Under certain conditions bonuses can be awarded to players who perform well above expectation. In addition, their opponents are compensated for facing an underrated player.
Awarding Bonus Points
The conditions under which a player is eligible for a bonus are as follows:
- the player must have a full rating (i.e. 20 or more games) and a K-factor of 32 or 40
- the player must have at least 5 rated games in the tournament
- the initial calculation (i.e. pre-bonus) of the post-tournament rating must
- be less than 2100
- exceed a threshold
The threshold referred to in the last item is the player's 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 post-tournament rating is then adjusted by adding the bonus.
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.
- pre-tournament full rating: 1906
- k-factor: 40
- number of rounds: 9
- post-tournament pre-bonus rating: 1975
- tournament performance rating: 2109
- threshold: 1906 + 32 + (9 − 4) × 3 = 1953
- bonus awarded: yes (2100 > 1975 > 1953)
- bonus points: (1975 − 1953) × 1.25 = 28
- new rating: 1975 + 28 = 2003
- cap: none (2003 < 2100 & 2003 < 2109)
The opponents of any player who gained a bonus are deemed to have played an underrated player. Therefore the tournament is re-rated from scratch with one difference: instead of starting with their pre-tournament ratings, any players who received a bonus start with their post-tournament ratings (including bonuses) from the initial calculation.
When the tournament is re-rated, a player whose opponents included those receiving bonuses loses less (or gains more) rating points than in the initial calculation due to the increase of those opponents' pre-tournament ratings.
Frequency of Bonuses
In the year 2012 there were 172 bonuses awarded in 115 tournaments.
- the largest bonus was 125 (and in total there were 10 that exceeded 100)
- the lowest bonus was 1 (and in total there were 61 that were below 20)
- the average bonus was 35.7
You may, upon seeing you've got a bonus, wish to verify it by going through the above set of calculations. Beware, however, that if you've played any provisionally rated opponents then you may be only able to get an approximate value. To explain why, note that tournaments are rated in 5 basic steps:
- re-estimate the provisional ratings
- calculate all other ratings
- calculate and apply bonuses
- re-estimate the provisional ratings again (because they depend on the bonuses)
- calculate all other ratings again (because they depend on the provisional ratings)
Provisional ratings can change during the re-estimation phases and so the inputs to the bonus calculation in step 3 may not be the same as the inputs at the end (the data you would use to check your bonus) if you've played any players with provisional ratings.
Q1. So why not recalculate the bonus one more time at the end? Unfortunately, that would make the provisional ratings inconsistent, which would be worse (see section 1.2 of this article).
Q2. Then why not include the bonus calculations in the re-estimations instead of dealing with provisional ratings and bonuses separately? Of all the functions involved in rating a tournament, the bonus function is the only one that is discontinuous (because of the threshold) and this could prevent the iterations converging to a solution.