714. Equations. The equations used to calculate ratings are as follows:

714a) For previously unrated and provisionally rated players, the performance rating is:

where Rp is the performance rating, Rc is the average rating of the player’s opponents, W is the number of wins, L is the number of losses, N is the total number of games played.

714b) For players with established ratings the new rating is

In applying this equation to players of 2199 or over, change 32 to 16. For players who start an event below 2199 and then in the event go above 2199 the gains are computed normally, namely with 32 in 714b and then the increase over 2199 is cut in half. Where Rn is the post event (new) rating before the application of bonus or participation points, Ro is the pre event (old) rating, S is the score, and Sx is the expected score. This is determined by the following table to two significant decimals (a more accurate determination of the expected score may be used in the actual calculation):

Expected Result of Game (For example, the higher rated player should score 3-1 for a difference in rating of 189-197 points.)
Sx = Rating of higher player - Rating of lower player	Percentage wins for higher rated player	Percentage wins for lower rated player
0-3	.50	.50
4-10	.51	.49
11-17	.52	.48
18-25	.53	.47
26-32	.54	.46
33-39	.55	.45
40-46	.56	.44
47-53	.57	.43
54-61	.58	.42
62-68	.59	.41
69-76	.60	.40
77-83	.61	.39
84-91	.62	.38
92-98	.63	.37
99-106	.64	.36
107-113	.65	.35
114-121	.66	.34
122-129	.67	.33
130-137	.68	.32
138-145	.69	.31
146-153	.70	.30
154-162	.71	.29
163-170	.72	.28
171-179	.73	.27
180-188	.74	.26
189-197	.75	.25
198-206	.76	.24
207-215	.77	.23
216-225	.78	.22
226-235	.79	.21
236-245	.80	.20
246-256	.81	.19
257-267	.82	.18
268-278	.83	.17
279-290	.84	.16
291-302	.85	.15
303-315	.86	.14
316-328	.87	.13
329-344	.88	.12
345-357	.89	.11
358-374	.90	.10
375-391	.91	.09
392-411	.92	.08
412-432	.93	.07
433-456	.94	.06
457-484	.95	.05
485-517	.96	.04
518-559	.97	.03
560-619	.98	.02
620-734	.99	.01
735 and over	1.00	.00

714c) Except for players with provisional ratings, bonus points are awarded in tournaments with 4 or more rounds actually played according to the following rules.

A: Participation Bonus (No Restrictions)
Rated 0000 - 1000 2.00 Points per game played
Rated 1001 - 1800 1.50 Points per game played
Rated 1801 - 2000 1.00 Points per game played
Rated 2001 - 2200 0.75 Points per game played
Rated 2201 + 0.50 Points per game played

B: Result Bonus (Performance Rating must exceed highest CFC Rating ever)
0% - 59% No points
60% - 70% 5 Points
71% - 89% 10 Points
90% + 15 Points

715. Initial Ratings. Previously unrated players are rated by equation 714a for their first 24 games. The equation is applied cumulatively - i.e. the rating after the second event will include the performance in both the first and second events. During this period their ratings are considered provisional. Beginning with the event in which they play their 25^th rated game, their ratings become established and are computed by equation 714b, and, if appropriate, 714c, or 714d.

716a) If a player’s post tournament rating (including any participation and bonus points) is less than 800, and the player had a permanent rating before the tournament greater than 799, the player is entered in the rating list at 799.

716b) If a player’s post tournament rating (including any participation and bonus points) is less than 800, and the player had a permanent rating before the tournament less than or equal to 799, the player is entered in the rating list at the greater of the player’s pre and post tournament ratings.

716c) If a player’s post tournament rating (including any participation and bonus points) is less than 200, the player is entered in the rating list at 200. This applies to both provisional and permanent ratings.

717. Order of Calculation. When an event is rated, performance ratings under equation 714a are obtained, first for unrated players, then for provisionally rated players. For each rated player is calculated: Ro-400(W-L)/N. The mean of these is AR. When unrated plays unrated in this first pass, the opponent’s rating is estimated as AR-200+400(W-L). After this, the previously unrated players are rerated on the basis of the ratings of their opponents just calculated. Finally, the players having established ratings are rated, first those with ratings below 800. A game with a previously unrated or previously provisionally rated player enters the rating of a player with an established rating on the basis of the opponent’s post-event (new) rating. In the case of a player having an established rating below 800, the following is used to calculate the rating of opponents having established ratings 800 and above: the higher of the player’s pre- and post-event ratings.