PLEASE NOTE: both sections have been superseded by articles on the ICU ratings web site: unrated players, bonus points.
This article describes the current ICU rating system (implemented by Ray O'Brien and in operation since 1999) and elaborates on a previous article. Details are given of how unrated players are treated and how bonuses are calculated.
Unrated Players
The unrated players in a tournament are those that have no rating or just a provisional rating (i.e. all players who have accumulated less than 20 rated games prior to the tournament). Their rating after the tournament is their average performance rating for all the games they have played up to and including the tournament. If the opponent's rating is R, then the performance rating for one game is R for a draw, R + 400 for a win and R - 400 for a loss.
If an opponent has an established rating then that is used in the calculation of a player's performance rating. However, if the opponent is unrated (including provisionally rated) then the rating used is their rating at the end of the tournament. This solves one problem (what rating to use when the opponent has none prior to the tournament) but creates a catch-22 situation: in order to calculate an unrated player's performance rating the performance ratings of the unrated opponents must already be known.
This problem is overcome by employing iterative estimation. Initial guesses are made for all performance ratings and used to calculate a new set of estimates. If the new estimates differ significantly from the initial guesses then the calculation is repeated starting from the new estimates. This procedure is iterated until the estimates converge (i.e. until no significant differences are detected between successive estimates).
Having established performance ratings for all unrated players, the rest of the players (i.e those with established ratings) are then rated using formulae from the previous article. The ratings used for unrated opponents of rated players are the post-tournament performance ratings. Note that this means rated players can gain or lose rating points when they play unrated opponents.
Bonus Points
Please note: this section has been superseded by an article on the ICU Ratings site.
Under certain conditions bonuses can be awarded to players who perform well above expectation and at the same time the damage inflicted on their victim's ratings can be reduced.
Star Player's Reward
The conditions under which a player is eligible for a bonus are as follows:
- the player's K-factor must be over 24;
- the number of rated games must be more than 4;
- the post-tournament rating must be less than 2100;
- the post-tournament rating must be greater than a certain threshold.
The threshold referred to in the last item is the pre-tournament rating, plus 32, plus 3 for each game after the fourth. If all the above conditions are met, then the bonus is the difference between the post-tournament rating and the threshold. If the player's K-factor is 40 (as opposed to 32) then the bonus is increased by 25%. The bonus is added to the post-tournament rating to get a new post-tournament rating.
A check is applied to limit the bonus. If the new post-tournament rating exceeds either 2099 or the player's tournament performance rating then it is reduced to whatever is the lowest of the two. The tournament performance rating is the performance rating just for games in the tournament.
Victim's Compensation
Calculating the bonuses isn't the end of the matter because (or so the theory goes) the opponents of a player whose pre-tournament rating looks like an underestimate should be compensated. This is achieved as follows.
If no bonuses apply to any players then the post-tournament ratings (as calculated above) stand and no further adjustments are applied. However, if one or more players receive a bonus then the tournament is completely re-rated from scratch with the following difference: instead of starting with their actual pre-tournament ratings, any players who received a bonus are deemed to have started the tournament with the post-tournament ratings (including bonuses) that had just been calculated.
When the tournament is re-rated, players whose opponents included those receiving bonuses lose less (or gain more) rating points than in the initial calculations due to the increase in their opponents' pre-tournament ratings.