25.10.2005
**New principles of ranking chess players**

The attempts to compare strength of the chess players of different periods and continents led to the appearance of first rating systems in the 20th century, that were used in different countries, and one of them, Arpad Elo’s system of individual coefficients, became the official system of FIDE. During 35 years that passed from its advent, Elo system revealed its merits and demerits. Now there is a need to correct some of the principles of the rating calculation. We would like to include the following rather important changes into the rating system without changing substantially the approach to recalculation the quantitative expression of a player’s strength after several games, based on difference between expected and real results of the games.

1). **The suggestion is to take into account not only the result of the game, but also the colors.** Without going into details, let us give an example. In Elo system, a draw in a game of players with the same rating does not change their rating. In our system, White loses and Black gains about 2,5 points.

2). As it is well-known, rating can change greatly depending on the period of time, during which the games are collected for the regular recalculation (year, six months, three months taken for official FIDE rating recalculation, one month). The effect of this factor is best seen when a chess player has a long series of victories (or losses) during this period. For example, Robert Fischer had had such a series in his candidate matches before he became a champion. If his rating had been calculated after the first match that he had won 6:0, then the next match result 6:0 would have been more expected and would have added far less points to his rating. Now there is a technical possibility to recalculate ratings essentially more frequently than once in three months. **Our proposal is to recalculate the ratings after each game.** It will lead to the more dynamic process of rating change. Of course the recalculation itself can be held after the end of the tournament and not the day a game took place.

3).** The suggestion is to make a more precise calculation (to 0,1 or even 0,01 points) of ratings to avoid coincidence.** The problem is that the increase of the number of players with ratings leads to the increase of probability of ratings coincidence for different players, and such coincidences can be inconvenient in some cases (for example, when there is a need for dividing the players in different groups depending on their ratings). Let us remind that in the first Elo rating lists the values were approximated to 5 points, and now FIDE uses approximation to 1 point, but this still does not save from the identical ratings.

4).** In the proposed system rating cannot fall beneath a certain level** (for example, this level is 100 points less than the one got before). If the chess player has not played for three or more years, then when he comes back to chess he gets his maximal previous rating minus 100 points. It is significant that 100 points in our system corresponds to 200 points in Elo system.

5). **Rating is calculated separately for classical and rapid chess**. And a total rating can be calculated on the basis of two ratings with their certain weights.

6). **A chess player without a rating is given the rating that is 10 points (or some other amount) less than the lowest rating in the tournament**.

7). To avoid confusion with Elo rating,** we will use another scale**, where 1000 points correspond with 2800 Elo points.

8). **To the moment there is a program that will allow to start test rating according to our system** (separately for classical and rapid chess).

Valeriy Nevzorov,

Professor, SPbSU, theory of probability and mathematical statistics department