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?).