Why are the rating walls of each rank weird numbers instead of multiples of 25?
1dan is 1919. Why is not 1925 or 1900?
Rating walls: OGS Ranks - Google Sheets
The underlying Glicko2 algorithm works with rating numbers like 1919, 1925, etc. That system is not directly aware of what the absolute rank is (like in terms of where the boundary for shodan lies), and really only compares ratings in a relative sense.
Hence, the rating numbers is translated into a kyu-dan rank via a conversion that is calibrated such that 1 dan is assigned to a reasonable seeming point, in comparison to how these ranks are assigned by other servers and associations. Note that there is not exact global consistency in terms of the exact strength that should be assigned shodan.
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We had a pretty diagram for that
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OGS uses base 19 under the hood, which kind of makes sense because the standard Go board has 19 lines, not 25.
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A Glicko rating is converted to kyu/dan rank using the formula rank = ln(rating / 525) * 23.15. Source
That equation was designed so that each player in a handicap game has a roughly equal chance of winning. (That’s the the goal of the integer kyu/dan rank system.) As rank increases, the rating points gap between each rank gets larger – each handicap stone is “worth more”. This is because the stronger the player, the better he uses each stone.
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Why is 1919 weird and 1925 not weird?
Can a number ĂĽberhaupt be weird?
You label the number as weird. Just your opinion.
Can a system be aware of something?
Why does this make sense?
Ratings correspond to winrates, and ranks correspond to handicap stones. The rating walls are “weird” because the winrate corresponding to a strength difference of 1 stone depends on the level of the players. For instance consider players A, B, C, D who are 3d, 1d, 10k, 12k. If the system is well calibrated, then B has 50% winrate against A if B gets 2 handicap stones and the komi is negative (about -6.5). Same thing with D against C. However, in even games, the winrate of B against A is lower than the winrate of D against C.
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Rating difference in Elo based rating systems has a definite statistical meaning. It directly correlates to winning probability. For example, a 100 point rating gap means that the higher rated player has roughly 2 to 1 odds to win an even game against the lower rated player.
| Elo rating gap | Win probability |
|---|---|
| 0 | 50% |
| 14 | 52% |
| 36 | 55% |
| 72 | 60% |
| 110 | 65% |
| 150 | 70% |
| 240 | 80% |
| 366 | 90% |
This system was invented by mathematician Arpad Elo to rate chess players (Elo rating system - Wikipedia)
In chess rating systems, Elo ratings are commonly used to express player skill. But in go, it is more common to express player skill by go ranks (as in kyu and dan ranks), which are based on handicap gaps (at least historically).
So you’d usually want to map those Elo ratings to go ranks, because that’s what go players are used to. To do that, you’d need to analyze a large database with game results between players of (roughly) known rank.
From such a data set, you can determine the typical win probability between ranks and thus the typical Elo rating gaps between ranks. And from there you can fit a smooth curve through your data points.
Note that the rating gap is not constant between all ranks. It has been observed that a 5d typically has a higher win% against a 4d, than a 9k typically has against a 10k, so the rating gaps around 4d would be wider than the rating gaps around 10k.
OGS arrived at the formula that @jimbotronic quoted, but other go rating systems will work differently and/or use a different conversion formula between Elo ratings and go ranks. For example the EGF rating system doesn’t even use Elo ratings (although it is also based on the analysis described above, and it is possible to convert EGF ratings to Elo ratings. It is notable that EGF Elo rating gaps between ranks are wider than OGS Elo rating gaps at the high end of the rating scale, because the EGF data set shows more skewed win probabilities at high ranks. Perhaps player population and/or game conditions and frequency are factors that should also be accounted for?).
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I mean that metaphorically, in the sense that the system does not work directly with the kyu-dan rank system, but instead just the raw rating value, which needs to be converted to the kyu-dan ranks. The raw rating number is not calibrated to some absolute reference, but rather the conversion is calibrated such that the kyu-dan ranks are roughly similar to those ranks provided by others.
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There is this nice Wikipedia article that explains why base 19 makes sense for the game of go.
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Off topic: Now I’m looking for the narrative structure in Benjito’s comment.
This thread reminds me of historians arguing that the 18th century ended in june 1914, rather than december 1900.
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I like that theory, because I swear the 1990’s didnt end until like 2007 
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I share that feeling although i don’t see any proof that a 6d playing a 1d with 5 stones has an advantage on a 6k playing a 11k (everyone knows how to play better)
And so saying that handicap games are easier at higher levels is a bit astounishing as i get the reverse feedback from players who tend to give less stones.
1919 = 19 * 101
1925 = 5^2 * 7 * 11
both pretty weird, but one is 11-limit and the other is 101-limit, so clearly 1919 is far far weirder
Wonder how you define weird in this context?
Bigger prime numbers may be more supernatural, unearthly. You know they are the ones securing your bank accounts.
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The winrate of 6d vs 1d is the same (50%) as 6k vs 11k - assuming handicap is set fairly (incl. the last half stone / komi) and the ranks are correct.
Rating gaps between ranks 1 stone apart gets wider because that rating difference corresponds to non-handicapped play, and a 6d has much higher winrate vs a 5d than a 6k vs a 7k in even games (consistence icreases with strength).
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This is why 1919 is weirder than 1925: