Rating Calculation by Stephen Morris The Irish ratings were computerised in 1990 and the manner of calculating changes differs from the old system. This article describes the way in which ratings change and how to determine this manually without having to wait for the next rating list. This is of interest to the practical player. Ratings are a system used to approximate playing strength and the combination of all the ratings in the system make up a pool. This pool is similar to the national money supply in that if ratings are too high then the system suffers from inflation (high prices) and if ratings are too low then deflation occurs (low prices). The rating system strives to attain a happy medium where players have gradings which match their strength. NOTE: The computer system uses four places of decimals but this article uses just two for simplicity. I would like to acknowledge John Crowley for kindly supplying me with information about the computerised rating system. Method of Calculation: Three items of information are needed for calculating rating changes: 1. K-factor 2. Expected score 3. Actual score The K-factor is simply a number which reflects a player's age, rating and time at present rating. Young improving players have big K-factors (e.g. 40) while older, established players have smaller K-factors (e.g. 24). Table 1 illustrates the different K-factors. Player's Description K-factor Rating 2100 or higher 16 Player under 21 years of age 40 Player 21 years or older, rated less than 2100 and not settled 32 (It takes 8 years to settle) All others 24 Table 1 K-factor Rules The expected score is a number between 0 and 1 which reflects your chance of winning against a specific rating, e.g. I have an expected score of 0.25 against someone 200 points higher rated. My opponent has an expected score of 0.75. My expected score and my opponent's expected score both add up to 1. The K-factor and the expected score are both obtained by consulting a lookup table. The actual score is the result of the game, 1, 0.5 or 0, i.e. a win, draw or a loss. The rating change is calculated as follows: Rating Change = K-factor * (Actual Score - Expected score) This formula is the key to calculating ratings and the examples below illustrate its use in conjunction with Table 2. Example 1 Player A is rated 1850 with a K-factor of 40 beats Player B rated 2250 with a K-factor of 16 The rating difference is 400 points. From Table 2 this rating difference gives player A an expected score of 0.10 and player B an expected score of 0.90 So, player A's rating increases by: K * (1.0 - 0.1) = 40 * (0.9) = 36 points Player B's rating decreases by: K * (0 - 0.9) = 16 * (0.1) = 14 points Example 2 Player A is rated 1850 with a K-factor of 40 draws with Player B rated 2250 with a K-factor of 16 The rating difference is 400 points. From Table 2 this rating difference gives player A an expected score of 0.10 and player B an expected score of 0.90 So, player A's rating increases by: K * (0.5 - 0.1) = 16 points Player B's rating decreases by: K * (0.5 - 0.9) = 6 points Example 3 Player A is rated 1850 with a K-factor of 40 loses to with Player B rated 2250 with a K-factor of 16 The rating difference is 400 points. From Table 2 this rating difference gives player A an expected score of 0.10 and player B an expected score of 0.90 So, player A's rating decreases by: K * (0 - 0.1) = 4 points Player B's rating increases by: K * (1 - 0.9) = 2 points Example 4 Player A is rated 1750 with a K-factor of 40 loses to Player B rated 1450 with a K-factor of 40 The rating difference is 300 points. From Table 2 this rating difference gives player A an expected score of 0.84 and player B an expected score of 0.16 So, player A's rating decreases by: K * (0 - 0.84) = 34 points Player B's rating increases by: K * (1.0 - 0.16) = 34 points The Lookup Table Table 2 below illustrates the expected scores for each player given a specific rating difference. H = Higher rated player's expected score L = Lower rated player's expected score Rating Difference H L 0-6 0.5 0.5 7-13 0.51 0.49 14-20 0.52 0.48 21-27 0.53 0.47 28-34 0.54 0.46 35-41 0.55 0.45 42-48 0.56 0.44 49-56 0.57 0.43 57-63 0.58 0.42 64-70 0.59 0.41 71-77 0.60 0.40 78-85 0.61 0.39 86-92 0.62 0.38 93-99 0.63 0.37 100-107 0.64 0.36 108-115 0.65 0.35 116-122 0.66 0.34 123-130 0.67 0.33 131-138 0.68 0.32 139-147 0.69 0.31 148-155 0.70 0.30 156-164 0.71 0.29 165-172 0.72 0.28 173-181 0.73 0.27 182-190 0.74 0.26 191-200 0.75 0.25 201-209 0.76 0.24 210-219 0.77 0.23 220-230 0.78 0.22 231-240 0.79 0.21 241-251 0.80 0.20 252-263 0.81 0.19 264-275 0.82 0.18 276-287 0.83 0.17 288-301 0.84 0.16 302-315 0.85 0.15 316-330 0.86 0.14 331-346 0.87 0.13 347-363 0.88 0.12 364-381 0.89 0.11 382-401 0.90 0.10 402-424 0.91 0.09 425-449 0.92 0.08 450-477 0.93 0.07 478-511 0.94 0.06 512-551 0.95 0.05 552-603 0.96 0.04 604-675 0.97 0.03 676-797 0.98 0.02 798-1720 0.99 0.01 Over 1720 1.00 0.00 Table 2 Expected Scores for the Range of Rating Differences THE END