[1] 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.
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.
[3] This was the system of the West German Chess Federation from 1948 until 1992, designed by Anton Hoesslinger and published in 1948.
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 number 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 number, again in percent, is added to the average of the tournament entrants' scores; thus in all cases recalibrating all players after each tournament completely.
Unlike other modern, nationally used chess systems, lower numbers indicate better performance.
[4] 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.
The maximum gain in a single cycle is 90 points, which would entail beating much higher-rated opponents at every match.
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".
[8] 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.
Women's tournaments currently commence 200 points lower, including its Category 1.
Then the expected score, against each, is determined from a table, which publishes this for every band of rating difference.
Elo devised a linear approximation to his full system, negating the need for look-up tables of expected score.
[15] The USCF used a modification of this system to calculate ratings after individual games of correspondence chess, with a K = 32 and C = 200.
TSF (Turkey Chess Federation) uses a combination of ELO and UKD system.
It is based on computer analysis of a large database of games and is intended to be more accurate than the Elo system.
[19] In their follow-up study, they used Rybka 3 to estimate chess player ratings.