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

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=Publications=
 
=Publications=
 
* [[Shogo Takeuchi]], [[Tomoyuki Kaneko]], [[Kazunori Yamaguchi]], [[Satoru Kawai]] ('''2007'''). ''Visualization and Adjustment of Evaluation Functions Based on Evaluation Values and Win Probability''. [http://www.informatik.uni-trier.de/~ley/db/conf/aaai/aaai2007.html AAAI 2007], [https://www.aaai.org/Papers/AAAI/2007/AAAI07-136.pdf pdf]
 
* [[Shogo Takeuchi]], [[Tomoyuki Kaneko]], [[Kazunori Yamaguchi]], [[Satoru Kawai]] ('''2007'''). ''Visualization and Adjustment of Evaluation Functions Based on Evaluation Values and Win Probability''. [http://www.informatik.uni-trier.de/~ley/db/conf/aaai/aaai2007.html AAAI 2007], [https://www.aaai.org/Papers/AAAI/2007/AAAI07-136.pdf pdf]
* [[Kenneth Wingate Regan|Kenneth W. Regan]],  [[Tamal T. Biswas]], [[Jason Zhou]] ('''2014'''). ''Human and Computer Preferences at Chess''. [http://www.cse.buffalo.edu/~regan/papers/pdf/RBZ14aaai.pdf pdf]
+
* [[Kenneth W. Regan]],  [[Tamal T. Biswas]], [[Jason Zhou]] ('''2014'''). ''Human and Computer Preferences at Chess''. [http://www.cse.buffalo.edu/~regan/papers/pdf/RBZ14aaai.pdf pdf]
* [[Tamal T. Biswas]], [[Kenneth Wingate Regan|Kenneth W. Regan]] ('''2015'''). ''Measuring Level-K Reasoning, Satisficing, and Human Error in Game-Play Data''. [[IEEE]] [http://www.icmla-conference.org/icmla15/ ICMLA 2015], [http://www.cse.buffalo.edu/~regan/papers/pdf/BiRe15_ICMLA2015.pdf pdf preprint]
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* [[Tamal T. Biswas]], [[Kenneth W. Regan]] ('''2015'''). ''Measuring Level-K Reasoning, Satisficing, and Human Error in Game-Play Data''. [[IEEE]] [http://www.icmla-conference.org/icmla15/ ICMLA 2015], [http://www.cse.buffalo.edu/~regan/papers/pdf/BiRe15_ICMLA2015.pdf pdf preprint]
 
* [[Shogo Takeuchi]], [[Tomoyuki Kaneko]] ('''2015'''). ''[http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=7336038 Estimating Ratings of Computer Players by the Evaluation Scores and Principal Variations in Shogi]''. [http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=7335993 ACIT-CSI]
 
* [[Shogo Takeuchi]], [[Tomoyuki Kaneko]] ('''2015'''). ''[http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=7336038 Estimating Ratings of Computer Players by the Evaluation Scores and Principal Variations in Shogi]''. [http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=7335993 ACIT-CSI]
  
=Postingss=
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=Postings=
 +
==1999==
 
* [https://www.stmintz.com/ccc/index.php?id=52542 Elo performance?] by [[Stefan Meyer-Kahlen]], [[CCC]], May 22, 1999 » [[Match Statistics]], [[Playing Strength]]
 
* [https://www.stmintz.com/ccc/index.php?id=52542 Elo performance?] by [[Stefan Meyer-Kahlen]], [[CCC]], May 22, 1999 » [[Match Statistics]], [[Playing Strength]]
 +
==2000 ...==
 
* [https://www.stmintz.com/ccc/index.php?id=261636 likelihood instead of pawnunits? + chess knowledge] by [[Ingo Lindam]], [[CCC]], October 25, 2002
 
* [https://www.stmintz.com/ccc/index.php?id=261636 likelihood instead of pawnunits? + chess knowledge] by [[Ingo Lindam]], [[CCC]], October 25, 2002
 
* [http://www.talkchess.com/forum/viewtopic.php?t=30695 Winning percentage and centipawns] by [[Luca Hemmerich]], [[CCC]], November 18, 2009
 
* [http://www.talkchess.com/forum/viewtopic.php?t=30695 Winning percentage and centipawns] by [[Luca Hemmerich]], [[CCC]], November 18, 2009
 +
==2010 ...==
 
* [http://www.talkchess.com/forum/viewtopic.php?t=43323 Pawn Advantage, Win Percentage, and Elo] by [[Adam Hair]], [[CCC]], April 15, 2012
 
* [http://www.talkchess.com/forum/viewtopic.php?t=43323 Pawn Advantage, Win Percentage, and Elo] by [[Adam Hair]], [[CCC]], April 15, 2012
 
* [http://www.talkchess.com/forum/viewtopic.php?t=44670 normal vs logistic curve for Elo model] by [[Daniel Shawul]], [[CCC]], August 02, 2012
 
* [http://www.talkchess.com/forum/viewtopic.php?t=44670 normal vs logistic curve for Elo model] by [[Daniel Shawul]], [[CCC]], August 02, 2012
 
* [http://www.talkchess.com/forum/viewtopic.php?t=50266 Houdini, much weaker engines, and Arpad Elo] by [[Kai Laskos]], [[CCC]], November 29, 2013 » [[Houdini]], [[Match Statistics]] <ref>[https://en.wikipedia.org/wiki/Arpad_Elo Arpad Elo - Wikipedia]</ref>
 
* [http://www.talkchess.com/forum/viewtopic.php?t=50266 Houdini, much weaker engines, and Arpad Elo] by [[Kai Laskos]], [[CCC]], November 29, 2013 » [[Houdini]], [[Match Statistics]] <ref>[https://en.wikipedia.org/wiki/Arpad_Elo Arpad Elo - Wikipedia]</ref>
 +
* [http://macechess.blogspot.de/2014/03/pawn-advantage-in-ice.html Pawn Advantage in iCE] by [[Thomas Petzke]], [http://macechess.blogspot.de/ mACE Chess], March 16, 2014 » [[iCE]]
 
* [https://chesscomputer.tumblr.com/post/98632536555/using-the-stockfish-position-evaluation-score-to/embed Using the Stockfish position evaluation score to predict victory probability] by unavoidablegrain, [https://en.wikipedia.org/wiki/Tumblr Tumblr], September 28, 2014 » [[Stockfish]]
 
* [https://chesscomputer.tumblr.com/post/98632536555/using-the-stockfish-position-evaluation-score-to/embed Using the Stockfish position evaluation score to predict victory probability] by unavoidablegrain, [https://en.wikipedia.org/wiki/Tumblr Tumblr], September 28, 2014 » [[Stockfish]]
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==2015 ...==
 +
* [https://rjlipton.wordpress.com/2015/10/06/depth-of-satisficing/ Depth of Satisficing] by [[Kenneth W. Regan|Ken Regan]], [https://rjlipton.wordpress.com/ Gödel's Lost Letter and P=NP], October 06, 2015  » [[Depth]], [[Match Statistics]], [[Pawn Advantage, Win Percentage, and Elo]], [[Stockfish]], [[Komodo]] <ref>[http://www.talkchess.com/forum/viewtopic.php?t=57890 Regan's latest: Depth of Satisficing] by [[Carl Lumma]], [[CCC]], October 09, 2015</ref>
 +
* [https://rjlipton.wordpress.com/2016/12/08/magnus-and-the-turkey-grinder/ Magnus and the Turkey Grinder] by [[Kenneth W. Regan|Ken Regan]], [https://rjlipton.wordpress.com/ Gödel's Lost Letter and P=NP], December 08, 2016 » [[Match Statistics]] <ref>[https://rjlipton.wordpress.com/2016/11/30/when-data-serves-turkey/ When Data Serves Turkey] by [[Kenneth W. Regan|Ken Regan]], [https://rjlipton.wordpress.com/ Gödel's Lost Letter and P=NP], November 30, 2016</ref> <ref>[https://en.wikipedia.org/wiki/World_Chess_Championship_2016 World Chess Championship 2016 from Wikipedia]</ref> <ref>[http://www.talkchess.com/forum/viewtopic.php?t=62435 Regan's conundrum] by [[Carl Lumma]], [[CCC]], December 09, 2016</ref>
 
* [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=7&t=72140 UCI Win/Draw/Loss reporting] by [[Gian-Carlo Pascutto]], [[CCC]], October 22, 2019
 +
==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]]
 +
* [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=
 
* [https://en.wikipedia.org/wiki/Elo_rating_system Elo rating system from Wikipedia]
 
* [https://en.wikipedia.org/wiki/Elo_rating_system Elo rating system from Wikipedia]
* [http://www.ratingtheory.com/index.htm Back to Basics in Rating Theory] by [http://www.ratingtheory.com/author.htm Royal Clifford Jones, Jr.]
 
* [http://macechess.blogspot.de/2014/03/pawn-advantage-in-ice.html Pawn Advantage in iCE] by [[Thomas Petzke]], [http://macechess.blogspot.de/ mACE Chess], March 16, 2014 » [[iCE]]
 
* [https://rjlipton.wordpress.com/2015/10/06/depth-of-satisficing/ Depth of Satisficing] by [[Kenneth Wingate Regan|Ken Regan]], [https://rjlipton.wordpress.com/ Gödel's Lost Letter and P=NP], October 06, 2015  » [[Depth]], [[Match Statistics]], [[Pawn Advantage, Win Percentage, and Elo]], [[Stockfish]], [[Komodo]] <ref>[http://www.talkchess.com/forum/viewtopic.php?t=57890 Regan's latest: Depth of Satisficing] by [[Carl Lumma]], [[CCC]], October 09, 2015</ref>
 
* [https://rjlipton.wordpress.com/2016/12/08/magnus-and-the-turkey-grinder/ Magnus and the Turkey Grinder] by [[Kenneth Wingate Regan|Ken Regan]], [https://rjlipton.wordpress.com/ Gödel's Lost Letter and P=NP], December 08, 2016 » [[Match Statistics]] <ref>[https://rjlipton.wordpress.com/2016/11/30/when-data-serves-turkey/ When Data Serves Turkey] by [[Kenneth Wingate Regan|Ken Regan]], [https://rjlipton.wordpress.com/ Gödel's Lost Letter and P=NP], November 30, 2016</ref> <ref>[https://en.wikipedia.org/wiki/World_Chess_Championship_2016 World Chess Championship 2016 from Wikipedia]</ref> <ref>[http://www.talkchess.com/forum/viewtopic.php?t=62435 Regan's conundrum] by [[Carl Lumma]], [[CCC]], December 09, 2016</ref>
 
 
* [http://wismuth.com/elo/calculator.html Elo Win Probability Calculator] by [[Mathematician#FLabelle|François Labelle]]
 
* [http://wismuth.com/elo/calculator.html Elo Win Probability Calculator] by [[Mathematician#FLabelle|François Labelle]]
  
 
=References=
 
=References=
 
<references />
 
<references />
 
 
'''[[Evaluation|Up one Level]]'''
 
'''[[Evaluation|Up one Level]]'''

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

Postings

1999

2000 ...

2010 ...

2015 ...

2020 ...

External Links

References

Up one Level