Bassem Amin Nigel Short David Howell Jeffery Xiong Aleksej Dreev Oleksandr Beljavs'kyj Maxim Rodshtein Daniil Dubov Zachar Jefymenko Liviu Dieter Nisipeanu Evgenij Naer Ivan Sokolov Ferenc Berkes Michail Tal' Vadim Milov Jon Ludvig Hammer Emil Sutovskij Markus Ragger Michail Krasenkov Il'ja Smiryn Aleksandr Chalifman Zurab Azmaiparashvili Ihor Kovalenko Gabriel Sargsyan Gawain Jones Baskaran Adhiban Bei Computern ist die Verteilung nicht nur per Punkte-Definition gleich, sondern auch vom Kurvenverhalten her darüber hinaus sehr ähnlich, allerdings gibt es bei ähnlich starken Maschinen eine weitere Spielstärkenspreizung in den verschiedenen Partiephasen.

Auch Rundenturniere werden nach der durchschnittlichen Elo-Zahl der Teilnehmer in Kategorien eingeteilt.

Hierbei entspricht ein Unterschied um eine Kategorie 25 Elo-Punkten. Die zurzeit stärksten Turniere erreichen die Kategorie 22, was einem Durchschnitt von bis Elo-Punkten entspricht.

Das Elo-System teilt die Schachspieler mit Hilfe einer Wertungszahl in neun Klassen ein, wobei die untere Grenze der obersten Klasse bei und die obere Grenze der untersten Klasse bei liegt.

Die Wertungszahlen eines einzelnen Spielers sind intervallskaliert und annähernd normalverteilt und schwanken mit einer Standardabweichung von um einen mittleren Wert.

Es gibt viele Spieler mit Spielstärken unter , das Elo-System ist auf diesem Spielniveau in der Vorhersagesicherheit aber nur eingeschränkt gültig.

Wichtig ist insbesondere auf Hobbyspielerniveau, dass ein Spieler seine Zahl auch gegen stärkere Gegner verteidigen kann, ohne sich auf besondere Eigenschaften wie unbewusste psychische Schwächen oder schlechtes Zeitmanagement von Neulingen konzentrieren zu müssen.

Utopisch hohe Werte werden durch Niederlagen schnell, exakt und zuverlässig korrigiert. Die recht stabile Elo-Zahl wird mit verschiedenen Verfahren ermittelt.

Manche gehen von wenigen Spielen aus oder von ähnlich starken Turnierteilnehmern , nach vielen Partien erreichen alle sehr ähnliche Gleichgewichte.

Ausgehend von dieser Hypothese lässt sich für zwei Gegner statistisch voraussagen, mit welcher Wahrscheinlichkeit der eine Spieler gewinnen wird.

Im Sonderfall der identischen Wertungszahl sind die Wahrscheinlichkeiten gleich hoch. Bei einem Turnier lässt sich anhand der Wertungszahl eines Spielers und des Durchschnitts der Wertungszahlen seiner Gegner voraussagen, welche Punktzahl er wahrscheinlich erzielen wird.

Nach Abschluss des Turniers wird das tatsächliche Ergebnis mit dem statistisch vorausgesagten Ergebnis verglichen und aus der Abweichung die neue Wertungszahl des Spielers errechnet.

Diese Folgerung ist aber keineswegs zwingend, da Wahrscheinlichkeits- bzw. Präferenzrelationen nicht notwendigerweise transitiv sind. Transitivität ist jedoch eine notwendige Voraussetzung für ein sinnvolles Rating-System.

Aus dieser Annahme folgt neben der Transitivität auch die oben dargestellte Multiplikativität der Erwartungswerte. Will man mithilfe der Elo-Zahlen — oder anderer Ratings, dies betrifft nicht nur das Elo-System — die Stärken von Spielern aus unterschiedlichen Epochen vergleichen, so sollte ein Rating von z.

Players whose ratings are too low or too high should, in the long run, do better or worse correspondingly than the rating system predicts and thus gain or lose rating points until the ratings reflect their true playing strength.

An Elo rating is a comparative rating only, and is valid only within the rating pool where it was established.

The Harkness system was reasonably fair, but in some circumstances gave rise to ratings which many observers considered inaccurate.

Elo's system replaced earlier systems of competitive rewards with a system based on statistical estimation.

Rating systems for many sports award points in accordance with subjective evaluations of the 'greatness' of certain achievements. For example, winning an important golf tournament might be worth an arbitrarily chosen five times as many points as winning a lesser tournament.

A statistical endeavor, by contrast, uses a model that relates the game results to underlying variables representing the ability of each player.

Elo's central assumption was that the chess performance of each player in each game is a normally distributed random variable.

Although a player might perform significantly better or worse from one game to the next, Elo assumed that the mean value of the performances of any given player changes only slowly over time.

Elo thought of a player's true skill as the mean of that player's performance random variable. A further assumption is necessary because chess performance in the above sense is still not measurable.

One cannot look at a sequence of moves and derive a number to represent that player's skill. 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 , [4] 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.

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