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Rating System

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:

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 Opp. rating Result
5-1-2006 127 85 Win
5-1-2006 127 105 Win
12-1-2006 127 121 Win
12-1-2006 127 102 Win
19-1-2006 127 147 Lose
19-1-2006 127 128 Win
26-1-2006 127 101 Lose

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 Opp. rating Result Adj. opp. rating
5-1-2006 127 85 Win 87
5-1-2006 127 105 Win 105
12-1-2006 127 121 Win 121
12-1-2006 127 102 Win 102
19-1-2006 127 147 Lose 147
19-1-2006 127 128 Win 128
26-1-2006 127 101 Lose 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 Opp. rating Result Adj. opp. rating Basic rating points
5-1-2006 127 85 Win 87 137
5-1-2006 127 105 Win 105 155
12-1-2006 127 121 Win 121 171
12-1-2006 127 102 Win 102 152
19-1-2006 127 147 Lose 147 97
19-1-2006 127 128 Win 128 178
26-1-2006 127 101 Lose 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
Opp.
rating
Result Adj.
opp.
rating
Basic
rating
points
Game
weight
Weighted
rating
points
5-1-2006 127 85 Win 87 137 88 12056
5-1-2006 127 105 Win 105 155 89 13795
12-1-2006 127 121 Win 121 171 90 15390
12-1-2006 127 102 Win 102 152 91 13832
19-1-2006 127 147 Lose 147 97 93 9021
19-1-2006 127 128 Win 128 178 92 16376
26-1-2006 127 101 Lose 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
8-11-2007 121 99 Lose 99 49 247 12054
8-11-2007 121 116 Lose 116 66 246 16236
1-11-2007 121 112 Win 112 162 245 39852
1-11-2007 121 95 Lose 95 45 244 11070
25-10-2007 121 102 Win 102 152 243 36632
18-10-2007 121 106 Lose 106 56 242 13496
11-10-2007 121 94 Win 94 144 241 34704
4-10-2007 121 155 Win 155 205 240 49405
4-10-2007 121 128 Lose 128 78 239 18798
27-9-2007 125 127 Win 127 177 238 41506.5
27-9-2007 125 118 Lose 118 68 237 15946
20-9-2007 125 94 Lose 94 44 236 10318
20-9-2007 125 147 Lose 147 97 235 22746.5
13-9-2007 125 84 Lose 85 35 234 8207.5
13-9-2007 125 73 Lose 85 35 233 8207.5
6-9-2007 125 55 Lose 85 35 232 8207.5
6-9-2007 125 81 Win 85 135 231 31657.5
30-8-2007 121 153 Lose 153 103 230 23226.5
30-8-2007 121 126 Win 126 176 229 39688
23-8-2007 121 125 Lose 125 75 228 16912.5
23-8-2007 121 126 Win 126 176 227 39688
16-8-2007 121 126 Win 126 176 226 39688
16-8-2007 121 147 Win 147 197 225 44423.5
9-8-2007 121 88 Win 88 138 224 31119
9-8-2007 121 147 Win 147 197 223 44423.5
2-8-2007 121 112 Win 112 162 222 36531
2-8-2007 121 127 Win 127 177 221 39913.5
26-7-2007 121 66 Win 81 131 220 28361.5
26-7-2007 121 152 Win 152 202 219 43733
19-7-2007 121 115 Win 115 165 218 35722.5
19-7-2007 121 124 Lose 124 74 217 16021
12-7-2007 121 66 Win 81 131 216 28361.5
12-7-2007 121 122 Lose 122 72 215 15588
5-7-2007 121 109 Win 109 159 214 34423.5
5-7-2007 121 124 Lose 124 74 213 16021
22-6-2007 120 127 Win 127 177 212 37081.5
22-6-2007 120 123 Lose 123 73 211 15293.5
15-6-2007 120 127 Win 127 177 210 37081.5
15-6-2007 120 90 Win 90 140 209 29330
7-6-2007 120 69 Win 80 130 208 27235
7-6-2007 120 119 Lose 119 69 207 14455.5
31-5-2007 120 81 Lose 81 31 206 6308.5
31-5-2007 120 109 Lose 109 59 205 12006.5
24-5-2007 120 125 Lose 125 75 204 15262.5
24-5-2007 120 109 Win 109 159 203 32356.5
3-5-2007 120 114 Win 114 164 202 33374
3-5-2007 120 170 Win 160 210 201 42735
26-4-2007 121 105 Win 105 155 200 30690
19-4-2007 121 124 Lose 124 74 199 14652
19-4-2007 121 170 Lose 161 111 198 21978
5-4-2007 121 90 Win 90 140 197 27720
5-4-2007 121 110 Lose 110 60 196 11880
29-3-2007 123 82 Win 83 133 195 25336.5
29-3-2007 123 103 Win 103 153 194 29146.5
22-3-2007 123 85 Win 85 135 193 25717.5
22-3-2007 123 105 Lose 105 55 192 10477.5
15-3-2007 123 88 Win 88 138 191 26289
15-3-2007 123 122 Win 122 172 190 32766
8-3-2007 123 85 Lose 85 35 189 6667.5
8-3-2007 123 105 Win 105 155 188 29527.5
1-3-2007 123 85 Lose 85 35 187 6667.5
1-3-2007 123 152 Lose 152 102 186 19431
22-2-2007 123 111 Win 111 161 185 29382.5
22-2-2007 123 128 Lose 128 78 184 14235
8-2-2007 123 127 Lose 127 77 183 14052.5
8-2-2007 123 125 Win 125 175 182 31937.5
1-2-2007 123 125 Lose 125 75 181 13687.5
1-2-2007 123 86 Win 86 136 180 24820
25-1-2007 128 117 Lose 117 67 179 11758.5
25-1-2007 128 110 Lose 110 60 178 10530
18-1-2007 128 94 Draw 94 94 177 16497
18-1-2007 128 101 Lose 101 51 176 8950.5
11-1-2007 128 110 Lose 110 60 175 10530
11-1-2007 128 95 Win 95 145 174 25447.5
4-1-2007 128 124 Win 124 174 173 30537
4-1-2007 128 117 Lose 117 67 172 11758.5
19-12-2006 128 113 Win 113 163 171 27791.5
19-12-2006 128 130 Lose 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
9-11-2006 125 150 Lose 150 100 165 16550
9-11-2006 125 150 Win 150 200 164 33100
2-11-2006 125 93 Win 93 143 163 23666.5
2-11-2006 125 110 Win 110 160 162 26480
27-10-2006 128 94 Win 94 144 161 22824
27-10-2006 128 89 Lose 89 39 160 6181.5
20-10-2006 128 96 Win 96 146 159 23141
20-10-2006 128 129 Lose 129 79 158 12521.5
13-10-2006 128 64 Win 88 138 157 21873
13-10-2006 128 90 Lose 90 40 156 6340
28-9-2006 129 87 Win 89 139 155 21128
28-9-2006 129 69 Win 89 139 154 21128
21-9-2006 129 88 Win 89 139 153 21128
14-9-2006 129 91 Draw 91 91 152 13832
14-9-2006 129 85 Win 89 139 151 21128
7-9-2006 129 71 Win 89 139 150 21128
7-9-2006 129 110 Lose 110 60 149 9120
29-8-2006 130 115 Win 115 165 148 23760
29-8-2006 130 149 Win 149 199 147 28656
22-8-2006 130 111 Lose 111 61 146 8784
17-8-2006 130 153 Lose 153 103 145 14832
17-8-2006 130 127 Win 127 177 144 25488
10-8-2006 130 103 Lose 103 53 143 7632
10-8-2006 130 127 Win 127 177 142 25488
3-8-2006 130 83 Win 90 140 141 20160
3-8-2006 130 126 Lose 126 76 140 10944
27-7-2006 127 92 Win 92 142 139 19312
27-7-2006 127 124 Win 124 174 138 23664
20-7-2006 127 117 Win 117 167 137 22712
20-7-2006 127 128 Lose 128 78 136 10608
13-7-2006 127 98 Win 98 148 135 20128
13-7-2006 127 74 Win 87 137 134 18632
6-7-2006 127 98 Win 98 148 133 20128
22-6-2006 129 93 Win 93 143 132 18375.5
22-6-2006 129 107 Lose 107 57 131 7324.5
15-6-2006 129 93 Lose 93 43 130 5525.5
15-6-2006 129 107 Win 107 157 129 20174.5
8-6-2006 129 155 Lose 155 105 128 13492.5
8-6-2006 129 74 Win 89 139 127 17861.5
1-6-2006 129 118 Win 118 168 126 21588
1-6-2006 129 107 Win 107 157 125 20174.5
25-5-2006 127 87 Win 87 137 124 16508.5
25-5-2006 127 151 Lose 151 101 123 12170.5
18-5-2006 127 64 Win 87 137 122 16508.5
18-5-2006 127 88 Win 88 138 121 16629
11-5-2006 127 129 Win 129 179 120 21569.5
11-5-2006 127 129 Lose 129 79 119 9519.5
4-5-2006 127 78 Win 87 137 118 16508.5
4-5-2006 127 129 Win 129 179 117 21569.5
20-4-2006 129 117 Lose 117 67 116 7604.5
20-4-2006 129 114 Lose 114 64 115 7264
13-4-2006 129 150 Lose 150 100 114 11350
13-4-2006 129 114 Win 114 164 113 18614
6-4-2006 129 130 Win 130 180 112 20430
6-4-2006 129 81 Win 89 139 111 15776.5
30-3-2006 124 95 Win 95 145 110 15370
30-3-2006 124 127 Win 127 177 109 18762
23-3-2006 124 77 Win 84 134 108 14204
16-3-2006 124 97 Win 97 147 107 15582
16-3-2006 124 101 Win 101 151 106 16006
9-3-2006 124 112 Win 112 162 105 17172
9-3-2006 124 89 Win 89 139 104 14734
2-3-2006 124 94 Win 94 144 103 15264
2-3-2006 124 95 Lose 95 45 102 4770
23-2-2006 134 102 Win 102 152 101 14896
23-2-2006 134 126 Win 126 176 100 17248
16-2-2006 134 70 Win 94 144 99 14112
16-2-2006 134 103 Lose 103 53 98 5194
9-2-2006 134 95 Win 95 145 97 14210
9-2-2006 134 126 Lose 126 76 96 7448
2-2-2006 134 105 Lose 105 55 95 5390
26-1-2006 127 101 Lose 101 51 94 4641
19-1-2006 127 147 Lose 147 97 93 8827
19-1-2006 127 128 Win 128 178 92 16198
12-1-2006 127 102 Win 102 152 91 13832
12-1-2006 127 121 Win 121 171 90 15561
5-1-2006 127 105 Win 105 155 89 14105
5-1-2006 127 85 Win 87 137 88 12467
Total 27547 3341655
Rating 121.3