# EGF Rating System

GoR, the rating scheme used by the European Go Federation is an Elo type rating system described in detail on the European Go Database website. Formerly, it was maintained by Ales Cieply at http://gemma.ujf.cas.cz/~cieply/GO/gor.html

## Winning percentages

The basis of an Elo system is estimating the chances that one player will defeat another based on their ratings. The ratings used by the EGF depend in part upon your rank, with 20k-1k ranks distributed over the range 100-2000, 1d-7d distributed over the range 2100-2700 and pro ranks above that. The rating that (nominally) belongs to a certain rank can be seen in the table below.

The chance Se(A) of player A (with the lower rating) winning against a higher rated opponent is given by the following formula:

The chance that player B wins is equal to the chance that A does not win, and can easily be derived from the table below by subtracting the percentages from 100%.

where D is the rating difference and a is a factor that depends on rating, and varies from a value of 200 at 20 kyu to a value of 70 at 7 dan. The table below lists a and shows the estimated winning percentage according to the EGF formula. The same data has been used to generate the graph to the right.

As we can see, the graph gets steeper for higher rated players. What this means is that the EGF rating considers it more likely for a 5 dan to win against a 4 dan, than for a 4 kyu to win against a 5 kyu, but also more likely for the 5 dan to lose to a 6 dan than for the 4 kyu to lose to a 3 kyu. This represents the fact that stronger players tend to have a more stable performance, with fewer "upset" victories or defeats.

rating rank K a 0 25 50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500 Estimated winning percentage against a player X rating points stronger, where X is: 100 20k 116 200 50.0% 46.9% 43.8% 40.7% 37.8% 34.9% 32.1% 29.4% 26.9% 24.5% 22.3% 20.2% 18.2% 16.5% 14.8% 13.3% 11.9% 10.7% 9.5% 8.5% 7.6% 200 19k 110 195 50.0% 46.8% 43.6% 40.5% 37.5% 34.5% 31.7% 29.0% 26.4% 24.0% 21.7% 19.6% 17.7% 15.9% 14.2% 12.8% 11.4% 10.2% 9.0% 8.0% 7.1% 300 18k 105 190 50.0% 46.7% 43.5% 40.3% 37.1% 34.1% 31.2% 28.5% 25.9% 23.4% 21.2% 19.0% 17.1% 15.3% 13.7% 12.2% 10.9% 9.6% 8.6% 7.6% 6.7% 400 17k 100 185 50.0% 46.6% 43.3% 40.0% 36.8% 33.7% 30.8% 28.0% 25.3% 22.9% 20.6% 18.4% 16.5% 14.7% 13.1% 11.6% 10.3% 9.1% 8.1% 7.1% 6.3% 500 16k 95 180 50.0% 46.5% 43.1% 39.7% 36.5% 33.3% 30.3% 27.4% 24.8% 22.3% 20.0% 17.8% 15.9% 14.1% 12.5% 11.1% 9.8% 8.6% 7.6% 6.7% 5.9% 600 15k 90 175 50.0% 46.4% 42.9% 39.4% 36.1% 32.9% 29.8% 26.9% 24.2% 21.7% 19.3% 17.2% 15.3% 13.5% 11.9% 10.5% 9.2% 8.1% 7.1% 6.2% 5.4% 700 14k 85 170 50.0% 46.3% 42.7% 39.1% 35.7% 32.4% 29.3% 26.3% 23.6% 21.0% 18.7% 16.6% 14.6% 12.9% 11.3% 9.9% 8.7% 7.6% 6.6% 5.8% 5.0% 800 13k 80 165 50.0% 46.2% 42.5% 38.8% 35.3% 31.9% 28.7% 25.7% 22.9% 20.4% 18.0% 15.9% 14.0% 12.2% 10.7% 9.3% 8.1% 7.1% 6.1% 5.3% 4.6% 900 12k 75 160 50.0% 46.1% 42.3% 38.5% 34.9% 31.4% 28.1% 25.1% 22.3% 19.7% 17.3% 15.2% 13.3% 11.6% 10.1% 8.8% 7.6% 6.6% 5.7% 4.9% 4.2% 1000 11k 70 155 50.0% 46.0% 42.0% 38.1% 34.4% 30.9% 27.5% 24.4% 21.6% 19.0% 16.6% 14.5% 12.6% 10.9% 9.5% 8.2% 7.0% 6.1% 5.2% 4.5% 3.8% 1100 10k 65 150 50.0% 45.8% 41.7% 37.8% 33.9% 30.3% 26.9% 23.7% 20.9% 18.2% 15.9% 13.8% 11.9% 10.3% 8.8% 7.6% 6.5% 5.6% 4.7% 4.0% 3.4% 1200 9k 60 145 50.0% 45.7% 41.5% 37.3% 33.4% 29.7% 26.2% 23.0% 20.1% 17.5% 15.1% 13.0% 11.2% 9.6% 8.2% 7.0% 6.0% 5.1% 4.3% 3.6% 3.1% 1300 8k 55 140 50.0% 45.5% 41.2% 36.9% 32.9% 29.1% 25.5% 22.3% 19.3% 16.7% 14.4% 12.3% 10.5% 8.9% 7.6% 6.4% 5.4% 4.6% 3.9% 3.3% 2.7% 1400 7k 51 135 50.0% 45.4% 40.8% 36.5% 32.3% 28.4% 24.8% 21.5% 18.5% 15.9% 13.6% 11.5% 9.8% 8.3% 7.0% 5.9% 4.9% 4.1% 3.4% 2.9% 2.4% 1500 6k 47 130 50.0% 45.2% 40.5% 36.0% 31.7% 27.7% 24.0% 20.6% 17.7% 15.0% 12.8% 10.8% 9.0% 7.6% 6.3% 5.3% 4.4% 3.7% 3.0% 2.5% 2.1% 1600 5k 43 125 50.0% 45.0% 40.1% 35.4% 31.0% 26.9% 23.1% 19.8% 16.8% 14.2% 11.9% 10.0% 8.3% 6.9% 5.7% 4.7% 3.9% 3.2% 2.7% 2.2% 1.8% 1700 4k 39 120 50.0% 44.8% 39.7% 34.9% 30.3% 26.1% 22.3% 18.9% 15.9% 13.3% 11.1% 9.2% 7.6% 6.2% 5.1% 4.2% 3.4% 2.8% 2.3% 1.9% 1.5% 1800 3k 35 115 50.0% 44.6% 39.3% 34.2% 29.5% 25.2% 21.3% 17.9% 14.9% 12.4% 10.2% 8.4% 6.9% 5.6% 4.5% 3.7% 3.0% 2.4% 2.0% 1.6% 1.3% 1900 2k 31 110 50.0% 44.3% 38.8% 33.6% 28.7% 24.3% 20.4% 16.9% 14.0% 11.5% 9.3% 7.6% 6.1% 5.0% 4.0% 3.2% 2.6% 2.1% 1.6% 1.3% 1.1% 2000 1k 27 105 50.0% 44.1% 38.3% 32.9% 27.8% 23.3% 19.3% 15.9% 13.0% 10.5% 8.5% 6.8% 5.4% 4.3% 3.4% 2.7% 2.2% 1.7% 1.4% 1.1% 0.8% 2100 1d 24 100 50.0% 43.8% 37.8% 32.1% 26.9% 22.3% 18.2% 14.8% 11.9% 9.5% 7.6% 6.0% 4.7% 3.7% 2.9% 2.3% 1.8% 1.4% 1.1% 0.9% 0.7% 2200 2d 21 95 50.0% 43.5% 37.1% 31.2% 25.9% 21.2% 17.1% 13.7% 10.9% 8.6% 6.7% 5.2% 4.1% 3.2% 2.5% 1.9% 1.5% 1.1% 0.9% 0.7% 0.5% 2300 3d 18 90 50.0% 43.1% 36.5% 30.3% 24.8% 20.0% 15.9% 12.5% 9.8% 7.6% 5.9% 4.5% 3.4% 2.6% 2.0% 1.5% 1.2% 0.9% 0.7% 0.5% 0.4% 2400 4d 15 85 50.0% 42.7% 35.7% 29.3% 23.6% 18.7% 14.6% 11.3% 8.7% 6.6% 5.0% 3.8% 2.8% 2.1% 1.6% 1.2% 0.9% 0.7% 0.5% 0.4% 0.3% 2500 5d 13 80 50.0% 42.3% 34.9% 28.1% 22.3% 17.3% 13.3% 10.1% 7.6% 5.7% 4.2% 3.1% 2.3% 1.7% 1.2% 0.9% 0.7% 0.5% 0.4% 0.3% 0.2% 2600 6d 11 75 50.0% 41.7% 33.9% 26.9% 20.9% 15.9% 11.9% 8.8% 6.5% 4.7% 3.4% 2.5% 1.8% 1.3% 0.9% 0.7% 0.5% 0.3% 0.2% 0.2% 0.1% 2700 7d 10 70 50.0% 41.2% 32.9% 25.5% 19.3% 14.4% 10.5% 7.6% 5.4% 3.9% 2.7% 1.9% 1.4% 1.0% 0.7% 0.5% 0.3% 0.2% 0.2% 0.1% 0.1% For comparison, these are the winning percentages in the basic Elo formula used in Chess (percentages not rating dependent). This is equivalent to using a value of 173.7 for the variable 'a' in the formula above.: 50.0% 46.4% 42.9% 39.4% 36.0% 32.7% 29.7% 26.7% 24.0% 21.5% 19.2% 17.0% 15.1% 13.3% 11.8% 10.4% 9.1% 8.0% 7.0% 6.1% 5.3%

## Rating changes as a result of games

The number K in the above table influences how much you rating changes based on the result of a game.

The new rating Rn for a player is calculated from his old rating Ro as

In this formula, S is the result of the game (1= won, 0.5 = jigo, 0 = lost) and Se is the expected result from the table above (in the range 0-1).

Here we see how K affects the rating change resulting from a game. And as S-Se is never more than 1 or less than -1, K also represents the maximum rating change per game at a certain level.

## Distribution of GoR per rank

Although there is a nominal rating associated with each rank, the actual rating of players of the same rank varies. The graph below shows how it varies, with most ranks roughly showing a gaussian distribution around the nominal rating:

### Method of generating the graph

This graph plots the frequency of post-tournament ratings per grade in the EGF rating database, for all tournaments in or after the year 2000. The height of the graph at rating point X represents how often a certain post tournament rating occurred.

To smooth the graph, each data point also affects its neighbours, adjusted by distance. A rating at 0 points distance adds 25, at 1 point distance 24, at 5 points distance 20, and so on downto 0 at 25 points distance or more. Since this method adds 625 to the volume of each rating graph for each data point, the end result was scaled back by that factor.

I have discarded any data points where a pre tournament rating was reset based on a jump of at least 2 grades, and where the post tournament rating was 100 points lower than that reset grade. Because a player can never lose more than 100 points in one tournament, such data point are very common among lower kyu players (because ratings change more quickly the lower they are). This caused very noticable artificial bumps around those ratings.

The graph does not plot values below value 25 to eliminate artifacts caused by single outliers (there are some errors in the EGF data, I have informed Ales Cieply of those I have found).

7D includes all Pro grades, which results in noticable bumps, especially around 2760 (3p) and 2820 (5p).