Editing Go ranks and ratings (section)

===Elo ratings as used in Go===
{| class="wikitable" style="font-size:90%; float: right"
!Elo Rating !!Go rank
|- 
| 2940 || 9 dan professional
|- 
| 2910 || 8 dan professional
|- 
| 2880 || 7 dan professional
|- 
| 2850 || 6 dan professional
|- 
| 2820 || 5 dan professional
|- 
| 2790 || 4 dan professional
|- 
| 2760 || 3 dan professional
|- 
| 2730 || 2 dan professional
|- 
| 2700 || 7 dan amateur or 1 dan professional
|- 
| 2600 || 6 dan (amateur) 
|- 
| 2500 || 5 dan
|- 
| 2400 || 4 dan
|- 
| 2300 || 3 dan 
|- 
| 2200 || 2 dan
|- 
| 2100 || 1 dan
|- 
| 2000 || 1 kyu
|- 
| 1900 || 2 kyu
|- 
| 1800 || 3 kyu
|- 
| 1500 || 6 kyu
|- 
| 1000 || 11 kyu
|- 
| 500 || 16 kyu
|- 
| 100 || 20 kyu
|-
|}

The [[European Go Federation|European Go Federation (EGF)]] implementation of the [[Elo rating|Elo rating system]] attempts to establish rough correspondence between ratings and kyu/dan ranks. This is done by varying some of the components of the Elo formula to achieve a close match to the adjacent table. The probability (S<sub>E</sub>) that the player with the lower rating, player A, wins against a higher rated player B is given by the formula

:<math>S_E(A) = \frac{1}{e^{D/a} + 1}</math>

* ''D'' is the rating difference: <math>R_B - R_A\,</math>
* ''a'' is varied depending on the prior rating of player A.

The probability that player B wins is calculated as
:<math>S_E(B) = 1 - S_E(A)\,</math>

The new rating of a player is calculated as

:<math>R_n = R_o + K(S - S_E)\,</math>

* ''R''<sub>''n''</sub> = new rating
* ''R''<sub>''o''</sub> = old rating
* ''S'' = score (1, 0.5 or 0)
* ''S''<sub>''E''</sub> = expected score
* ''K'' is varied depending on the rating of the players

''K'' is varied depending on the rating of the players, because of the low confidence in (lower) amateur ratings (high fluctuation in the outcome) but high confidence in pro ratings (stable, consistent play). K is 116 at rating 100 and 10 at rating 2700<ref name=GoR>{{cite web | url =http://europeangodatabase.eu/EGD/EGF_rating_system.php | title = EGF Official ratings system | author = European Go Database}}</ref>

In the EGF system, the Elo points won by the winner almost equal the ones lost by the loser and the maximum points movement is the constant ''K'' (from above). However, there is a slight inflationary mechanism built into the ratings adjustment after each game to compensate for the fact that newcomers usually bring fewer ELO points into the pool than they take out with them when they cease active play. Other Elo-flavor ratings such as the AGA, IGS, and DGS systems use [[maximum likelihood estimation]] to adjust ratings, so those systems are anchored by prior distributions rather than by attempting to ensure that the gain/loss of ratings is zero sum.