A friend asked me last week: “So, is rank relative?”, and I answered “Yes, no problem”, but I soon realized the issue he had in mind. So, if there is only a small sample of people who play exclusively among themselves, is it possible for someone to achieve a high rank using the same mathematical formula? Since the formula only takes into account wins, losses and rank difference, could someone theoretically became a dan player just by consistently winning within a group of 10 weak players (an extreme case: the ATF - Association of Ten Friends) or does the formula prevents that? Of course, as soon as the sample is huge and players start competing against the best of the world, things tend to balance out, but I had the same doubt, if the formula allows that. If that’s the case, different servers and associations would have a “conversion formula”?
Here in CJKT association amateur rankings, they are probably truly relative, we don’t have a formula per say, but ranking up by joining tournaments (almost exclusively for dan players, for kyu players they can be “granted” like by Go schools, or associations by other means). And after the tournaments, only a predefined percentage of players within certified tournaments would get “promoted”, hence it is really relative to others.
And we do observe the effect that in the area where there are more Go classes and Go players like in urban area, the ranking spread is wider (more tournaments, and some would just happen to have weaker players compositions, while others have stronger ones, and they would both promote the same percentage of winners). While in places with few players where only limited tournaments are possible and most would run into each other every other tournaments, the spread would be smaller, and generally stronger.
In essence, you’d establish which handicaps between the players more or less achieves equilibrium (where everybody wins about 50% of their games). That would give you relative ranks. Only when some players of the group get in contact with the wider community, the group would be able to anchor their internal ranks to the absolute rank scale with labels like 15k or 1d.
But you might also be able to roughly estimate absolute rank by determining how much handicap you can give to novice players (who have played less than a dozen or so games).
In my experience, if you can consistently score about 50% giving 7 stones handicap to novices on a 9x9 board, your absolute rank is probably in the ballpark of 1d EGF.
Yes
No
Mathematically this is only exactly possible if you assume the player base follows the same distribution of win%. Then you can map distributions.
But since at least one of the groups is small, you can’t assume its distribution is equal to the big group.
And even if they are large, they’d need to be statistically similar, for example not one group catering to mostly amateurs and the other a practice ground for semi-pros.
Anchoring is the only way, but it will fall apart if three people anchor in a non-linear way. It is fine for approximations of course.
When an isolated group gets in contact with the wider go community, I’d recommend to (initially) use the strongest player of the group as an anchor because stronger players tend to be more consistent (assuming they play sufficient games with the both the group and the wider go community to function as a reliable anchor).
Then, attempts to say something like “If you are such kyu in OGS, then you would be approximately such kyu in Fox or Tygem if you start playing consistently there, just add/subtract this number”, are nonsense?
There exist comparison tables, such as Rank - worldwide comparison at Sensei's Library, although those may be outdated and inaccurate (especially at lower ranks).
This reminded me of the amateur communities/ranks risen in the late 19th to early 20th century, when travel was still inconvenient and expensive for the most part. Only those well to do players have the options to “visit” other places. At the time, Taiwan was a Japanese colony and there were self-proclaimed amateur Go players with “dan rankings” usually based on their only account of meeting certain strong known Go players in Japan, and play a game of certain handicaps (like 2 stones with a 5d). On occasion there are several Japanese dan players (registered in associations in Japan at the time) who went to Taiwan and meet these self-proclaimed dan players, and even opened schools/clubs as teachers or as judges for local Taiwan tournaments. And the results in earlier days, when the communications were few to none, the discrepancy is pretty high (won easily with the fair handicap 手合), and over time, as more and more Japanese dan players visited and even stayed, the discrepancy shrank. (However, since the very top fights were exclusively between Japanese players, they did act like anchors eventually)