Handbook of Ratings by Alexander Karminsky & Andrey Polozov

Author:Alexander Karminsky & Andrey Polozov
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(6.8)

Here W ij stands for the wins of the ith opponent over the jth one. Note that the absolute value of the pair ratings Rij and Rji has not been determined and is irrelevant yet. The correlations of ratings of 2 to 1, 10 to 5, or 300 to 150 have just the same meaning. We have only a certain correlation of ratings. Thus according to the results of the tournament (or several tournaments), we have a set of pair ratings for the participants. Here, part of the table cells can be empty. It is not as if the tournament is certainly held in the form of the round robin. This may be the Swiss system, where pairs are formed according to the results of the previous rounds. Or it can be the Olympic play-off system. The system of tournament generally can imply any combination of various systems. To build the rating, now we need to reduce such a matrix to a set of numbers (ratings) that definitely characterize each of the participants in comparison with their opponents. We need to be able to range the participants in accordance with their achievements. According to the traditional scoring system, in round-robin and Swiss tournaments rating is provided by summarizing the points gained, all wins, draws and losses being set equal. The strict condition is put here that the number of games for all participants should be the same.

Rating of the participant. The second definition, which we use in the natural rating system, is the definition that the players’ rating in the tournament (tournaments) is equal to the weighted average of all pair ratings of the given participant

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