German Chess Federation.
• 1949 – The Harkness system is submitted to the USCF. The British Chess Federation adopts it later and uses it at least as late as 1967 (Harkness 1967:184).
• 1950 – The USCF starts using the Harkness system and publishes its first rating list in the November issue of Chess Life. Reuben Fine is first with a rating of 2817 and Sammy Reshevsky is second with 2770 (Lawrence 2009).
• 1959 – The USCF names Arpad Elo the head of a committee to examine all rating systems and make recommendations.
• 1961 – Elo develops his system and it is used by the USCF (Harkness 1967:184). It is published in the June 1961 issue of Chess Life (Elo 1978:197).
• 1970 – FIDE starts using the Elo system. Bobby Fischer is at the top of the list (Elo 1978:68,89).
• 1978 – Elo's book (The Rating of Chessplayers, Past and Present) on his rating system is published.
• 1993 – Deutsche Wertungszahl replaces the Ingo system in Germany.
• 2001 – the Glicko system is published.
• 2005 – Chessmetrics is published by Jeff Sonas.