Chessmetrics

Chessmetrics is a system for rating chess players devised by Jeff Sonas. It is intended as an improvement over the Elo rating system.
Implementation.
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.
Formulas.
Performance rating adjustment after tournament:
Weighting of past tournaments (age in months):
Criticism.
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.
The system has also been described as "the most complete and resounding attempt made to determine the best chess player in history". However, the system is more accurate in measuring a player's success in competition than quality of play.
GM John Nunn also suggests that Chessmetrics can only be used to compare the level of a player against their peers and that it is not appropriate to use Chessmetrics to compare players of different era. He highlights 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 suggested to Nunn that his level of play was at best 2100 by today's standards.
Popularity.
The original article on Chessmetrics was published in Chessbase in October 2002. Since then, Chessmetrics has become reasonably well known and features numerous articles in Chessbase and The Week in Chess.
Chess author John L. Watson has also referred to Chessmetrics numbers.