Chess rating system

A chess rating system is a system used in chess to estimate the strength of a player, based on their 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, Lichess, 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 . 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.
This was the system of the West German Chess Federation from 1948 until 1992, designed by Anton Hoesslinger and published in 1948. It was replaced by an Elo system, Deutsche Wertungszahl. It influenced some other rating systems. 
It is simple. New players receive a high, fixed starting score. Players' new ratings centre on the average rating of entrants to their competition: then if having achieved better than a net draw set of result, "minus" the amount of percentage points it is over 50% (e.g. a 12–4 or 24–8 wins-to-losses result is, as ever, noted as a 75% tournament outcome) – if having achieved worse than this then the amount, again in percent, is "added" to the average of the tournament entrants' scores; thus in all cases recalibrating all players after each tournament completely. A consequence is at most 50 points gained or shed per tournament (namely by a totally winning or totally losing participant) away from the "tournament average". Unlike other modern, nationally-used chess systems, lower numbers indicate better performance.
Harkness system.
This system was noted in "Chess Review" by tournament organizer Kenneth Harkness, who expounded his invention of it in articles of 1956, 14 years later. It was used by the USCF from 1950 to 1960 and other leagues.
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 per percentage point exceeding 50. If they score less, their new rating is the competition average minus 10 points per percentage point shy of 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 .
English Chess Federation system.
The English Chess Federation Grading System was devised by Richard W. B. Clarke, published in 1958. Each game has a large potential effect. Points (grades) are never immediately effective for every game won, lost or drawn, in a registered competition (including English congresses, local and county leagues, and registered, approved team events) but are averaged into personal grade (ECF Grade) over a cycle of at least 30 games. 
A player's contributing score for such averaging is taken to be his or her opponent's grade (but the gap is deemed to be 40 points, if greater than such a grade gap). However this is adjusted by adding 50 points for a win, subtracting 50 points for a loss, and making no adjustment, for a draw. Negative grades are deemed to be nil, so a personal score of 50 arose quickly in the lower leagues and experienced novices aspire to a 100 grading. The cyclical averaging and cycle-persistent Grades are its hallmarks. The maximum gain in a single cycle is 90 points, which would entail beating much higher-rated opponents at every match. The opposite applies to losses.
The ECF grades (confirms personal averages) for about 200,000 games a year. An ECF grade approximates to an Elo rating by multiplying by 7.5 and adding 700 so 100 "ECF" is about 1450 "Elo"; 200 "ECF" is about 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.
FIDE divides all its normal tournaments into categories by a narrower 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. Women's tournaments currently commence 200 points lower, including its Category 1.
The USCF uses the USCF system, a modification of the Elo system, in which the K factor varies and it gives bonus points for superior performance in a tournament. USCF ratings are generally 50 to 100 points higher than the FIDE equivalents.
Example.
Elo gives an example of amending the rating of Lajos Portisch, a 2635-rated player before his tournament, who scores 10½ points of a possible 16 winning points (as this is against 16 players). First, the difference in rating is recorded for each other player he faced. Then the expected score, against each, is determined from a table, which publishes this for every band of 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". This is an impossible score as not 0, or 1 but as this is higher than 0.5 even a draw will very slightly damage Portisch's rating; conversely a draw will very slightly improve Hort's rating.
Portisch's expected score is summed for each of his matches, which gave a total expected score of 9.66. Then the formula is:
K is 10; W is the actual match/tournament score; We is the 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, negating the need for look-up tables of expected score. With that method, a player's new rating is
formula_1
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: 
formula_2
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, is a more modern approach, which was invented by Mark Glickman as an improvement of the Elo system. The Glicko-2 system is a refinement and is used by Chess.com, Australian Chess Federation and some other online websites.
Turkey UKD system.
TSF(Turkey Chess Federation) uses Ukd system.
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.
Rating Systems using Computers as a Reference.
Many rating systems give a rating to players at a given time, but cannot compare players from different eras. In 2006, Matej Guid and Ivan Bratko pioneered a new way of rating players, by comparing their moves against the recommended moves of a chess engine. The authors used the program Crafty and argued that even a lower-ranked program (Elo around 2700) could identify good players. In their follow-up study, they used Rybka 3 to estimate chess player ratings.
In 2017, Jean-Marc Alliot compared players using Stockfish 6 with an ELO rating around 3300, well above top human players.
External links.
Liches.org or chess.com