In 2018 I made a special study about an existing opening of which there exist perfomance statistics in which a color has 0, 1 and 2 extra moves see http://chess-brabo.blogspot.com/2018/12/an-extra-move-part-3.html
The conclusion was that one extra move corresponds with a ratinggap of 65 elo and 2 extra moves would be 131 elo. Be aware this is a non tactical position.
1/100th of a pawn would be maximum a few rating points and definitely not 65. It also doesn't map with other papers I read about it which talk about 40/100th of pawn for a move.
So I've the impression somewhere there is a disconnect. Maybe you take another definition of move.
The conclusion was that one extra move corresponds with a ratinggap of 65 elo and 2 extra moves would be 131 elo. Be aware this is a non tactical position.
1/100th of a pawn would be maximum a few rating points and definitely not 65. It also doesn't map with other papers I read about it which talk about 40/100th of pawn for a move.
So I've the impression somewhere there is a disconnect. Maybe you take another definition of move.
Interesting that the commoner value does not depend as much on the game phase as one might have thought. Though I suppose for the actual king, the fact that one less likely to get checkmated in the endgame might bias ones perception of the strength of the king.
More curiously though, it looks like the minor pieces gain value relative to a pawn, and the rook is specifically stronger in the midgame. I wonder whether that's a genuine effect or whether it's at least partly influenced by the engine happening to gravitate towards a different type of position in that commoner game.
EDIT: I wonder if the relatively low commoner value in the endgame is due to some possible redundancy with the actual king also filling the same role in the endgame.
More curiously though, it looks like the minor pieces gain value relative to a pawn, and the rook is specifically stronger in the midgame. I wonder whether that's a genuine effect or whether it's at least partly influenced by the engine happening to gravitate towards a different type of position in that commoner game.
EDIT: I wonder if the relatively low commoner value in the endgame is due to some possible redundancy with the actual king also filling the same role in the endgame.
Last year I used Logistic Regression to investigate piece values in Atomic (www.gilgamath.com/atomic-three.html), and then in Antichess (www.gilgamath.com/antichess-one.html) based on games scraped from Lichess. This approach has some challenges, mostly to do with when one snapshots the board, and how look-ahead works. I suspect a survival analysis approach might be better because of how it deals with conditional hazards. I also found it fruitful to express piece value in equivalent Elo (or Glicko, whatever) terms, since players have an intuitive grasp of Elo value, rather than relative to the pawn value. That said, I found relative values in Atomic to be: p: 1, n: 1.5, b: 1.8, r: 3.4, q: 7.8, close to your values but with exaggerated values to Rook and Queen.
In Antichess, of course, piece values tend to be negative, and you wish to hold on to your least negative valued pieces. It really doesn't make sense to quote these relative to the Pawn, then. In Elo terms, I found p: -47, n: -44, b: -69, r: -76, q: -63, k: -9. This is consistent with my experience that Bishops and Rooks are often turned into loose cannons in Antichess, but I am surprised at the Queen value.
All of this is predicated on _average_ play by the community, not _optimal_ play.
In Antichess, of course, piece values tend to be negative, and you wish to hold on to your least negative valued pieces. It really doesn't make sense to quote these relative to the Pawn, then. In Elo terms, I found p: -47, n: -44, b: -69, r: -76, q: -63, k: -9. This is consistent with my experience that Bishops and Rooks are often turned into loose cannons in Antichess, but I am surprised at the Queen value.
All of this is predicated on _average_ play by the community, not _optimal_ play.