Fischer or Lasker

@tpr said ^

"he did beat Spassky, but he only faced against one player"

• Fischer also played a secret training match against Gligoric 6-3 with 1 draw
  https://www.chessgames.com/perl/chess.pl?tid=71896

"Chessmetrics isn’t really a “reliable source”"

• Chessmetrics is reliable. The statistician Sonas took all chess results and calculated elo backwards in time based on thos

That's only two players bro :/
And yes, if Chessmetrics were to be reliable, the peak elos you said should be correct. But still, you have to include other factors like longevity and consistency.

@tpr said ^

"he did beat Spassky, but he only faced against one player"

• Fischer also played a secret training match against Gligoric 6-3 with 1 draw
  https://www.chessgames.com/perl/chess.pl?tid=71896

"Chessmetrics isn’t really a “reliable source”"

• Chessmetrics is reliable. The statistician Sonas took all chess results and calculated elo backwards in time based on those.

I don't want to get involved in your discussion, but it's extremely hard to compare level across times, as for example around 1900 the number of competitors was much lower than around 2000. It's very hard to develop a system which calculates ratings adequately at various levels. Say, if you want to have similar values for #1 across time, similar values for #20 will be misleading when the players' pools differ a lot in size. The difference between #1 and #20 was understandably much bigger than now when the number of active competitors was incomparably lower.

Yes, there are more people now, more chess players, and more grandmasters.
There are now 1296 active grandmasters.
In 1914 there were only 5: Lasker, Capablanca, Alékhine, Tarrasch, and Marshall.

Nevertheless the chessmetrics calculation is sound.
Elo takes new results and calculates elo forward in time.
Chessmetrics takes past results and calculates elo backwards in time.
The predictive power is great.

All present and past players relate to each other through games.
Nakamura relates to Morphy in 4 steps: Morphy number.

@tpr said in #23:

... Elo takes new results and calculates elo forward in time.
Chessmetrics takes past results and calculates elo backwards in time.
The predictive power is great. ...

And what tests do we have of this "great" predictive power for the results of a century of time travel?
And what exactly is it that is supposedly being predicted?
http://www.chessmetrics.com/cm/CM2/MonthlyLists.asp?Params=190905SSSSS3S000000000000111000000000000010100
Does April 1911__2837-Lasker predict how Lasker would do in 2026, immediately after stepping out of the DeLorean?
Or does it perhaps predict his rating after a week of catch-up study?
Or maybe a month? A year?
What reason is there to believe that all of these numbers would be the same?
What reason is there to believe that a number for 1911 accurately predicts any of these numbers?
We have NO DATA for what happens after more than a century of time travel by strong chess players.
Were there any chess players among the patients described by Oliver Sacks in Awakenings?

Actually I'd take chessmetrics calculations with a grain of salt. I'll give few reasons to show why

1. If you look at Fischer he didn't play between 1972 and 1992. So in statistics do you assume 1992 Fischer had same strength as 1972 Fischer. For example Spassky who was 2560 and scored 12.5/30 against Fischer who was 2785 in his last rating would have a performance rating of 2726.5 since his expected score was 6.45 points. You get similar issues with Kasparov or any other player who has retired but returned for a few games.

2. In a closed pool ratings don't reflect playing strength but instead reflect results between them. A well known example of this was Claude Bloodgood who got up to a USCF rating of 2759 by solely playing in the prison system.

3. It doesn't take into account rating inflation or deflation. So if in a particular period of time all the players got noticeably stronger that won't be captured in chessmetrics as a 1900 vs 2100 or a 2000 vs 2200 has same expected results.

Just to give an example of how it can differ Morphy's peak rating in chessmetrics is 2743 but if he was dropped into the present he'd probably only be around 2300-2400. That's why chessmetrics data isn't absolute and while it's interesting to quantify dominance of players across different eras the further you go back in time the bigger the error margins become.

I'll also add that I'm not saying calculations are unsound, simply that when using them you need to understand the limitations and assumptions made to produce them. Chessmetrics is good at determining who was the strongest player at any given time as errors resulting from different eras don't apply when players are playing in same year against opponents in the same pool.

"Spassky who was 2560 and scored 12.5/30 against Fischer"

• So Fischer in 1992 was 2660. Age gets the better of us all. Rating is a function of time. It goes up and then it goes down again. So Fischer lost -120 rating over 20 years, that is -6 per year. Chessmetrics gives the rating as a function of time.

"a closed pool"

• Top players are no closed pool: they interact with each other globally. It may well be that a 1500 player in India is stronger than a 1500 player in Germany, but at the top there is enough interaction.

"inflation or deflation"

• That is more of a problem at lower levels. When FIDE corrected ratings, it was for lower ratings only.

@tpr said ^

Yes, there are more people now, more chess players, and more grandmasters.
There are now 1296 active grandmasters.
In 1914 there were only 5: Lasker, Capablanca, Alékhine, Tarrasch, and Marshall.

Nevertheless the chessmetrics calculation is sound.
Elo takes new results and calculates elo forward in time.
Chessmetrics takes past results and calculates elo backwards in time.
The predictive power is...

The story about 5 grandmasters named by the tzar is well-known, but is it true? I heard that it was first mentioned in Marshall's book decades later, and that it wasn't very reliable. (If it were so, it would've been mentioned much more often in chess press of 1910's and 1920's, wouldn't it?)

In terms of chess strength at peak, it is Fischer. In terms of longevity it is Lasker.

In a matchup with Fischer in his prime and Lasker in his prime, Fischer would win IMO

@tpr said ^
(...)

"a closed pool"

• Top players are no closed pool: they interact with each other globally. It...
  If top players mostly played against each other, they would be very close to a closed pool.

Deflation at the top since 2015 is real, as well as inflation at the top was real in the preceding decades.
It's also true that nowadays top players work on chess harder than 10 years ago, and much harder than several decades ago, so the competition is higher.

@ILikeBlitz said ^

The story about 5 grandmasters named by the tzar is well-known, but is it true? I heard that it was first mentioned in Marshall's book decades later, and that it wasn't very reliable. (If it were so, it would've been mentioned much more often in chess press of 1910's and 1920's, wouldn't it?)

In Russian, "Вельтмейстер" which became "Гроссмейстер" (both derived from German), were merely honorary title for the world's best players, just for the purpose of publicity for future tournaments.
It did not require a specific performance to be reached and then awarded. It was somewhat close to the Ballon d'Or in football or the World Cup "Best XI".

So, technically, they were not GMs. (Capablanca, Tarrasch, Alekhine...).

Гроссмейстер latter became an official independent chess title for best soviet players (I belive, it was a decision from Lenin himself, if I'm not wrong), and after, it became the translation in Russian for the international and official "Grandmaster" title when it appeared.