The basic formulae for calculating provisional ratings are described in a separate article. There is, however, an additional aspect to dealing with opponents who are unrated or provisionally rated: what should their start rating be for the tournament?
The ICU system uses two guiding principles:
- Estimates should be obtained for the start ratings of unrated players using the tournament data.
- Estimates of provisional ratings should include data from the current tournament, as well as previous tournaments.
These principles are both implemented by setting the start ratings of unrated or provisionally rated players to their new ratings at the end of the tournament.
Before any calculations are performed, the new ratings for unrated and provisionally rated players are unknown and yet are required in order to proceed. How is this contradiction resolved?
All ratings are obtained by iterative estimation. The new ratings calculated for unrated and provisionally rated players in one iteration provide their start ratings for the next iteration while the start ratings for players with full ratings (including foreign players) are held fixed. If the new estimates are not significantly different from the previous estimates then an acceptable solution has been found and the iteration halts. Otherwise it repeats until convergence is achieved. The first iteration is initialised with the original provisional ratings (or zero for unrated players).
In order for the estimation process to work, each unrated or provisionally rated player must have at least one opponent who is either fully rated or who has played a fully rated opponent. This is the reason why it is not possible to rate tournaments without any fully rated players. Also, with tournaments that have few fully rated players, there can sometimes be groups of unrated or provisionally rated players who only play amongst themselves and who therefore cannot be rated.
The article on Improvements to the ICU Rating Algorithm which touches on the maximum number of iterations and the threshold for deciding when convergence has been reached.
The article on Bonus Rating Points. If there are any bonuses for players with full ratings, their start ratings are also set to their new ratings and the whole iterative process is repeated for a second time.