Go ranks and ratings
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The traditional board game Go (igo, baduk, weichi or weiqi) has a number of national, regional and online systems of measuring levels of skill, as ranks and ratings. A Go rank is comparable to a rank in some Asian-originated martial arts. A rating rigorously calculated on the basis of game results is less traditional (common on Go servers).
Contents |
[edit] Ranks
| Note: The order of the table may need change to be consistent with the content. See the discussion for details.
Professional (Expert) ranks |
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| Amateur (Advanced) ranks |
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| Single-digit kyu (Elementary to Intermediate) ranks |
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| Double-digit kyu (Introductory) ranks |
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Levels of players are defined by ranks in Go. Strictly speaking, we should only say rank, but not rating or level or grade. The rank system is tabulated from the lowest to highest ranks:
| Rank Type | Range | Stage |
|---|---|---|
| double-digit kyu (級,급) (gup in Korean) | 10-30k | Introductory |
| single-digit kyu | 1-9k | Elementary to Intermediate |
| amateur dan (段,단) | 1-7d (where 8d is special title) | Advanced |
| professional dan (段,단) | 1-9p (where 10p is special title) | Expert |
There is no universally applied system. The means of awarding each of those ranks and the corresponding levels of strength vary from country to country and among online go servers.
[edit] Origin
From about the 16th century, the Japanese formalised the teaching and ranking of Go. The system is comparable to that of martial arts schools; and is considered to be derived ultimately from court ranks in China.
[edit] Kyu
Kyu (pronounced like the letter "Q" and abbreviated as "k") is the first stage. This stage is very broad, in which there are full of different levels of players in this stage. Traditionally a newcomer starts at 30 kyu (30k), and proceed numerically downward as strength increases to 1 kyu.
[edit] Introductory: 10k-30k
This is a double digit kyu (DDK) world. The ranks here are reserved for starters. When you first come into the world of Go, you start at 30k traditionally. Note the word "traditionally". 30k is just the normal standard. Some may say you start at 20k. Some may jokingly say you start at even 40k or 50k (non-existent ranks)[1].
Ranks between about 10k and 30k have very limited usefulness and meaning since there are few discernible differences in each level. It is not surprising to see a 19k defeat a 15k player, so these ranks are of little significance. They are mainly used in teaching, to mark their learning progression.
The requirement of a "rank up" at this stage is very loose. Learning a few basic things or concepts may guarantee you a jump to another rank. That is why players in the weak double-digit kyu ranges (DDK, 10-30k) often progress very quickly, especially young children. A jump from 30k to 10k could happen within weeks or even days for quick learners.
Beginners often learn and play on 9×9 boards first. As they progress, they start to play on a 13×13 boards. A 19×19 board is the standard size in Go world. Small board Go is enjoyable, and more complex than other games, but serious players will eventually wind up on full sized boards.
[edit] Elementary: 5-9k
After attaining 9k or better, one has come into next stage, the single digit kyu world (SDK, 1k-9k). This is the lower class of the single digit kyu world.
Unlike the double-digit kyu (DDK) world, the ranks here are much more stable. Each rank counts heavily and means something. It becomes progressively harder to gain each new rank.
The progression from DDK to SDK is a significant turning-point for learners, as in one saying "you are not a Go player if you cannot attain a SDK".
Although a new SDK has gone through all the very basic learning, concepts and rules, he has not mastered every elementary Go concept and correctly apply them in playing. The moves are still very crude with many major mistakes. Go is one of the deepest games - easy to learn, hard to play (well).
At this level, nearly all players prefer the 19Х19 board.
The best computer Go are still stuck around the lowest-class of SDK, ie 8-10k. Other programs remain at the DDK range. Unlike other board games like chess, computer Go is only a good opponent for very elementary SDK Go players or DDK players.
[edit] Intermediate: 1-5k
Now we come to the upper class of the single digit kyu (SDK) world.
To reach this level of skill is a great achievement. It may take a good year or more to come to this upper class. They have gone through a lot of training and practice. They know how to make use of each stone, but not to waste them as many elementary players tend to do. They start to understand how to play Go in a broader mind, that is play out the moves carefully after the consideration of the effects on each sector of the board as a whole.
To progress even further may take years; many players never achieve a dan level rank.
Some intermediate and advanced players avoid playing weaker opponents, especially DDK level. They fear that they will become weaker by falling into bad habits. Others remember that if no stronger players had been willing to play them, they could not have advanced. They "pay it forward", helping serious beginners to improve their strength.
[edit] Advanced: amateur dan
One rank higher than a 1 kyu player will bring you into another stage - (amateur) dan. Dan (abbreviated as "d") ranks are for expert amateur players. Unlike kyu ranking system, Dan ranks ascend numerically with strength, to a normal high of 7 dan. In Asia, 8 dan is not really an amateur rank. It is rather a special and honorary title. A small number of 8 dan can be attained by winning some of the national tournaments.
Achieving a "1 dan" rank implies a general competence in the game. This usually requires a number of years of playing seriously, though exceptionally talented players have risen from first exposure to the game to 1 dan in a year.
Although the difference in skill levels between 1k and 1d is not meant to be huge (it is more or less the same between 1k and 2k, or 3k and 4k), the transition from 1 ranking symbol into another makes people feel more glorious. Recognition as dan players are the ambition of many single-digit-kyu players.
In Japan, before the year 2001, only amateur ranks up to 7 dan were recognised. Now amateur ranks are recognised up to 8 dan. 8 dan is a special and honorary title for amateur which is awarded to the winner of the World Amateur Go Championship. Within the European Go Federation, ranks are recognised up to 7 dan. The American Go Association currently recognizes rankings up to 7 dan amateur.
[edit] Expert: professional dan
The professional dan ranking system is similar to amateurs dans but with more ranks. For historical reasons, it ranges from 1-dan (entry-level expert) to 9-dan.
To distinguish between pro dan and amateur dan, the former is often written "p" (sometimes called ping) and the latter "d". There was no such abbreviation in the past, and this is not generally used as an abbreviation beyond the Internet, where it is common, but not universal.
Each dan rank has its own name. The following are the Japanese names for each dan rank:
- Shodan, 1-dan (entry-level expert)
- Nidan, 2-dan
- Sandan, 3-dan
- Yondan, Yodan 4-dan
- Godan, 5-dan
- Rokudan, 6-dan
- Nanadan (Shichidan), 7-dan
- Hachidan, 8-dan
- Kudan, 9-dan
- Judan, 10-dan (Note: It is not a rank attained in the normal way. It's a special and honorary title given to the champion in a tournament)
For details, see "More on professional dan (in another section)".
[edit] More on ranking system
[edit] Increasing efforts with diminishing returns
What the whole list of go ranks cannot show is the asymptotic shape of the skill improvement over time (increasing efforts with diminishing returns). It is summarized in the saying "(Go is) Easy to learn and difficult to master".
Here's some examples to illustrate the concept of "increasing efforts with diminishing returns":
- A newcomer could rush through from 30k to about 11k in a month - possibly a week if the player is a serious learner or has a mind for the game;
- However a player might take several months to a year attain a rank up when it reaches a single-digit kyu. The lower the single-digit kyu, the more time and efforts are required for a rank up;
- It may take a year to a decade to reach amateur 1 dan;
- It's hard to imagine how hard it can be for one to progress from one pro dan to another pro dan. It requires much more effort and talent, great enthusiasm and dedication. You have to commit full-time to studying Go.
The handicap between these stages would be about 9 stones each, but the time to achieve the levels is highly uneven, even if the effort might have been the same. Few make it to a 5 dan amateur ranking (i.e. ELO 2500 in Europe) and only after great enthusiasm and dedication, taking many, many years. This level reflects a deep and subtle level of understanding of the strategy of the game, coupled with a keen, well-practiced ability to judge abstruse, complex, tactical situations.
[edit] Handicaps
Within most systems and at most levels, handicap is given to offset the strength difference between players of different ranks.
There are 2 types of handicaps in game of Go, ie handicap stones or compensation points. In a handicap game, the weaker player takes Black, the stronger White.
The difference in ranks is a good guide to how many handicap stones may be given to adjust the game for a more even struggle. As a general rule, each rank represent 1 stone strength, where 1 stone is said to be worth about 10 to 12.5 points. For example, a 3k player would normally give a 7k player 4 handicap stones, in order to have an even game. However it is traditional that handicaps are up to 9 stones only.
Handicap stones are either determined at a fixed area and seqences by the association or countries or servers (fixed handicap placement), or determined by oneself, i.e. one is free to place them anywhere on the go board (free handicap placement).
[edit] Compensation points
Compensation points (Komi) are mostly used when players' ranks are equal. They are used to offset the advantage of being black (moving first). Playing first is regarded as a significant advantage in modern Go. This advantage needs to be compensated. There are still no absolute standards on the number of compensation points due to the difficulty of determining a fair value. 6.5 points are used in Japan and Korea. 7.5 points are used in China and America (see AGA rules).
These values include an extra 0.5 point for White. The 0.5 point is used to prevent a draw from occurring.
[edit] Different ranking bases
Formal player ranks are established through Go competitions and tournaments. They occur in many countries and online via Go servers. Go tournaments in Europe use the McMahon score to calculate handicaps between unequal players, with a preference for pairing players with equal scores. Matches last for some specific number of rounds (e.g. 4) in which each player will play a game in each round, increasing his McMahon score by one point for each win. The European ranking calculation is described in the article titled EGF Official ratings
In a small club, ranks may be decided informally and adjusted when players consistently win or lose. In a large club, a mathematical ranking system gives better results. Players can then be promoted or demoted based on their strength as calculated from their wins and losses.
[edit] Is the ranking system perfect?
Ranks enable any two players to determine their respective strengths and to handicap a game so that either side has a fair chance of winning. However strength is not something which can be quantifiable and comparable in a linear way. Someone of 115 strength does not always beat someone of 114 strength; someone of 200 strength is not necessarily twice as strong as someone of 100 strength. Amateur dans have been known to beat pro dan, and a 1p can beat a 9p[2].
Rankings offer convenient but rough comparisons. Like many other ranking systems, these rankings are not absolute.
[edit] More on professional dan
[edit] How to become professional
Professional dan rankings are normally awarded in Japan, China, South Korea or Taiwan, through one of the professional Go associations, most notably the Hanguk Kiwon (Korea) or Nihon Ki-in (Japan).
The attainment of professional qualification differs in different countries:
- In China a few amateurs are given the 1p grade as probationers, on the basis of success in amateur tournaments.
- In Japan student professionals are called insei, and have to play in internal insei competitions to qualify; mostly they are adolescents, and must decide whether to continue based on their chances of a career in Go, or go to university. Insei rarely take part in amateur events, but some of the top amateurs are ex-insei.
- In South Korea four amateurs become professional every year, at the top of a ferocious league system of 80 aspiring pros. Once within the professional system, promotion is based on game results.
Most professional players begin studying Go seriously when they are children, with some (such as Cho Chikun) turning pro before age 11. In order to qualify as a first dan professional (1p), one must have deep resources of game experience and study. Tactically, professionals thoroughly understand good shape, tesuji, and life and death. Pros mostly have similar levels of pure technical skill. They differ more in positional judgement: deep evaluation of future game positions and a great variety of tactical and strategic means to obtain that imagined future position are requirements for professional players. It is of basic importance for a player to know whether they are behind or have the advantage, because it influences the risks that should be taken and subsequently the strategies chosen in a game.
Knowledge of opening patterns (fuseki) and tactical patterns (joseki) are by-products of years of study and playing Go; memorization is not the basis for strong play. Fuseki and joseki knowledge is far less central in Go than openings are in Chess. The decisive part of the game, resulting in win or loss, may occur 100 moves or more later.
[edit] Discrepancies among professionals
The differences between professional levels are much smaller: perhaps of the order of three to four handicap stones between an average 1p and a prime 9p, as a rough rule of thumb. Thus the difference between professional dan levels corresponds to one-third or one-fourth handicap stone, and the strength of a typical professional will correspond to that of an amateur 9-dan (if it existed) or higher in theory.
Each country has different rules for promotion. Ranks may therefore differ somewhat from country to country. Generally Asian professionals are stronger than Western or European professionals.
Professionals may also differ in actual strength for a number of reasons, including promotion, not keeping up with actual gains in strength, or the fact that professional ranks, unlike kyu or amateur dan, may rise but never fall (even if the player grows weaker). This has posed some of the problems. There are currently over one hundred people who have the rank of 9p (the highest professional rank), though many of them no longer play competitively due to age. A further distinction is that some 9p players regularly hold titles, others won some titles, some entered the title leagues, and many 9p never had the luck to achieve any of above.
To make the situation look even worse, there are some instances where a low pro dan can beat some of the highest pro dans, although it is not very common.[3]
The Japanese Oteai system, dating back to 1924, was reformed in 2004 to alleviate some rank inflation that had crept in over the years. Today's system uses various benchmarks; for example, winning certain tournaments or a certain number of games, to be promoted a rank. The Korean system has also been similarly changed in the past few years.
[edit] Pro and amateur dan
In theory, professional dans should beat all levels of amateur dans. In reality, the very top amateurs have proven very strong, even against professionals, though they do not have an official, professional rank. The conventional wisdom is that such players may achieve some of the insight of a pro, though perhaps not the detailed knowledge.
In China, Japan, and Korea, there are two distinct ranking sets, one for amateur players and one for professional players (who receive a fee for each game they play, bonuses for winning, and fees for other related activities such as teaching).
In the Japanese professional ranking system, distinction between ranks was traditionally considered to be roughly one third of a handicap stone (making the difference 3 pro dan equal to one amateur dan). The strength of new professionals (1 dan) was usually comparable to that of the highest ranked amateurs. Currently the professional ranks are assumed to be more bunched together, covering not much more than two amateur dans; so that pro 1 dans win some games against 9 dans. There are also a number of amateur players acknowledged as having pro 6 dan understanding of the game.
In South Korea, there are several amateur systems in use, with the recent introduction of official 7, 6 and 5 dan amateur ranks, each of which is somewhat stronger than the corresponding European grade. A 7 dan amateur will have won three national events, and will be effectively of lower-ranked pro standard. The older gup system does not easily match others. In practice, in Korean clubs, grades may be worked out against the resident strongest amateur.
In Taiwan, a distinctive system of pro dan ranks is used, with the order reversed, so that 1 dan is the highest, 9 the lowest. [citation needed]
The Taiwan Chi Yuan Culture Foundation also employs a dan system similar to that in Japan. It ranks its professional players from beginner dan (初段) up to 9 dan, being the highest. List of professional players in taiwan. However, the amateur ranking system is established by another organization. Taiwan Go Association. certifies amateur player through competitions, ranking player from beginner dan (初段) to 6 dan with 7 dan being honorary.
In Germany and The Netherlands a "classes"-system (German: "Klassen") was established. It comprised a further subdivision into Kyu/Dan halfgrades with classes 18 and 17 = amateur 1 dan with the 17 being on the stronger side. It is still in use for club ladders etc. where you get promoted or demoted after a won or lost game, respectively.
[edit] Discrepancies among different player pools
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".
[edit] Go rating with ELO
As in other sports where it is not practical to hold an all-against-all championship to establish who is strongest (chess, backgammon, racquetball, etc.) a statistical method is employed. Variations of the ELO rating system are nowadays often used in Go. In order to roughly correspond to FIDE chess ratings, an average 1 dan should have Go rating about 2100 and the difference between grades should be about 100. A player with a rating of 2000 might be an average 1 kyu, a recently improved 2 kyu or a 1 dan who has lost many games recently.
There is a difference between kyu/dan ranks, which represent peak personal achievements, and ELO ratings, which measure current playing strength. A player who was 3 dan fifteen years ago will know the necessary strategies and concepts for teaching weaker players, but he will probably lose points to settle below 2300 if he again enters tournaments against active 3 dan players. ELO ratings have caused much consternation among those who feel it is dishonorable to lose rank.
Another departure from tradition is that ELO ratings are calibrated by winning percentage, not by stone handicaps. An extra handicap stone has much less influence on winning percentage at a low level of play than at a high level of play. Therefore, from the perspective of ELO ratings, traditional ranks are too spread out at the low level and too compressed at a high level. To put it another way, a 6-dan player has a much better chance of beating a 5-dan player than a 15-kyu player has of beating a 16-kyu player, so the ELO system must conclude either that the top players need to be further apart in rating than 100 points, or the bottom players need to be closer in rating than 100 points.
[edit] Converting ELO ratings into Go ranks
The EGF implementation of the ELO system attempts to establish rough correspondence between ratings and Go (kyu/dan) ranks.
Points Go rank ------ ------- 2900 9 pin (9 dan professional) 2780 5 pin (5 dan professional) 2660 1 pin (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
0 21 kyu
-100 22 kyu
-200 23 kyu etc.
Because of the low confidence in (lower) amateur ratings (high fluctuation in the outcome) but high confidence in pro ratings (stable, consistent play), the value of K in the following formula varies:
- Rn = Ro + K(S − Se)
where Rn = new rating, Ro = old rating, S = score, Se = expected score and the constant K is between 30 and 20 for players below 2400 ELO (e.g. 4 dan) and K = 10 for players above.
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 in to 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.
Because of the few ranked even games played between amateurs and professionals, it is difficult to establish a single ELO table where both pools are represented. Using the rough equivalence between handicap stones and rating difference (1 stone = 100 ELO points) a professional 9 dan (9p) would have +/- 2900 ELO points, but on the basis of winning probabilities, we should suspect a professional 9 dan to be rated well over 3000.
[edit] Winning probabilities
The rating indirectly represents the probability of winning 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 [4], 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[5]. The IGS has a fixed standard deviation for all levels of play, but a non-standard distribution [6]. The following table displays some of the differences:
| Rating Org. | 2kyu rating | 1kyu rating | 1dan rating | 2dan rating | 1kyu win vs. 2kyu | 1dan win vs. 2kyu | 2dan win vs. 2kyu |
|---|---|---|---|---|---|---|---|
| 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% |
Note how different the expectations of each system are regarding even games between players of unequal strength. If you can win 90% of even games against a 2 kyu player, the AGA believes you are 1.33 ranks higher, the EGF believes you are 2.42 ranks higher, and the IGS believes you are 2.80 ranks higher! The lack of agreement stems from a tradition of playing handicap games between players of different ranks, so there is a lack of data regarding non-handicap games between mismatched opponents.
[edit] Higher-rank players have extreme winning chances
For even games between players less than one rank apart, it doesn't matter very much which distribution curve is used: roughly accurate ELO ratings will emerge on the basis of many even games. However, because games between unequal players are traditionally played at handicap, ELO rating systems consider a stone of handicap to equal the rating points in one rank, and process a handicap game result as if it had been an even game between players of less than one rank apart. This calibrates the rating-based ranks to be a stone of handicap apart, which is in conflict with ranks being a certain winning percentage apart.
Much evidence suggests that, if all games were played with no handicap, higher-rank players would have winning chances far beyond those predicted by the EGF, IGS, and DGS systems. Someone who can beat a 2 kyu player half the time at a four-stone handicap is 3.5 ranks higher, i.e. "2.5 dan". If these two play at an even game, could the 2 kyu player win 1 game in 25, as the EGF formula predicts, or 1 game in 15 as the IGS formula predicts? It seems far more reasonable that it would be 1 game in 2500, as the AGA formula predicts, although it is hard to discriminate any number that small from zero.
In Go, once a player has achieved an advantage, conservative moves are even more effective than in chess. In chess you must take some risks to avoid a draw, but in modern go a draw is impossible, due to the komi system, so the tiniest advantage in skill results in victory. Also, an average game of Go lasts for 120 moves, compared to 40 in chess, so there are more opportunities for a weaker player to make sub-optimal moves. Furthermore, due to the territory scoring system in Go, a positional advantage is a more effective buffer against tactical blunders than in chess.
The ability to transform small advantages (e.g. 5.5 points; equivalent to the first move or half a rank difference) into sure wins increases greatly with playing strength. What is true for amateurs with an ELO difference of 900 holds as much for professionals with a smaller ELO difference.
[edit] Statistics on even games
The table shows statistics on winning a game with the opponent that is one (G+1), two (G+2), three (G+3) and four (G+4) grades stronger than the player whose strength is indicated in the first column. The data were collected from all events included in the GoR tournament database.
G + 1 G + 2 G + 3 G + 4
G Nw Ng Pw Nw Ng Pw Nw Ng Pw Nw Ng Pw --- ----------------- ----------------- ----------------- ----------------- 20K 670 1950 34.4 422 1251 33.7 151 605 25.0 78 391 19.9 19K 303 769 39.4 136 447 30.4 56 191 29.3 28 126 22.2 18K 438 1005 43.6 230 579 39.7 123 330 37.3 29 122 23.8 17K 392 878 44.6 314 700 44.9 73 207 35.3 29 141 20.6 16K 543 1177 46.1 224 568 39.4 78 238 32.8 43 161 26.7 15K 567 1330 42.6 303 741 40.9 137 347 39.5 49 164 29.9 14K 489 1062 46.0 286 690 41.4 81 219 37.0 55 219 25.1 13K 568 1267 44.8 279 656 42.5 142 336 42.3 46 156 29.5 12K 609 1335 45.6 458 1078 42.5 129 314 41.1 39 183 21.3 11K 770 1653 46.6 323 795 40.6 89 253 35.2 35 150 23.3 10K 1038 2301 45.1 486 1196 40.6 117 432 27.1 72 296 24.3 9K 1066 2329 45.8 453 1103 41.1 124 397 31.2 41 233 17.6 8K 1089 2476 44.0 540 1361 39.7 146 449 32.5 52 246 21.1 7K 1279 2857 44.8 577 1506 38.3 130 433 30.0 47 215 21.9 6K 1533 3525 43.5 660 1625 40.6 185 573 32.3 57 292 19.5 5K 1711 3900 43.9 807 2113 38.2 159 565 28.1 73 373 19.6 4K 2058 4551 45.2 797 2057 38.7 189 690 27.4 55 359 15.3 3K 2201 5116 43.0 876 2572 34.1 171 796 21.5 42 327 12.8 2K 2356 5737 41.1 739 2402 30.8 112 652 17.2 28 346 8.1 1K 2791 7169 38.9 687 2659 25.8 160 1069 15.0 43 508 8.5 1D 2669 7012 38.1 869 3441 25.3 207 1504 13.8 44 757 5.8 2D 1976 5752 34.4 683 2981 22.9 156 1291 12.1 19 468 4.1 3D 1888 5424 34.8 673 3300 20.4 107 1362 7.9 1 136 0.7 4D 1436 4675 30.7 341 2485 13.7 8 261 3.1 0 0 - 5D 918 3231 28.4 35 538 6.5 0 0 - 0 0 - 6D 100 664 15.1 0 0 - 0 0 - 0 0 -
Number of games included in statistics: 137872 (date: 09/2004)
Notation:
Nw = number of wins
Ng = number of games
Pw = proportion of wins = Nw/Ng
The zeros in the last line (6 dans vs. stronger opponents) just show a lack of data of amateur 6 dans playing on even with 2, 3, or 4 stones stronger (professional) opponents. The table as a whole supports the notion that, as the average strength of both players increases, a difference in rank (i.e. a stone handicap) represents a greater winning probability. Consider the decline of winning chances in the 4th column from 20% with weak kyus to a mere 0.7% when Dan players are involved.
On the other hand, the table has far more upsets (i.e. lower-ranked players beating higher-ranked players) than the AGA formula would predict. One possible explanation is the large number of go tournaments played with the McMahon system. Under this system, in a match between players of different ranks, it is likely that the weaker player is actually stronger than his or her reported rank, and that the stronger player is likewise weaker than his or her reported rank.
[edit] Game depth
The ELO rating depth also states something about the depth of the game. In the abstract, the total depth of a game is defined by the number of ranks between a random player and the theoretical best play by an infallible creature.
In practice, the depth of the game is the number of ranks between a beginner and the best player in the world. The number of ranks in this latter, practical definition is increased by the age and popularity of the game, as a richer literature and greater playing pool both tend to move apart the end points of the scale. Even so, the practical definition allows a rough comparison of Go to chess, as both have an extensive literature and a huge playing population.
A rank in this definition does not necessarily correspond to a traditional Go rank. Using the EGF scale of standard deviation there are about 25 standard deviations between 20 kyu and 9 dan.
Chess ratings run a range from about 1000 to 2800, but they are differently scaled. Converting the FIDE formula
to be on the same scale as the EGF formula yields
and (2800-1000)/174 = 10.4. Therefore, when converted to be on a similar standard deviation, we can say that chess has a depth of about 10.4 compared to a depth of about 25 for Go.
It is a bit artificial to cut off chess ratings at 1000, but this is no more artificial than cutting off Go ranks at 20kyu. The USCF measures chess ratings down to zero, usually among kindergarten players, so one could argue that there are as many as 16 ranks of depth in chess. However, the AGA also has no cutoff, and measures ratings below 40 kyu as well as above 9 dan, so if chess can be said to have 16 ranks, then Go can be said to have over 50 ranks.
[edit] Notes and references
- ^ "The Interactive Way To Go" uses 50kyu for starters.
- ^ For example, Abe Yumiko 1-dan beats 9-dan
- ^ At the extreme, it is possible for a 1p to beat a 9p: for example, see Abe Yumiko 1-dan beats 9-dan.
- ^ Inside the AGA Ratings System refers to the standard deviation used to calculate winning expectancies as px_sigma.
- ^ EGF Official ratings uses the logistic rather than the normal curve, but the parameter referred to as "a" is roughly comparable to standard deviation for games between players less than one rank apart.
- ^ The IGS Rating System implies a distribution function which is not a bell curve, but a "pointy hat".
