Chessmetrics

Chessmetrics is a system for rating chess players devised by Jeff Sonas. It is intended as an improvement over the Elo rating system.

Chessmetrics is a weighted average of past performance. The score considers a player's win percentage against other players weighted by the ratings of the other players and the time elapsed since the match. A 10% increase in performance is equivalent to an increase of 85 rating points.

The weighting of previous matches digresses linearly from 100% for just-finished matches to zero for matches conducted more than two years ago.

Performance rating adjustment after tournament:

Weighting of past tournaments (age in months):

In 2006 economists Charles C. Moul and John V. C. Nye used Chessmetrics to determine the "expected" results of games, and wrote:

Ratings in chess that make use of rigorous statistics to produce good estimates of relative player strength are now relatively common, but comparing ratings across different time periods is often complicated by idiosyncratic changes (cf. Elo, 1968 for the pioneering discussion). Sonas uses the same rating formula throughout our sample and updates this rating monthly instead of annually, as is more common. Moreover, retrospective grading allows him to establish rankings that are unbiased estimates of the "true" relative strengths of players.

Jeff Sonas, Chessmetrics' author, claims that Chessmetrics has advantages over Elo ratings:

Chessmetrics occasionally gives strange-looking results, particularly for players with long periods of inactivity. For instance, World Chess Champion Emanuel Lasker was inactive for much of 1912–1914, and as a consequence dropped from #1 to #12 in the world in the Chessmetrics rankings, just before his famous victory ahead of all the world's other leading players at the 1914 Saint Petersburg chess tournament. Also, Chessmetrics included a 1903 match with Chigorin where Lasker was handicapped by having to play the Rice Gambit in every game; normally fixed-openings games are not counted for ratings. Neither of the contestants nor the general public thought it a real test of strength.

Chessmetrics can only be used to compare the level of a player against their peers; it is not appropriate to use Chessmetrics to compare players of different era. For example, GM John Nunn has highlighted the absurdity of attempts to compare the objective playing strengths of players from different eras: He used the example of Hugo Suechting, world ranked 27 and rated 2559 by Chessmetrics in 1911, after the Elite tournament in Karlsbad. An analysis of Suechting's games from that period suggests that his level of play was at best 2100 by today's standard.

...
Wikipedia