Difference between revisions of "Pawn Advantage, Win Percentage, and Elo"

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* [http://www.talkchess.com/forum/viewtopic.php?t=65764 Statistical interpretation of search and eval scores] by [[J. Wesley Cleveland]], [[CCC]], November 18, 2017 » [[Match Statistics]], [[Score]]
 
* [http://www.talkchess.com/forum/viewtopic.php?t=65764 Statistical interpretation of search and eval scores] by [[J. Wesley Cleveland]], [[CCC]], November 18, 2017 » [[Match Statistics]], [[Score]]
 
* [http://www.talkchess.com/forum3/viewtopic.php?f=2&t=68072 Why Lc0 eval (in cp) is asymmetric against AB engines?] by [[Kai Laskos]], [[CCC]], July 25, 2018 » [[Asymmetric Evaluation]], [[Leela Chess Zero]]
 
* [http://www.talkchess.com/forum3/viewtopic.php?f=2&t=68072 Why Lc0 eval (in cp) is asymmetric against AB engines?] by [[Kai Laskos]], [[CCC]], July 25, 2018 » [[Asymmetric Evaluation]], [[Leela Chess Zero]]
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* [http://www.talkchess.com/forum3/viewtopic.php?f=7&t=72140 UCI Win/Draw/Loss reporting] by [[Gian-Carlo Pascutto]], [[CCC]], October 22, 2019
 
==2020 ...==
 
==2020 ...==
 
* [https://lczero.org/blog/2020/04/wdl-head/ Win-Draw-Loss evaluation] by [[Alexander Lyashuk|crem]], [[Leela Chess Zero|LCZero blog]], April 20, 2020 » [[TCEC Season 17#Superfinal|TCEC Season 17 Superfinal]]
 
* [https://lczero.org/blog/2020/04/wdl-head/ Win-Draw-Loss evaluation] by [[Alexander Lyashuk|crem]], [[Leela Chess Zero|LCZero blog]], April 20, 2020 » [[TCEC Season 17#Superfinal|TCEC Season 17 Superfinal]]
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* [http://www.talkchess.com/forum3/viewtopic.php?f=7&t=74339 Stockfish has included WDL stats in engine output] by Deberger, [[CCC]], July 02, 2020 » [[Stockfish]]
  
 
=External Links=
 
=External Links=

Latest revision as of 09:05, 11 April 2021

Home * Evaluation * Pawn Advantage, Win Percentage and Elo

An examination by Sune Fischer and Pradu Kannan in December 2007 on the approximate relations between Win Percentage, Pawn Advantage, and Elo rating advantage for computer chess resulted in following findings.

Relationship

It was found that the the approximate relationship between the winning probability W and the pawn advantage P is

PawnWinELOFormula1.jpg

The inverse relationship can be given as

PawnWinELOFormula2.jpg

From the above, the relationship between the equivalent Elo rating advantage R and the pawn advantage P can be given as

PawnWinELOFormula3.jpg

Data Acquisition

Data was taken from a collection of 405,460 computer games in PGN format. Whenever exactly 5 plys in a game had gone by without captures, the game result was accumulated twice in a table indexed by the material configuration. The data was accumulated twice because it was assumed that material values were equal for both colors. So if there was data for a KPK material configuration, the data was also tallied for the KKP. Only data pertaining to the material configuration was taken. This was considered reasonable because the material configuration is the most important quantity that affects the result of a game.

Data Reduction and Modeling

For each material configuration, a pawn value was computed using conventional pawn-normalized material ratios that are close to those used in strong chess programs (P=1, N=4, B=4.1, R=6, Q=12). The relationship between Win Percentage and Pawn Advantage was assumed to follow a logistic model [1] with its sigmoid curve, namely,

PawnWinELOFormula4.jpg

where K is an unknown non-zero constant. When applying the condition that the win probability is 0.5 if there is no pawn advantage, the solution to the above seperable differential equation becomes

PawnWinELOFormula5.jpg

For K=4, the proposed logistic model and the data is plotted here for comparison:

Wp2pa.PNG

See also

Publications

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