Rating System

Ratings etc. Results Home page

A player's rating is a number calculated from their performance at our weekly meetings. Stronger players will have higher ratings and weaker players lower ones. It would be expected that a player with a higher rating would usually beat a player with a lower rating. Obviously, this will not always be the case and if two players' ratings are close then the outcome is in more doubt. The system we use is based on the Weighted Rolling System used by the ABSP.

The explanation of the rating system on this page is, necessarily, long and detailed. Sorry.

Rationale

The rating system is designed with the idea that it should reflect the current strength of a player in our ordinary club games. Consequently performance in more recent games has a greater effect on the rating than performance in games that took place a long time ago. Also if a player wins against a strong opponent theire rating increases more than if they beat a weak opponent. Similarly, losing to a strong player doesn't affect a player's rating as much as losing to a weak opponent.

Ratings are updated at the end of each month and that rating is the one used for a player during the next month. It seems unlikely that a player's underlying ability will fluctuate much over time periods of less than a month so the seeming increased accuracy of updating ratings more frequently would probably be spurious.

The rating system is only a rough guide to performance. Whilst a player with a rating of 150 should usually beat a player with a rating of 90, two players with ratings of, say, 124 and 127 are probably more or less equally matched in reality.

Ratable games

Normal club games played at our regular Thursday meetings are used in calculating the ratings. We do not use:

• Games that form part of a threesome. (If an odd number of players turns up one week then one player will play simultaneously against two others.)
• Handicap tournament games. (In our annual handicap tournament each player receives a certain number of points to start with; the number for each player being adjusted to even out the chances of weaker and stronger players winning.)
• Games against an unrated player

The first two types of game are not used because it is assumed that players will not be playing their normal game or will have some sort of additional advantage or disadvantage.

Games against unrated players are not used because the opponents rating is a vital part of the rating calculation. Unrated players may be new members to the club or visiting guests. We do not give a rating to players who have played less than thirty ratable games. Note that if a rated player plays an unrated player the game is not ratable for the rated player but is ratable for the unrated player.

Rated games

In order to keep the ratings current only games played in the previous two years are used in the calculation. This means that the maximum number of games that theoretically can be included in the rating calculation is 210. This is unlikely to be achieved in practice as most years there is at least one week where games aren't played and also it is very rare for a player to attend every meeting in a year.

A player will not be given a rating until they have played at least thirty ratable games, which regularly attending members will accumulate in four or five months. If a member stops attending for a while then, eventually, their rating will be calculated on fewer games as older ones are dropped because of the two-year rule. (And after two years' of non-attendance their rating will no longer be calculated.

Calculating the Rating

This explanation will be using some example data (given in a table at the foot of this page), for calculating a particular player's club rating at the end of December 2007.

To calculate a new rating we need, for each game, the Player's Rating at the time of the game (PR), their Opponent's Rating at the time of the game (OR) and the result of the game (win, lose or draw) from the point of view of the player. An example of the data needed (from one month only) is shown in table 1. Notice that the players rating stays constant throughout the month, because we only update ratings at the end of each month.

The minimum permitted rating is 50. If a player's calculated rating is less than 50 it is adjusted upwards to 50.

Table 1: Data needed for rating calculation (one month only)

Date	Rating at date	Opponent's rating	Result
05/01/2006	127	85	Win
05/01/2006	127	105	Win
12/01/2006	127	121	Win
12/01/2006	127	102	Win
19/01/2006	127	147	Loss
19/01/2006	127	128	Win
26/01/2006	127	101	Loss

If the opponent's rating is very different from the player's it could lead to wild fluctuations in a player's rating or, for example, a player's rating going up when they lose a game. To avoid this the opponents rating is converted to an Adjusted Opponent's Rating (AOR). The conversion is done as follows:

If PR is more than 40 greater than OR	AOR = PR - 40
If PR is more than 40 less than OR	AOR = PR + 40
Otherwise	AOR = OR

If a player hasn't got a rating yet then the opponent's rating is used unadjusted, whatever it it.

Table 2 shows the effect of applying this procedure to this particular month's data. One opponent's rating is adjusted up to 87 (on the 5th).

Table 2: Adjusted Opponent's Rating calculated for each game

Date	Rating at date	Opponent's rating	Result	Adjusted opponent's rating
05/01/2006	127	85	Win	87
05/01/2006	127	105	Win	105
12/01/2006	127	121	Win	121
12/01/2006	127	102	Win	102
19/01/2006	127	147	Loss	147
19/01/2006	127	128	Win	128
26/01/2006	127	101	Loss	101

The Basic Rating Points (BRP) are now calculated according to the following formulae:

If player won game	BRP = AOR + 50
If player drew game	BRP = AOR
If player lost game	BRP = AOR - 50

The effect of applying these formulae to data in table 2 can be seen in table 3.

Table 3: Basic rating points calculated

Date	Rating at date	Opponent's rating	Result	Adjusted opponent's rating	Basic rating points
05/01/2006	127	85	Win	87	137
05/01/2006	127	105	Win	105	155
12/01/2006	127	121	Win	121	171
12/01/2006	127	102	Win	102	152
19/01/2006	127	147	Loss	147	97
19/01/2006	127	128	Win	128	178
26/01/2006	127	101	Loss	101	51

The next step is to make more recent games count more than ones that were played some time ago. This is done through a system of weightings. The most recent game is given a weighting (GW) of 250. The last-but-one game is given a weighting of 249, the one before that 248. This continues, with the weighting reduce by one each time we go back a game. If a player has the maximum possible 210 games included in the calculation then the oldest game will have a weighting of 41.)

In this example the game weightings ranged from 88 to 94 (they are are the earlier data from the full example at the bottom of the page).

The next step is to calculate the Weighted Rating Points (WRP). The weighted rating points are calculated by multiplying the basic rating points by the average month weighting:

WRP = BRP× AMW

The weighted rating points for our example month can be seen in table 4

Table 4: Weighted Rating Points calculated

Date	Rating at date	Opponent's rating	Result	Adjusted opponent's rating	Basic rating points	Game weight	Weighted rating points
05/01/2006	127	85	Win	87	137	88	12056
05/01/2006	127	105	Win	105	155	89	13795
12/01/2006	127	121	Win	121	171	90	15390
12/01/2006	127	102	Win	102	152	91	13832
19/01/2006	127	147	Loss	147	97	93	9021
19/01/2006	127	128	Win	128	178	92	16376
26/01/2006	127	101	Loss	101	51	94	4641

We now calculate the Total Weighted Rating Points TWRP and the Total Weight (TW). These are simply calculated by adding up all the respective values. As can been seen from the table containing the full data for all 163 games in our example:

TWRP = 33411655

TW = 27547

The new rating is can now be found by dividing the total weighted rating points by the total weight:

Rating = TWRP ÷ TW

Rating = 3341655 ÷ 27547

Rating = 121.3

We always round down ratings to the whole number so our player's new rating is 121.

Example data for a rating calculation

Date	Rating at date	Opp. rating	Result	Adj. opp. rating	Basic rating points	Game weight	Weighted rating points
13-12-2007	120	102	Win	102	152	250	37924
13-12-2007	120	111	Win	111	161	249	40169.5
15-11-2007	121	116	Win	116	166	248	40836
08-11-2007	121	99	Loss	99	49	247	12054
08-11-2007	121	116	Loss	116	66	246	16236
01-11-2007	121	112	Win	112	162	245	39852
01-11-2007	121	95	Loss	95	45	244	11070
25-10-2007	121	102	Win	102	152	243	36632
18-10-2007	121	106	Loss	106	56	242	13496
11-10-2007	121	94	Win	94	144	241	34704
04-10-2007	121	155	Win	155	205	240	49405
04-10-2007	121	128	Loss	128	78	239	18798
27-09-2007	125	127	Win	127	177	238	41506.5
27-09-2007	125	118	Loss	118	68	237	15946
20-09-2007	125	94	Loss	94	44	236	10318
20-09-2007	125	147	Loss	147	97	235	22746.5
13-09-2007	125	84	Loss	85	35	234	8207.5
13-09-2007	125	73	Loss	85	35	233	8207.5
06-09-2007	125	55	Loss	85	35	232	8207.5
06-09-2007	125	81	Win	85	135	231	31657.5
30-08-2007	121	153	Loss	153	103	230	23226.5
30-08-2007	121	126	Win	126	176	229	39688
23-08-2007	121	125	Loss	125	75	228	16912.5
23-08-2007	121	126	Win	126	176	227	39688
16-08-2007	121	126	Win	126	176	226	39688
16-08-2007	121	147	Win	147	197	225	44423.5
09-08-2007	121	88	Win	88	138	224	31119
09-08-2007	121	147	Win	147	197	223	44423.5
02-08-2007	121	112	Win	112	162	222	36531
02-08-2007	121	127	Win	127	177	221	39913.5
26-07-2007	121	66	Win	81	131	220	28361.5
26-07-2007	121	152	Win	152	202	219	43733
19-07-2007	121	115	Win	115	165	218	35722.5
19-07-2007	121	124	Loss	124	74	217	16021
12-07-2007	121	66	Win	81	131	216	28361.5
12-07-2007	121	122	Loss	122	72	215	15588
05-07-2007	121	109	Win	109	159	214	34423.5
05-07-2007	121	124	Loss	124	74	213	16021
22-06-2007	120	127	Win	127	177	212	37081.5
22-06-2007	120	123	Loss	123	73	211	15293.5
15-06-2007	120	127	Win	127	177	210	37081.5
15-06-2007	120	90	Win	90	140	209	29330
07-06-2007	120	69	Win	80	130	208	27235
07-06-2007	120	119	Loss	119	69	207	14455.5
31-05-2007	120	81	Loss	81	31	206	6308.5
31-05-2007	120	109	Loss	109	59	205	12006.5
24-05-2007	120	125	Loss	125	75	204	15262.5
24-05-2007	120	109	Win	109	159	203	32356.5
03-05-2007	120	114	Win	114	164	202	33374
03-05-2007	120	170	Win	160	210	201	42735
26-04-2007	121	105	Win	105	155	200	30690
19-04-2007	121	124	Loss	124	74	199	14652
19-04-2007	121	170	Loss	161	111	198	21978
05-04-2007	121	90	Win	90	140	197	27720
05-04-2007	121	110	Loss	110	60	196	11880
29-03-2007	123	82	Win	83	133	195	25336.5
29-03-2007	123	103	Win	103	153	194	29146.5
22-03-2007	123	85	Win	85	135	193	25717.5
22-03-2007	123	105	Loss	105	55	192	10477.5
15-03-2007	123	88	Win	88	138	191	26289
15-03-2007	123	122	Win	122	172	190	32766
08-03-2007	123	85	Loss	85	35	189	6667.5
08-03-2007	123	105	Win	105	155	188	29527.5
01-03-2007	123	85	Loss	85	35	187	6667.5
01-03-2007	123	152	Loss	152	102	186	19431
22-02-2007	123	111	Win	111	161	185	29382.5
22-02-2007	123	128	Loss	128	78	184	14235
08-02-2007	123	127	Loss	127	77	183	14052.5
08-02-2007	123	125	Win	125	175	182	31937.5
01-02-2007	123	125	Loss	125	75	181	13687.5
01-02-2007	123	86	Win	86	136	180	24820
25/01/2007	128	117	Loss	117	67	179	11758.5
25/01/2007	128	110	Loss	110	60	178	10530
18/01/2007	128	94	Draw	94	94	177	16497
18/01/2007	128	101	Loss	101	51	176	8950.5
11/01/2007	128	110	Loss	110	60	175	10530
11/01/2007	128	95	Win	95	145	174	25447.5
04/01/2007	128	124	Win	124	174	173	30537
04/01/2007	128	117	Loss	117	67	172	11758.5
19-12-2006	128	113	Win	113	163	171	27791.5
19-12-2006	128	130	Loss	130	80	170	13640
23-11-2006	125	93	Win	93	143	169	23666.5
23-11-2006	125	62	Win	85	135	168	22342.5
16-11-2006	125	78	Win	85	135	167	22342.5
16-11-2006	125	127	Win	127	177	166	29293.5
09-11-2006	125	150	Loss	150	100	165	16550
09-11-2006	125	150	Win	150	200	164	33100
02-11-2006	125	93	Win	93	143	163	23666.5
02-11-2006	125	110	Win	110	160	162	26480
27-10-2006	128	94	Win	94	144	161	22824
27-10-2006	128	89	Loss	89	39	160	6181.5
20-10-2006	128	96	Win	96	146	159	23141
20-10-2006	128	129	Loss	129	79	158	12521.5
13-10-2006	128	64	Win	88	138	157	21873
13-10-2006	128	90	Loss	90	40	156	6340
28-09-2006	129	87	Win	89	139	155	21128
28-09-2006	129	69	Win	89	139	154	21128
21-09-2006	129	88	Win	89	139	153	21128
14-09-2006	129	91	Draw	91	91	152	13832
14-09-2006	129	85	Win	89	139	151	21128
07-09-2006	129	71	Win	89	139	150	21128
07-09-2006	129	110	Loss	110	60	149	9120
29-08-2006	130	115	Win	115	165	148	23760
29-08-2006	130	149	Win	149	199	147	28656
22-08-2006	130	111	Loss	111	61	146	8784
17-08-2006	130	153	Loss	153	103	145	14832
17-08-2006	130	127	Win	127	177	144	25488
10-08-2006	130	103	Loss	103	53	143	7632
10-08-2006	130	127	Win	127	177	142	25488
03-08-2006	130	83	Win	90	140	141	20160
03-08-2006	130	126	Loss	126	76	140	10944
27-07-2006	127	92	Win	92	142	139	19312
27-07-2006	127	124	Win	124	174	138	23664
20-07-2006	127	117	Win	117	167	137	22712
20-07-2006	127	128	Loss	128	78	136	10608
13-07-2006	127	98	Win	98	148	135	20128
13-07-2006	127	74	Win	87	137	134	18632
06-07-2006	127	98	Win	98	148	133	20128
22-06-2006	129	93	Win	93	143	132	18375.5
22-06-2006	129	107	Loss	107	57	131	7324.5
15-06-2006	129	93	Loss	93	43	130	5525.5
15-06-2006	129	107	Win	107	157	129	20174.5
08-06-2006	129	155	Loss	155	105	128	13492.5
08-06-2006	129	74	Win	89	139	127	17861.5
01-06-2006	129	118	Win	118	168	126	21588
01-06-2006	129	107	Win	107	157	125	20174.5
25-05-2006	127	87	Win	87	137	124	16508.5
25-05-2006	127	151	Loss	151	101	123	12170.5
18-05-2006	127	64	Win	87	137	122	16508.5
18-05-2006	127	88	Win	88	138	121	16629
11-05-2006	127	129	Win	129	179	120	21569.5
11-05-2006	127	129	Loss	129	79	119	9519.5
04-05-2006	127	78	Win	87	137	118	16508.5
04-05-2006	127	129	Win	129	179	117	21569.5
20-04-2006	129	117	Loss	117	67	116	7604.5
20-04-2006	129	114	Loss	114	64	115	7264
13-04-2006	129	150	Loss	150	100	114	11350
13-04-2006	129	114	Win	114	164	113	18614
06-04-2006	129	130	Win	130	180	112	20430
06-04-2006	129	81	Win	89	139	111	15776.5
30-03-2006	124	95	Win	95	145	110	15370
30-03-2006	124	127	Win	127	177	109	18762
23-03-2006	124	77	Win	84	134	108	14204
16-03-2006	124	97	Win	97	147	107	15582
16-03-2006	124	101	Win	101	151	106	16006
09-03-2006	124	112	Win	112	162	105	17172
09-03-2006	124	89	Win	89	139	104	14734
02-03-2006	124	94	Win	94	144	103	15264
02-03-2006	124	95	Loss	95	45	102	4770
23-02-2006	134	102	Win	102	152	101	14896
23-02-2006	134	126	Win	126	176	100	17248
16-02-2006	134	70	Win	94	144	99	14112
16-02-2006	134	103	Loss	103	53	98	5194
09-02-2006	134	95	Win	95	145	97	14210
09-02-2006	134	126	Loss	126	76	96	7448
02-02-2006	134	105	Loss	105	55	95	5390
26/01/2006	127	101	Loss	101	51	94	4641
19/01/2006	127	147	Loss	147	97	93	8827
19/01/2006	127	128	Win	128	178	92	16198
12/01/2006	127	102	Win	102	152	91	13832
12/01/2006	127	121	Win	121	171	90	15561
05/01/2006	127	105	Win	105	155	89	14105
05/01/2006	127	85	Win	87	137	88	12467
					Total	27547	3341655
						Rating	121.3

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