Help - How are ratings calculated ?

A programmer's view of the process.
V4 August 2020 [email protected]

This method became effective for over-the-board ratings on 1st July 2020 and for online ratings on the 1st September 2021.

Contents:

1. Definitions
2. Process
3. Output
4. Notes
5. K Rating Algorithm
6. Elo Rating Difference Table
7. P Rating Algorithm
8. Elo Performance Table

DEFINITIONS

1.	K Rating	An Elo current rating algorithm to determine a rating based on a previous rating and results versus opponents ratings. "The Rating of Chess Players, Past and Present" Arpad E. Elo 1978 Wikipedia Elo_rating_system
2.	P Rating	An Elo performance rating algorithm to determine a rating based solely on performance versus opponents ratings without reference to any previous rating. ECF includes a fictional draw against a fictional opponent of nominal rating.
3.	Partial Rating	A rating calculated from a small number of games (<10) using P Rating.
4.	Full Rating	a) A rating calculated using K Rating or b) A rating calculated using P Rating on at least 10 games.
5.	Fully Rated Players	All players who have a prior period Full Rating and have played at least one rated game in the prior 36 months (3 years).
6.	Partially Rated Players	All players who have a prior period Partial Rating and have played at least one rated game in the prior 36 months (3 years).
7.	New Players	All players who are neither Fully Rated Players nor Partially Rated Players and have played at least one game in the period being rated. Note that this will include returning players.
8.	All Players	All players who fall into one of the above definitions.

PROCESS

Pass 1. Rate New Players and Partially Rated Players versus Fully Rated Players

Perform P Rating to produce either a Partial Rating "A" or a Full Rating "A" for each player.

Pass 2. Rate New Players and Partially Rated Players versus All Players

Perform P Rating to produce either a Partial Rating "B" or a Full Rating "B" for each player.
Where opponents are New Players or Partially Rated Players, use their Partial Rating "A" or Full Rating "A" from Pass 1

Pass 3. Rate Fully Rated Players versus All Players

Perform K Rating to produce a new Full Rating "B" for every RATED PLAYER.
Where opponents are New Players or Partially Rated Players, use their Partial Rating or Full Rating "B" from Pass 2.

OUTPUT

All Players acquire either a Partial Rating "B" or a Full Rating "B" in the above process.
Full Rating "B" is used as the "Full Rating" in the next rating cycle.
Partial Rating "B" plays no further role in rating.

NOTES

The sets of Fully Rated Players, Partially Rated Players and New Players are defined only by reference to prior periods therefore the sets of players do not change throughout the process. Players are divided into two groups at the beginning of the process. Group one, the sets of New Players and Partially Rated Players, are always processed twice (pass 1 and 2) and group 2, the set of Fully Rated Players, are always only rated once (pass3).

K Rating Algorithm

No.	Variable	Calculation	Comment
1.	D	= Opponent Rating - Player Rating	Difference in Rating. Positive if opponent rating is greater.
2.	D Offset	= Lookup abs(D) in the Elo Rating Difference Table and restore the sign.	Convert [-392 ... 392] => [-8.4 ... +8.4] Very approx. 1 rating point per 40 rating points difference.
3.	Score	Win = 1, Draw = 0.5, Loss = 0
4.	Score Offset	Win = +10, Draw = 0, Loss = -10	Convert Win/Draw/Loss to +10/0/-10
5.	Player K	If age >= 18 or New Rating < Old Rating = 700 / No. of Games This Month if (20 x No. of Games this month) > 700 = 20 otherwise If age < 18 and New Rating > Old Rating = 700 / No. of Games This Month if (40 x No. of Games this month) > 700 = 40 otherwise
6.	Game Increment	= (D Offset + Score Offset) x Player K / 20
7.	Adjustment	= Adjustment A + Old Rating x Adjustment B	May be used in some years to slowly correct rating drift for all players. Usually zero.
8.	New Rating	= Old Rating + Sum of Game Increments + Adjustment (Minimum 100)
9.	New Rating Type	= "Full"	Always Full

Elo Rating Difference Table

P Rating Algorithm

No.	Variable	Calculation	Comment
1.	Dummy Opponent Rating	Effective 1st September 2024: For those with no prior full OTB standard play rating the default rating for holders of the following FIDE titles will be: = 2500 for FIDE GM = 2350 for FIDE IM = 2200 for FIDE FM = 2050 for FIDE CM = 2200 for FIDE WGM = 2100 for FIDE WIM = 2000 for FIDE WFM = 1800 for FIDE WCM. For those not holding FIDE titles the default rating will be: = 1800 for Adults (18+) = 100 x Age for Juniors (U18) both less 100 for all other time controls. Where a player has a higher lapsed full rating (categories A-E,K or X) from the applicable list, use that latest such rating or converted grade. For OTB standard play, where a player has never recorded a standard play result, but has a current OTB rapid chess rating category K or A that is higher than their default rating, then that rating will be used.
2.	Total No. Games	= Prior No. of Games + Current Total No. Games + 1 Dummy Draw	Include one Dummy Draw
3.	Total Opponents Ratings	= Prior No. of Games x Prior Average Opponent Rating + Total Actual Opponents Ratings + 1 x Dummy Opponent Rating	Include Dummy Opponent Rating
4.	Average Opponent Rating	= Total Opponents Ratings / Total No. Games
5.	Total Points	= Prior Total Points + Current Total Points + 0.5	Include a Dummy Draw of 0.5
6.	Average Score (p)	= Total Points / Total No. Games	Range is [0 ... 1] The dummy draw prevents a perfect 0 or 1.
7.	dp	Lookup Average Score (p) in Elo Performance Table.	Convert an Average Score (p) of [0 ... 1] to [-800 ... +800]
8.	New Player Rating	= Average Opponent Rating + dp (Minimum 100)
9.	New Rating Type	= "Full" if Total No. Games - 1 x Dummy Draw is 10 or more. = "Partial if otherwise.	P Rating can produce either Partial or Full Ratings

Elo Performance Table

Compact Format

p	dp	p	dp	p	dp	p	dp	p	dp	p	dp	p	dp	p	dp	p	dp	p	dp
1.00	800	0.90	366	0.80	240	0.70	149	0.60	72	0.50	0	0.40	-72	0.30	-149	0.20	-240	0.10	-366
0.99	677	0.89	351	0.79	230	0.69	141	0.59	65	0.49	-7	0.39	-80	0.29	-158	0.19	-251	0.09	-383
0.98	589	0.88	336	0.78	220	0.68	133	0.58	57	0.48	-14	0.38	-87	0.28	-166	0.18	-262	0.08	-401
0.97	538	0.87	322	0.77	211	0.67	125	0.57	50	0.47	-21	0.37	-95	0.27	-175	0.17	-273	0.07	-422
0.96	501	0.86	309	0.76	202	0.66	117	0.56	43	0.46	-29	0.36	-102	0.26	-184	0.16	-284	0.06	-444
0.95	470	0.85	296	0.75	193	0.65	110	0.55	36	0.45	-36	0.35	-110	0.25	-193	0.15	-296	0.05	-470
0.94	444	0.84	284	0.74	184	0.64	102	0.54	29	0.44	-43	0.34	-117	0.24	-202	0.14	-309	0.04	-501
0.93	422	0.83	273	0.73	175	0.63	95	0.53	21	0.43	-50	0.33	-125	0.23	-211	0.13	-322	0.03	-538
0.92	401	0.82	262	0.72	166	0.62	87	0.52	14	0.42	-57	0.32	-133	0.22	-220	0.12	-336	0.02	-589
0.91	383	0.81	251	0.71	158	0.61	80	0.51	7	0.41	-65	0.31	-141	0.21	-230	0.11	-351	0.01	-677
																		0.00	-800

---

[Next] [Index]