Editing Go ranks and ratings (section)

==Rating systems==
With the invention of calculators and computers, it has become easy to calculate a '''rating''' for players based on the results of their games. Commonly used rating systems include the [[Elo rating|Elo]] and [[Glicko rating system|Glicko]] rating systems. Rating systems generally predict the probability that one player will defeat another player and use this prediction to rank a player's strength.

===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.

===Other rating systems===

A variation of the Elo rating system called WHR ('Whole History Rating'), differs from standard Elo in that it retroactively re-rates players based on their entire history after each new result is added, rather than incrementally changing a player's rating on a game-by-game basis. This involves more intense computation than other methods, but is claimed that "in comparison to Elo, Glicko, TrueSkill, and decayed-history algorithms, WHR produces better predictions.".<ref>{{cite web|url=https://www.remi-coulom.fr/WHR/|title=Whole-History Rating: A Bayesian Rating System for Players of Time-Varying Strength|website=www.remi-coulom.fr|access-date=4 April 2018}}</ref><ref>{{Cite web |last=Coulom |first=Rémi |title=Whole-History Rating: A Bayesian Rating System for Players of Time-Varying Strength |url=https://www.remi-coulom.fr/WHR/WHR.pdf |access-date=6 May 2023}}</ref> The website [https://www.goratings.org/en/ Go Ratings] implements the WHR method to calculate global player rankings.

===Rating base===

The ratings of players are generally measured using the game results of Go competitions and [[tournament]]s. Most clubs and countries maintain their own ratings, as do Go playing servers. Go tournaments in Europe use the [http://gemma.ujf.cas.cz/~cieply/GO//gor.html EGF Official ratings]. <ref>{{Webarchive|url=https://web.archive.org/web/20171226050729/http://gemma.ujf.cas.cz/~cieply/GO/gor.html |date=2017-12-26 }}</ref>

In a small club, ranks may be decided informally and adjusted manually when players consistently win or lose. In larger clubs or country wide rating systems, a mathematical ranking system is generally easier to maintain. Players can then be promoted or demoted based on their strength as calculated from their wins and losses.

Most Go playing servers use a mathematical rating system to keep track of the playing strength of their members. Such ratings may or may not be translated to kyu and dan ranks for the convenience of the players.

Player pools that do not regularly mix (such as different countries, or sub-groups on online servers) often result in divergent playing strengths compared to the same nominal rank level of other groups. Players asked to give their rank will therefore often qualify it with "in my country" or "on this Internet server".<ref name=RankCompare/>

=== Winning probabilities ===
The rating indirectly represents the probability of winning an even game against other rated players. This probability depends only on the difference between the two players' ratings, but its magnitude varies greatly from one implementation to another. The American Go Association adopted a uniform standard deviation of 104,<ref>[https://web.archive.org/web/20190214230651/https://www.usgo.org/files/pdf/AGARatings-Simple.pdf Inside the AGA Ratings System] refers to the standard deviation used to calculate winning expectancies as px_sigma.</ref> i.e. slightly more than one rank, while the European Go Federation ratings have a sliding standard of deviation from 200 for beginners down to 70 for top players.<ref name=GoR/> The IGS has a fixed standard deviation for all levels of play, but a non-standard distribution.<ref>[http://www.pandanet.co.jp/English/commands/term/TOC.html The IGS Rating System] {{Webarchive|url=https://web.archive.org/web/20070825012128/http://www.pandanet.co.jp/English/commands/term/TOC.html |date=2007-08-25 }} implies a distribution function which is not a bell curve, but a "pointy hat".</ref> The following table displays some of the differences:

{|class="wikitable"
! rowspan="2" | Rating<br />organisation
! colspan="4" | Rating
! colspan="3" | Winning % of the stronger player
|-
!2 kyu
!1 kyu
!1 dan
!2 dan
!1k vs. 2k
!1d vs. 2k
!2d vs. 2k
|----
|AGA
| −250
| −150
|150
|250
|83.2%
|97.3%
|99.8%
|----
|EGF
|1900
|2000
|2100
|2200
|71.3%
|86.0%
|93.9%
|----
|IGS
|30
|31
|32
|33
|71.9%
|84.2%
|91.1%
|----
|}

=== Winning chances and handicaps in Go versus chess ===

While in chess a player must take some risks to avoid a draw, in Go draws (jigo) are either impossible (with superko and non-integer komi, such as 6.5 points, as is common) or less likely in the case of integer komi. Also, an average game of Go lasts for 240 moves (120 moves in chess terms), compared to 40 in chess, so there are more opportunities for a weaker player to make sub-optimal moves. The ability to transform a small advantage into a win increases with playing strength. Due to this ability, stronger players are more consistent in their results against weaker players and will generally score a higher percentage of wins against opponents at the same rank distance.<ref>{{cite web | url = http://gemma.ujf.cas.cz/~cieply/GO/statev.html | title = Statistics on Even Games | author = Official European Ratings | access-date = 2007-10-18 | archive-date = 2016-06-04 | archive-url = https://web.archive.org/web/20160604104237/http://gemma.ujf.cas.cz/~cieply/GO/statev.html | url-status = dead }}</ref>