EGF Rating System
GoR, the rating scheme used by the European Go Federation is an Elo type rating system ![[ext]](images/extlink.gif)
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
| Table of contents |
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, "e" is base of natural logarithm, 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. A bigger the number equals more chance of winning for the lower rated opponent. This indicates less rank stability for low rank players. 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.
| Estimated winning percentage against a player X rating points stronger, where X is: | |||||||||||||||||||||||||||||
| 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 | |||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 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).
See Also
- The GoREst rating estimator
- What rank corresponds to what rating: EGFRatingPerRank
- Statistics can be found at the European Go Database.
- Notes on various implementations
- Probability of Win a study using statistics from the EGD
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