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Apr 9, Apr 10, Sep 26, Feb 23, First of all, let's not pretend chess players don't care about ratings.
We do. Mar 17, Apr 17, May 10, Log In or Join. Forums Hot Topics. The USCF implemented Elo's suggestions in , and the system quickly gained recognition as being both fairer and more accurate than the Harkness system.
Elo's system was adopted by FIDE in Elo described his work in some detail in the book The Rating of Chessplayers, Past and Present , published in Subsequent statistical tests have shown that chess performance is almost certainly not normally distributed.
Weaker players have significantly greater winning chances than Elo's model predicts. However, in deference to Elo's contribution, both organizations are still commonly said to use "the Elo system".
Each organization has a unique implementation, and none of them precisely follows Elo's original suggestions. It would be more accurate to refer to all of the above ratings as Elo ratings, and none of them as the Elo rating.
Instead one may refer to the organization granting the rating, e. In the whole history of FIDE rating system, only 39 players to April , sometimes called "Super-grandmasters", have achieved a peak rating of or more.
However, due to ratings inflation, nearly all of these are modern players: all but two of these achieved their peak rating after Several chess computers are said to perform at a greater strength than any human player, although such claims are difficult to verify.
Computers do not receive official FIDE ratings. Matches between computers and top grandmasters under tournament conditions do occur, but are comparatively rare.
Also most computer players are software packages, making their playing strength and hence their rating dependent on the computer they are running on.
The Grand Master model K has an estimated Elo rating of ! As of April , the Hydra supercomputer was possibly the strongest "over the board" chess player in the world; its playing strength is estimated by its creators to be over on the FIDE scale.
This is consistent with its six game match against Michael Adams in in which the then seventh-highest-rated player in the world only managed to score a single draw.
However, six games are scant statistical evidence and Jeff Sonas suggested that Hydra was only proven to be above by that single match taken in isolation.
On a slightly firmer footing is Rybka. As of January , Rybka is rated by several lists within , depending on the hardware it is run on and the version of software used.
Without such calibration, different rating pools are independent, and can only be used for relative comparison within the pool.
The primary goal of Elo ratings is to accurately predict game results between contemporary competitors, and FIDE ratings perform this task relatively well.
A secondary, more ambitious goal is to use ratings to compare players between different eras. It would be convenient if a FIDE rating of meant the same thing in that it meant in If the ratings suffer from inflation , then a modern rating of means less than a historical rating of , while if the ratings suffer from deflation , the reverse will be true.
Unfortunately, even among people who would like ratings from different eras to "mean the same thing", intuitions differ sharply as to whether a given rating should represent a fixed absolute skill or a fixed relative performance.
Those who believe in absolute skill including FIDE would prefer modern ratings to be higher on average than historical ratings, if grandmasters nowadays are in fact playing better chess.
By this standard, the rating system is functioning perfectly if a modern rated player would have a fifty percent chance of beating a rated player of another era, were it possible for them to play.
Time travel is widely believed to be impossible, but the advent of strong chess computers allows a somewhat objective evaluation of the absolute playing skill of past chess masters, based on their recorded games.
Those who believe in relative performance would prefer the median rating or some other benchmark rank of all eras to be the same.
By one relative performance standard, the rating system is functioning perfectly if a player in the twentieth percentile of world rankings has the same rating as a player in the twentieth percentile used to have.
Ratings should indicate approximately where a player stands in the chess hierarchy of his own era. The average FIDE rating of top players has been steadily climbing for the past twenty years, which is inflation and therefore undesirable from the perspective of relative performance.
However, it is at least plausible that FIDE ratings are not inflating in terms of absolute skill. Perhaps modern players are better than their predecessors due to a greater knowledge of openings and due to computer-assisted tactical training.
In any event, both camps can agree that it would be undesirable for the average rating of players to decline at all, or to rise faster than can be reasonably attributed to generally increasing skill.
Both camps would call the former deflation and the latter inflation. Not only do rapid inflation and deflation make comparison between different eras impossible, they tend to introduce inaccuracies between more-active and less-active contemporaries.
Performance can only be inferred from wins, draws and losses. Therefore, if a player wins a game, they are assumed to have performed at a higher level than their opponent for that game.
Conversely, if the player loses, they are assumed to have performed at a lower level. If the game is a draw, the two players are assumed to have performed at nearly the same level.
Elo did not specify exactly how close two performances ought to be to result in a draw as opposed to a win or loss.
To simplify computation even further, Elo proposed a straightforward method of estimating the variables in his model i. One could calculate relatively easily from tables how many games players would be expected to win based on comparisons of their ratings to those of their opponents.
The ratings of a player who won more games than expected would be adjusted upward, while those of a player who won fewer than expected would be adjusted downward.
Moreover, that adjustment was to be in linear proportion to the number of wins by which the player had exceeded or fallen short of their expected number.
From a modern perspective, Elo's simplifying assumptions are not necessary because computing power is inexpensive and widely available.
Moreover, even within the simplified model, more efficient estimation techniques are well known. Several people, most notably Mark Glickman , have proposed using more sophisticated statistical machinery to estimate the same variables.
On the other hand, the computational simplicity of the Elo system has proven to be one of its greatest assets.
With the aid of a pocket calculator, an informed chess competitor can calculate to within one point what their next officially published rating will be, which helps promote a perception that the ratings are fair.
The USCF implemented Elo's suggestions in ,  and the system quickly gained recognition as being both fairer and more accurate than the Harkness rating system.
Subsequent statistical tests have suggested that chess performance is almost certainly not distributed as a normal distribution , as weaker players have greater winning chances than Elo's model predicts.
Significant statistical anomalies have also been found when using the logistic distribution in chess. The table is calculated with expectation 0, and standard deviation The normal and logistic distribution points are, in a way, arbitrary points in a spectrum of distributions which would work well.
In practice, both of these distributions work very well for a number of different games. Each organization has a unique implementation, and none of them follows Elo's original suggestions precisely.
It would be more accurate to refer to all of the above ratings as Elo ratings and none of them as the Elo rating. Instead one may refer to the organization granting the rating.
There are also differences in the way organizations implement Elo ratings. For top players, the most important rating is their FIDE rating.
FIDE has issued the following lists:. A list of the highest-rated players ever is at Comparison of top chess players throughout history.
Performance rating is a hypothetical rating that would result from the games of a single event only. Some chess organizations [ citation needed ] use the "algorithm of " to calculate performance rating.
According to this algorithm, performance rating for an event is calculated in the following way:. This is a simplification, but it offers an easy way to get an estimate of PR performance rating.
Permanent Commissions, A simplified version of this table is on the right. 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 to , category 2 is to , etc. For women's tournaments, the categories are rating points lower, so a Category 1 is an average rating of to , etc.
The top categories are in the table. FIDE updates its ratings list at the beginning of each month. In contrast, the unofficial "Live ratings" calculate the change in players' ratings after every game.
The unofficial live ratings of players over were published and maintained by Hans Arild Runde at the Live Rating website until August Another website, chess.
Rating changes can be calculated manually by using the FIDE ratings change calculator. In general, a beginner non-scholastic is , the average player is , and professional level is The K-factor , in the USCF rating system, can be estimated by dividing by the effective number of games a player's rating is based on N e plus the number of games the player completed in a tournament m.
The USCF maintains an absolute rating floor of for all ratings. Thus, no member can have a rating below , no matter their performance at USCF-sanctioned events.
However, players can have higher individual absolute rating floors, calculated using the following formula:. Higher rating floors exist for experienced players who have achieved significant ratings.
Such higher rating floors exist, starting at ratings of in point increments up to , , , A rating floor is calculated by taking the player's peak established rating, subtracting points, and then rounding down to the nearest rating floor.
Under this scheme, only Class C players and above are capable of having a higher rating floor than their absolute player rating.
All other players would have a floor of at most There are two ways to achieve higher rating floors other than under the standard scheme presented above.
Grischuk Grischuk. Mamedyarov Mamedyarov. So So. Radjabov Radjabov. Giri Giri. Wang Hao Wang Hao. Rapport Rapport. Dominguez Perez Dominguez Perez.
Karjakin Karjakin. Anand Anand. Even when we are at our best, we can still slip up and make a game-losing blunder.
Lower-rated players can still beat someone who is rated higher than them, and the Elo system calculates the probability of that happening.
However, if both players face each other in a match of multiple games, the player with the higher rating probably wins most of the games.
Another feature of this system is that the rating gap between the players dictates how many points they can win or lose. Since a much higher rated player is expected to win, they do not receive a lot of points for a victory against a player rated much lower.
Their opponent also does not lose a significant amount of points for the defeat. In turn, when the lower-rated player wins, this achievement is considered much more significant, and that player's reward is more points added to their rating.
The higher-rated player, though, is penalized accordingly. To determine the exact amount of points a player would win or lose after a game, several complex mathematical calculations are needed.Annals of Mathematical Statistics. In one of his articles, he emphasizes: "The measurement of the rating of an individual might well be compared with the measurement of the position of a cork bobbing up and down on the surface of agitated water with a yardstick tied to a rope and which is swaying in the wind. Line Color, six games are scant statistical Kudos Casino and Jeff Sonas suggested that Hydra was only proven to be above by that single match taken in isolation. On a slightly firmer footing is Rybka.