Rating principles

Summary

Comments

The difference in strength is adjusted by increasing the strength of the person receiving handicap. The handicap is the number of stones given, reduced by 0.5 since no komi is given (identical to EurpRatings).

The Afactor (table I) is a measure of the probability that a player can win from a stronger player. This factor is larger for kyu players than for dan players. This factor is the same as 'a' in the EuroRatings and was not present in the old formula.

The expected result is a value between 0.0 (loss) and 1.0 (win). It can be calculated from the adjusted strength difference and the afactor. Playing against an even opponent gives probability 0.5.

Handicap games do not count as much as even games. This is expressed by the handicapfactor.

Tournament games count more than club games. This is expressed by the PlaceFactor.

The ConFactor (table I) expresses the value of winning/losing a game, or the speed the rating changes. This is larger for weaker players and smaller the stronger players. (identical to EuroRatings)

The change in rating is computed by multiplying the mentioned factors.

Table I: The dependence of parameters ConFactor and AFactor on the rating. We use linear interpolation between the points given in the table. For ratings below -1950 and above 650, linear extrapolation is used.
Rating ConFactor AFactor Rating ConFactor AFactor
-1950 116 200 -550 47 130
-1850 110 195 -450 43 125
-1750 105 190 -350 39 120
-1650 100 185 -250 35 115
-1550 95 180 -150 31 110
-1450 90 175 -50 27 105
-1350 85 170 50 24 100
-1250 80 165 150 21 95
-1150 75 160 250 18 90
-1050 70 155 350 15 85
-950 65 150 450 13 80
-850 60 145 550 11 75
-750 55 140 650 10 70
-650 51 135

Examples

Suppose a player A is 20kyu(-1950). He wins against an opponent B which is -1950 too. The expected result is 0.5 since both players have the same strength. The ConFactor is 116. If this game is a club game, he increases 116*0.5*0.8=46.4 points to -1903.6. His opponent drops to 1996.4. Player A is now about one grade stronger than B. (92.8 rating points) So the next day, B gets 1 handicap from A (i.e. black without komi). This has a value of 5 points or 50 rating points. So the adjusted rating difference is 92.8-50=42.8. The AFactor is about 200. The expected result is 1/(1+exp(-42.8/Afactor))=0.45 for B and 0.55 for A. A wins again. A's Confactor is about 113, B's Confactor about 119. So A increases 113*(1-0.55)*0.8*0.95=38.6 points to -1864.9. He an 19 kyu now.

A is increasing rapidly since he is talented and reports his games promptly for processing in the rating list. A few weeks later he is -1450. He now plays a 4 stone game against a 8 kyu (-750) player C. Handicap games do not count so much. A 1 stone game gives a factor 0.95, a 4 stone game gives a factor 0.65. His Confactor is 90, strength difference 700, adjusted strength difference 350. He has a chance of 0.12 of winning, but he wins this game unexpectedly, which earns him 90*0.8*(1-0.12)*0.65=41.2 points. Player C only has a ConFactor of 55. So he loses only 55*0.8*(0.88-0)=25.2 points.

A few years later, player A has reached the level of 1 dan (50 ratingpoints). Winning a game against an opponent of the same strength in a tournament has a value of 24*0.5*1.2=14.4 points now.

-200.0 -150.0 -100.0 -50.0 0.0 +50.0 +100.0 +150.0 +200.0
20 kyu 37.4 44.7 52.6 60.9 69.6 78.3 86.6 94.5 101.8
15 kyu 26.1 32.2 39.0 46.3 54.0 61.7 69.0 75.8 81.9
10 kyu 16.3 21.0 26.5 32.6 39.0 45.4 51.5 57.0 61.7
5 kyu 8.7 11.9 16.0 20.7 25.8 30.9 35.6 39.7 42.9
1 dan 3.4 5.3 7.7 10.9 14.4 17.9 21.1 23.5 25.4
6 dan 0.9 1.6 2.8 4.5 6.6 8.7 10.4 11.6 12.3
Table II: How many points a player (of level 20 kyu,..., 6 dan) gains by beating an opponent that is two stones weaker (-200.0), ... , Equally strong (0.0), ... , two stones stronger (+200.0) in an even tournament game