You're right ofcourse. It would not be 0% but an exceedingly small number. So the perfect player would not have a rating of infinity, but it would be a very large number. But for all practical purposes, the perfect player would probably win all of the games that it can play before the heat death of the universe (I'm more a physicist than a mathematician).

Thank you (yes, consistency was unclear, I meant more consistent = higher expected win% against R-1 opponent). That graph is what I'm interested in and the rate on increase in elo gain per rank or 100 GoR and how well the EGF statistics match with the predictions from the EGF's rating model. What interests me most is the relationship between this and handicap stones and how the value of a handicap stone changes as players are stronger. How we have this discrete linear idea of strength difference on the board compared to the ELO differences shown in winrates. If that makes any sense.

There are other rating systems that rate players on an Elo scale, such as https://www.goratings.org/en/. This is fine if you are only interested in ordering players by "skill", but the drawback of an Elo scale is that you cannot easily determine proper handicaps from rating gaps.
The EGD was specifically designed to rate players on a rank scale (based on handicaps), because that is the traditional "rating" scale used in go.

From my earlier Elo gap per rank table, you can say that the value of a full handicap stone is greater as players get stronger: 200 Elo for a 6d, 100 Elo for a 1d and 50 Elo for a 10k.
The same is true for handicap in chess. Apparently, the value of knight-odds is about 600 Elo at a rating of 2400, but only about 200 Elo at a rating of 1100.

Per Elo gap of 2000, the winning probability of the weaker player decreases by a factor of about 10⁵.
So when we put a random player at 0 Elo and use 10^-788 as the probility of playing a perfect game, I get that a perfect player has a rating of about 2000 * 788 / 5 ~ 300,000 Elo on a 19x19 board.

This high number is still hard to put in context though. For purposes of handicap and ranks, I think an estimate of 13d EGF for a perfect player is much more meaningful. Also for AlphaGo Zero, for which Deepmind reported a rating of about 5200 Elo above a random player, I think an estimate of 12d EGF is much more meaningful.

I made a mistake (confusion between ln and log₁₀), it's 10^-342 instead of 10^-788 so a perfect player is about 140000 Elo above random play. That looks a huge number as we are used to thinking of Alphago as near-perfect, but what do we know about superhuman play? Maybe in 2050, Alphago will look very weak compared to more recent IAs.

Thanks for the correction.

So the Elo ratings of AI still have a lot of room for improvement. The gap between 2050 AI and 2020 AI could be as large as 20,000 Elo in even games with perfect komi, but I expect that in terms of handicap, the gap between 2050 AI and 2020 AI will be less than 10 points (so 2020 AI can still win when taking black and a few points reverse komi against 2050 AI).

My interest is partially coming from talking to some Irish ddks and weaker sdks recently about how "going up a stone in rank" doesn't mean the same thing going from 15k to 14k as it does going from 2k to 1k. Being able to visualise it as different jumps in Elo might be helpful for people coming from chess or similar backgrounds where Elo or similar is used.

Thanks.

Well, yes, it was supposed to carry that correlation forward, but I don't see how it could actually work:

1. Players use the rating to determine their rank
2. There are very few handicap games in the data

This means that (1.) the rank is not an input anymore, and (2.) the value of handicap is not an input.

This comes on top of the general problem that rating systems do not get enough data to reach any kind of conclusive answer anyway.

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A good system naturally covers all corner cases without further effort.

Handicaps vs rank gaps
About 10% of the EGD games are handicap games. Indeed that is not really enough to ensure that rank gaps and handicaps stay aligned over time. However, when we analyse those handicap games, the actual results seem to align quite well with expected results. On average the error seems to be less than a stone. So apparently, the EGD managed to keep rank gaps fairly well aligned with handicaps over more than 2 decades. That is encouraging. The system must be doing something right.

Overall rating drift
Besides aligning ranks gaps with handicap, there is also the matter of overall rating drift (inflation/deflation).
1. Before the internet, players would determine their rank by handicap in club games (outside of the EGD). When players entered their 1st tournament, they would declare their club rank at that moment and that would be their initial rating in the EGD.
2. Also, the EGD has a reset mechanism. When a player has improved a lot since their previous tournament (again determined by their current club rank from handicap games), they would declare their new rank on entering the next tournament. If that new rank is more than 1 rank above their previous highest declared rank, the system resets that player's rating to that new rank. So the player is not forced to sandbag and "steal" all their rating points from weaker players.
So the EGD is constantly being fed by club ranks. This is mostly sufficient to keep EGD ranks fairly well aligned to club ranks.

Internet players do complicate this picture a bit, because a new tournament player may have never played in a club when entering their 1st tournament. So they only know their rank on their favourite go server. And the tournament organisers will then guesstimate their equivalent EGF rank to play in the tournament.

The system depends on the right balance of pessimistic and optimistic rank declarations by tournament players to stay well aligned.
When players stop declaring club promotions when playing in tournaments, it becomes difficult to keep EGD ranks aligned to club ranks. If a previous 5k knows he has improved to 3k in their club, but does not update their rank when entering the next tournament, taking away rating points from his opponents to make his own rating rise to 3k, he is effectively sandbagging and causing deflation.

When looking at the EGD data, it does seem that overall, players tend to be pessimistic/conservative, delaying promotion until their EGD rating supports it. There are insufficient optimistic promotions to counter the deflation of pessimistic promotions.

3. So to counter the deflationary effect of improving players that don't promote themselves, we increase the rating bonus in the upcoming EGD update to constantly inject rating points into the system (at least in the kyu range).

Seems by far the thing that would make a go server more attractive to me.

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Patience, grasshopper.

Isn't that a feature of OGS?

Anyway I don't really see the point of having an AI analysis on a go server, as I can run Katago on my computer after the game.

Hm. So another go server is more advanced, having a feature integrated that you would otherwise need use a separate program for, and therefore KGS should abandon hope of being competitive in that regard?

I personally don't know how to use Katago or Leela and don't really want to learn how to use a separate program to analyze my games. Seems too complicated to me. Imo, if KGS had something comparable to what Lichess or Chess.com offers in the way of an easy-to-use AI that identified mistakes and missed opportunities and gave me the opportunity to learn from my mistakes without needing a degree in computer science, KGS would be a better go server than it currently is.

But that's probably true about many of the suggestions that have been floated. Thanks for reminding me that OGS is still actively developing its product - I'll check it out.

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Patience, grasshopper.