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The Rating Algorithm

Before an event, a player is either unrated, or has a rating based on having played $N$ games. A player's rating is termed ``provisional'' if it is based on 25 or fewer games, and is ``established'' otherwise. Assume the player competes in $m$ games during the event. Post-event ratings are computed in a sequence of five steps:

The calculations are carried out in the following manner:

Step 1:
Set initial ratings for unrated players.

Initial rating estimates are set for all unrated players in an event. The purpose of setting initial rating estimates for unrated players is (1) to be able to incorporate information about a game result against an unrated player, and (2) to choose among equally plausible ratings during a rating calculation for an unrated player (see the details of the ``special'' rating formulas in Section 2.2.

An initial rating for an unrated player is determined in the following order of precedence.

Step 2:
Calculate the ``effective'' number of games played by each player.

This number, which is typically less than the actual number of games played, reflects the uncertainty in one's rating, and is substantially smaller especially when the player's rating is low. This value is used in the ``special'' and ``standard'' rating calculations. See Section 2.1 for the details of the computation.

Step 3:
Calculate a first rating estimate for each unrated player. For most unrated players, this involves using the ``special'' rating formula (see Section 2.2). Exceptions include unrated players with high FIDE ratings, and unrated quick chess players with standard ratings based on 9 or 10 games. Let the ``prior'' rating, $R_0$, and the number of games, $N$, be the values assigned from Step 1. However, for only this step in the computation, set the number of effective games to 1 for each unrated player having a Step 1 rating based on $N=0$ games. If the resulting rating from Step 3 for the unrated player is less than 100, then change the rating to 100.

Step 4:
For every player, calculate an intermediate rating with the appropriate rating formula. In the calculations, use the opponents' pre-event ratings in the computation (for players with pre-event ratings), or the results of the Step 3 ratings for unrated opponents.

If the resulting rating from Step 4 is less than 100, then change the rating to 100.

Step 5:
Repeat the calculations from Step 4 for every player, again using a player's pre-event rating (or the results of Step 1 for unrated players) to perform the calculation, but using the results of Step 4 for the opponents' ratings. If the resulting rating from Step 5 is less than 100, then change the rating to 100.

These five steps result in the new set of post-event ratings for all players.


next up previous
Next: Details of the Rating Up: The USCF Rating System Previous: The USCF Rating System
Mark Glickman
2004-09-22