Thank you for your responses, I have a better feeling now.

@jlt: I was thinking about this distinction, but it seemed hard to estimate the difference and I was happy by a rough estimate.

We still have quite a big difference in the estimates...
I don't have time now, but maybe later I will search for some handicape games and try to play the endgame for both sides and compare with the end result. In this way, we should get an estimation for the change of the sum of mistakes per rank (at some rank).
I also don't know what variance per game or per player to expect, so we might get mislead by a small sample.

Or if somebody has time and will or some already reviewed handicap games, he can post it here.

Now that we have KataGo, you could use it to approximate this question. Go through the endgame moves of some player you want to test (for a top pro Katago being weaker than perfect play has more impact than for a kyu) and add up the points loss estimates per move from KataGo.

I was thinking about something similar with Katago, in a slightly different context. In a discussion on L19 a few months back, we got on the subject of how many points would you give up to have more time than your opponent. I think it would be interesting to find high dan games online (say on KGS, where time remaining is tracked) where Katago says:
1) the game is approximately even heading into the endgame, and
2) one player has considerably more thinking time than their opponent.

Then play the game out and see how the time crunch translates into a point gap throughout the course of the endgame. You'd need to have a lot of games to get some meaningful association, and there are some problems to worry about, but it seems like a fruitful research project.

Not about perfect play but it gives a rough idea of how many points mid-dan amateurs lose compared to professional play. Go World 6 to 10 (March-April to November-December 1978) ran a series called "Professional Endgame vs. Amateur Endgame" in which the same position was played twice, pro vs. ama and pro vs. pro, with the same pro being white both times. The results were:

GW#6
pro X vs. ama (3d): W+8
pro X vs. pro Y: B+4

GW#7
pro X vs. ama (2d): W+16
pro X vs. pro Y: W+4

GW#8
pro X vs. ama (4d): B+1
pro X vs. pro Y: W+7

GW#9
pro X vs. ama (3d): B+1
pro X vs. pro Y: B+7

GW#10
pro X vs. ama (3d): W+1
pro X vs. pro Y: B+7

How many moves were played?

Japanese amateur ranks were rather stronger 40 years ago than they are today. And there was still a range of 2+ stones in pro strength, so it matters how strong the pro was. And, as Robert indicates, it matters how far the game was from the end, how much each play gained at the start.

Anyway, my guess is that pro Y was 7 - 9 dan. And the numbers seem reasonable.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

I don't have access to my Go World collection right now but I will update when I do. If I remember correctly , it is something like 50-60 moves.


Indeed, that's why I made sure to include the publication date


I don't remember all the names, I will update when I get back to my GW collection. Not all pros were top pros though. One name I remember is Hotta 3p (Hotta Yozo?). Also, the players in each issue were not the same, my constantly labeling them X and Y may have been misleading in this respect.

Oh?

Care to expand? What happened? Less interest?

Take care.

_________________
一碁一会

Unless you prevent it, rank inflation is a thing. As for rank inflation in Japan, I was not there for that inflation, so I can't say why it happened.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

in my opinion, rank inflation happens much more frequently in casual environments where there isn't a strict system in place. take a typical go club in some rural area with just a few players. maybe one guy's a 3d. a visitor comes and plays a game and beats him. since he beat the 3d, he must be 4d. he goes back to his club, and when his 3d rival beats him, that rival is 5d now. something like that...

with internet go, the system is more objective, and you typically have several data points from a variety of different types of players. i think it's harder to inflate in that case.

_________________
be immersed

Update with names and ranks of the professionals involved in the articles I mentioned above. I added the length of the yose and corrected mistakes I had made in typing the results.