# How are chess players classified

## Elo rating

The **Elo rating** is a rating number that describes the skill level of go and chess players.

Arpad Elo developed the underlying objective scoring system in 1960 for the American chess federation USCF. It was taken over in 1970 by the world chess federation FIDE (at the congress in Siegen).

The World Chess Federation calls its system "FIDE rating system"; a rating in it is officially called "FIDE rating", but is usually simply referred to as "Elo rating". In addition to the international FIDE rating system, there are also national rating systems with different names. In Germany the national rating system is called DWZ, in Austria it is called *(national) Elo ratings* calculated and in Switzerland there is one *Leadership list* With *Leadership figures*. All these systems evaluate significantly more local tournaments, but also calculate the valuation numbers according to the methods of Arpad Elo with mostly only minor modifications and deviating factors.

### Calculation [edit | Edit source]

For example, someone who has just joined the chess club does not yet have an Elo rating. After a series of games against different players, your rating is first assessed. After this phase, the actual results of the games will be evaluated for the Elo points.

For the respective calculation of the new rating, the *expected score* important, which player A is likely to achieve against player B. The following applies: there is one point for a win, half a point for a draw and no point for a defeat.

**annotation**: If there was no draw, the expected number of points would be the probability that A wins. Since a game of chess can also end in a draw, the expected score is equal to the probability of winning plus one-half times the probability of drawing. The *Probabilities* For victory, draw and defeat, only those are not needed in the Elo system *Expected values*.

*E.*: Expected score for player A. In a series of 5 games, you can also_{A.}*E.*multiply by 5._{A.}*R.*: previous Elo rating of player A_{A.}*R.*: previous Elo rating of player B_{B.}

(If the rating difference is more than 400 points, the value 400 is used instead of the actual difference.)

The expected value for A is now *E. _{A.}* 100%. Player A's new rating is

*k*: is usually 15, for top players (Elo> 2400) 10, for fewer than 30 rated games 25*S.*: actual number of points played (1 for every win, 0.5 for every draw, 0 for every loss)_{A.}

**Note 1**: The number 400 contained in the formula and the original k-factor were chosen by Arpad Elo in such a way that the Elo numbers are as compatible as possible with the ratings of the rating system previously used by Kenneth Harkness. In fact, the Harkness model can be seen as a piecewise linear approximation to the Elo model.

**Note 2**: It can easily be shown in a mathematical way that *E.*_{A.} + *E.*_{B.} = 1 applies.

**Note 3**: The profit expectation of one player as a function of the point difference to the other is a logistical function in Elos model. To avoid any misunderstanding: That means, however *Not*that the game*strengthen* are modeled as logistically distributed random variables, because this is not the case - the property of the expected values characteristic of Elos model cannot be derived from any plausible distribution assumption (such as a normal distribution).

### An (invented) example [edit | Edit source]

The chess player Garri Kasparow (Elo: 2806) plays against the chess player Zsuzsa Polgár (Elo: 2577). According to the first formula, Kasparov (Player A) is expected to average against Polgar (Player B) *E. _{A.}* = 0.789 points per game gets:

After a game there are three options:

#### Polgar wins [edit | Edit source]

So *S. _{A.}* = 0. The new Elo scores

*R '*for Kasparov and

_{A.}*R '*for Polgar are

_{B.}So Kasparov loses eight Elo points, while Polgar gains eight Elo points.

#### Kasparov wins Edit source]

So *S. _{A.}* = 1. Kasparov receives two more Elo points, Polgar loses two:

#### Draw [edit | Edit source]

So *S. _{A.}* = 0.5. Kasparov loses three Elo points, Polgar wins three:

### Chess [edit | Edit source]

Before the Elo rating was introduced, chess players were classified into nine classes or categories. A class difference meant that the better player had 0.75 points as a result of a game *expect* may. In the Elo system, this difference in skill level corresponds to a difference of (almost exactly) 200 rating points.

According to the rating, chess players can be assigned to the following categories (women's titles in brackets):

It should be noted that the various titles of Grand Master (GM) and International Master (IM) are not only obtained on the basis of a certain Elo number, but also by fulfilling other specified standards. In order to receive the title after meeting all standards, a prospective GM must have achieved an Elo rating of at least 2500, an IM a number of at least 2400. The requirements for titles for women are each 200 Elo points lower than for corresponding titles for men.

The scope of a class is 200 Elo points. The system is calibrated so that a difference of 200 points corresponds to a win expectation of the stronger player of 75%, 400 points correspond to almost 94% profit expectation. The comparison is based on statistical methods. Even with a difference of 600 points, the stronger player always wins, in practical and statistical terms, although the level of play in humans depends of course on how well you are on the day and your motivation. With computers, the distribution is not only the same according to the 200-point definition, but also very similar in terms of cornering behavior, but with similarly powerful machines there is a further spread of skill levels in the various game phases.

### Tournament category [edit | Edit source]

Round tournaments are also divided into categories based on the average rating of the participants. A difference of one category corresponds to 25 Elo points. A tournament in category 1 is classified as a tournament whose participants have an average of 2250 to 2274 Elo points. The currently strongest tournaments reach category 21, which corresponds to an average of 2750 to 2774 Elo points.

### Statistics [edit | Edit source]

The Elo system divides the chess players into nine classes with the help of a rating number, with the lower limit of the upper class being 2600 and the upper limit of the lower class being 1200. The ratings of a single player are interval-scaled and almost normally distributed; they fluctuate around a mean value with a standard deviation of 200. There are many players with skill levels below 1200, but the Elo system is only valid to a limited extent in terms of predictive reliability at this level of play. It is particularly important at the amateur level that a player can defend his number against stronger opponents without having to concentrate on special characteristics such as unconscious psychological weaknesses or poor time management of newcomers. Utopian high values are corrected quickly, precisely and reliably through defeat. The fairly stable Elo number is determined using various methods. Some assume that there are few games or similarly strong tournament participants, after many games they all reach very similar equilibria.

The basis of the calculation is the hypothesis that the distribution of the playing strength in the totality of the players corresponds mathematically to the normal distribution (Gaussian bell curve). Based on this hypothesis, it can be statistically predicted for two opponents with what probability one player will win. In the special case of an identical valuation number, the probabilities are equally high. In a tournament, a player's rating and the average of their opponents' ratings can be used to predict what score they are likely to get. At the end of the tournament, the actual result is compared with the statistically predicted result and the player's new rating is calculated from the deviation.

### Problems of rating systems Edit source]

#### Deflation and inflation Edit source]

If you want to compare the strengths of players from different epochs with the help of the Elo numbers - or other ratings, this does not only apply to the Elo system, a rating of z. B. 1600 from 1970 equates to a rating of 1600 from 2000. In particular, since the average skill level at least does not deteriorate over time as a result of the further development of the theory, the average rating number should not decrease.

With the Elo system, the winner of a game wins just as many rating points as the loser loses: the average playing strength of both remains the same. Includes the *Ratings pool* only top players, the following phenomenon can be observed: Whenever a player is added to the ratings, he enters with a certain (low) number of points. In the course of his career he improves his strength, gains points, and later retires with a (high) number of points - as a result, points are withdrawn from the community and the average rating number drops; d. H. the system is deflationary.

If the rating pool is enlarged, the opposite effect occurs: many players leave the rating pool with a lower rating than was assigned to them when they entered - the system is now inflationary.

This was particularly the case earlier, when the World Chess Federation FIDE included chess players in the ranking list only from a rating of 2200. Since the Elo evaluation of tournaments is chargeable and thus represents a source of income for FIDE, this threshold has been lowered further and further, most recently in July 2009 to 1200.^{[1]} Nevertheless, it cannot be avoided that many players leave the rating pool with lower ratings than they received when they entered.

A moderate inflation is, however, absolutely desirable, this should take into account the further development of the playing strengths in the course of time, but here the problem of too high inflation usually arises.

So the Elo numbers were able to reach new records without actually being an absolute measure of the skill level. About 20 years ago there was z. B. only two players with an Elo number greater than 2700, and only about 10-20 players achieved a value over 2600. Today (as of July 2010) over 200 active players have an Elo number greater than 2600, 37 of them at least 2700; three players even have an Elo rating of 2800 or higher, which seemed unthinkable 20 years ago.

#### The thousand-game problem [edit | Edit source]

Another phenomenon is the so-called *Thousand game problem*: Often players of the same skill level meet again and again. Suppose two players with an Elo 2000 rating play ten games, one of which gets 80% of the points. After calculating the new Elo rating, the values are 2080 for the winner and 1920 for the loser. However, if the two players play 1000 games with the same point ratio without the rating being updated, the winner will be given a new rating that is higher than that of the current world champion.

However, this scenario is quite constructed: according to the statistic law of large numbers, one can expect that the two equally strong players (both had an Elo 2000 rating) will approach the expected 50% after many games. Furthermore, in practice there will never be 1000 games without a rating update.

The development of the value figures is also influenced by the evaluation period. Evaluation was carried out every six months until 2002 and quarterly until 2009. Since July 2009 it has been evaluated every two months.^{[1]} In principle, an evaluation after each tournament would make sense, as this way, players' form fluctuations can be better balanced. However, this is not currently planned.

### Skills of selected chess players [edit | Edit source]

The former world chess champion Garri Kasparov achieved the unmatched Elo rating of 2851 points in 1999. After the Elo rating was introduced in 1970, Bobby Fischer's record of 2785 (from July 1972) lasted for many years.

Grandmasters usually have an Elo rating of at least 2500, from 2600 points one can speak of the extended world elite. The status of July 2010 of the FIDE evaluation is shown in the following table with the twenty highest rated players, supplemented by the best woman and the best male and female players from Germany, Austria and Switzerland (in brackets: place in the women's ranking):

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