Difference between revisions of "Match Statistics"

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</pre>
 
</pre>
 
<span id="TournamentManager"></span>
 
<span id="TournamentManager"></span>
=Tournament Manager=
+
=Tournaments=
* [[Arena]]
+
* [[Chess Server]]
* [[Amoeba#TournamentManager|Amoeba Tournament Manager]]
+
* [[Engine Rating Lists]]
* [[ChessGUI]]
+
* [[Tournament Manager]]
* [[Cutechess-cli]]
+
* [[Tournaments and Matches]]
* [[LittleBlitzer]]
 
  
 
=See also=  
 
=See also=  
 
* [[Automated Tuning]]
 
* [[Automated Tuning]]
 
* [[Bishop versus Knight#WinningPercantages|Bishop versus Knight - Winning Percentages]]
 
* [[Bishop versus Knight#WinningPercantages|Bishop versus Knight - Winning Percentages]]
* [[Chess Server]]
 
 
* [[Depth#DiminishingReturns|Depth | Diminishing Returns]]
 
* [[Depth#DiminishingReturns|Depth | Diminishing Returns]]
 
* [[Draw]]
 
* [[Draw]]
* [[Engine Rating Lists]]
+
* [[Engine Similarity]]
 
* [[LOS Table]]
 
* [[LOS Table]]
 
* [[Pawn Advantage, Win Percentage, and Elo]]
 
* [[Pawn Advantage, Win Percentage, and Elo]]
 
* [[Playing Strength]]
 
* [[Playing Strength]]
 
* [[Search Statistics]]
 
* [[Search Statistics]]
 +
* [[Alexander Szabo#TechnologyCurve|The Technology Curve]]
 
* [[Time Management#Time%20Controls|Time Controls]]
 
* [[Time Management#Time%20Controls|Time Controls]]
 
* [[Jean-Marc Alliot#WhoistheMaster|Who is the Master?]]
 
* [[Jean-Marc Alliot#WhoistheMaster|Who is the Master?]]
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=Publications=  
 
=Publications=  
 
==1920 ...==  
 
==1920 ...==  
 +
* [[Mathematician#LLThurstone|L. L. Thurstone]] ('''1927'''). ''[https://psycnet.apa.org/record/1928-00527-001 A law of comparative judgement]''. [https://en.wikipedia.org/wiki/Psychological_Review Psychological Review], Vol. 34, No. 4 <ref>[https://en.wikipedia.org/wiki/Law_of_comparative_judgment Law of comparative judgment - Wikipedia]</ref>
 
* [[Ernst Zermelo]] ('''1929'''). ''Die Berechnung der Turnier-Ergebnisse als ein Maximumproblem der Wahrscheinlichkeitsrechnung''. [http://gdz.sub.uni-goettingen.de/dms/load/img/?IDDOC=82727 pdf] (German)
 
* [[Ernst Zermelo]] ('''1929'''). ''Die Berechnung der Turnier-Ergebnisse als ein Maximumproblem der Wahrscheinlichkeitsrechnung''. [http://gdz.sub.uni-goettingen.de/dms/load/img/?IDDOC=82727 pdf] (German)
 +
==1940 ...==
 
* [[Mathematician#AWald|Abraham Wald]] ('''1945'''). ''Sequential Tests of Statistical Hypotheses''. [https://en.wikipedia.org/wiki/Annals_of_Mathematical_Statistics Annals of Mathematical Statistics], Vol. 16, No. 2, [https://en.wikipedia.org/wiki/Digital_object_identifier doi]: [http://projecteuclid.org/euclid.aoms/1177731118 10.1214/aoms/1177731118]
 
* [[Mathematician#AWald|Abraham Wald]] ('''1945'''). ''Sequential Tests of Statistical Hypotheses''. [https://en.wikipedia.org/wiki/Annals_of_Mathematical_Statistics Annals of Mathematical Statistics], Vol. 16, No. 2, [https://en.wikipedia.org/wiki/Digital_object_identifier doi]: [http://projecteuclid.org/euclid.aoms/1177731118 10.1214/aoms/1177731118]
 
* [[Mathematician#AWald|Abraham Wald]] ('''1947'''). ''Sequential Analysis''. [https://en.wikipedia.org/wiki/John_Wiley_%26_Sons John Wiley and Sons], [http://www.abebooks.com/book-search/title/sequential-analysis/author/abraham-wald/ AbeBooks]
 
* [[Mathematician#AWald|Abraham Wald]] ('''1947'''). ''Sequential Analysis''. [https://en.wikipedia.org/wiki/John_Wiley_%26_Sons John Wiley and Sons], [http://www.abebooks.com/book-search/title/sequential-analysis/author/abraham-wald/ AbeBooks]
* [[Mathematician#RABradley|Ralph A. Bradley]], [[Mathematician#METerry|Milton E. Terry]] ('''1952'''). ''[http://biomet.oxfordjournals.org/content/39/3-4/324.citation Rank Analysis of Incomplete Block Designs: I. The Method of Paired Comparisons]''. [https://en.wikipedia.org/wiki/Biometrika Biometrika], Vol. 39, Nos. 3/4, [https://en.wikipedia.org/wiki/Digital_object_identifier doi]: 10.2307/2334029, [http://www.jstor.org/stable/2334029?seq=1#page_scan_tab_contents JSTOR 2334029]
+
==1950 ...==
 +
* [[Mathematician#Mosteller|Frederick Mosteller]] ('''1951'''). ''[https://psycnet.apa.org/record/1951-07176-001 Remarks on the method of paired comparisons: I. The least squares solution assuming equal standard deviations and equal correlations]''. [https://en.wikipedia.org/wiki/Psychometrika Psychometrika], Vol. 16, No. 1
 +
* [[Mathematician#RABradley|Ralph A. Bradley]], [[Mathematician#METerry|Milton E. Terry]] ('''1952'''). ''[http://biomet.oxfordjournals.org/content/39/3-4/324.citation Rank Analysis of Incomplete Block Designs: I. The Method of Paired Comparisons]''. [https://en.wikipedia.org/wiki/Biometrika Biometrika], Vol. 39, Nos. 3/4
 
==1960 ...==
 
==1960 ...==
* [[Mathematician#FNDavid|Florence Nightingale David]] ('''1962'''). ''[http://books.google.com/books/about/Games_Gods_and_Gambling.html?id=8ddP8zNx9nQC&redir_esc=y Games, Gods & Gambling: A History of Probability and Statistical Ideas]''. Dover Publications, ISBN-13: 978-0486400235
+
* [[Mathematician#WAGlenn|William A. Glenn]], [[Mathematician#HADavid|Herbert  A. David]] ('''1960'''). ''[https://www.jstor.org/stable/2527957?seq=1#page_scan_tab_contents Ties in Paired-Comparison Experiments Using a Modified Thurstone-Mosteller Model]''. [https://en.wikipedia.org/wiki/Biometrics_(journal) Biometrics], Vol. 16, No. 1
 +
* [[Mathematician#FNDavid|Florence Nightingale David]] ('''1962'''). ''[http://books.google.com/books/about/Games_Gods_and_Gambling.html?id=8ddP8zNx9nQC&redir_esc=y Games, Gods & Gambling: A History of Probability and Statistical Ideas]''. [https://en.wikipedia.org/wiki/Dover_Publications Dover Publications]
 +
* [[Mathematician#PVRao|P. V. Rao]], [[Mathematician#LLKupper|L. L. Kupper]] ('''1967'''). ''[https://www.tandfonline.com/doi/abs/10.1080/01621459.1967.10482901 Ties in Paired-Comparison Experiments: A Generalization of the Bradley-Terry Model]''. [https://en.wikipedia.org/wiki/Journal_of_the_American_Statistical_Association Journal of the American Statistical Association], Vol. 62, No. 317
 +
==1970 ...==
 +
* [https://www.semanticscholar.org/author/Roger-R.-Davidson/32819150 Roger R. Davidson] ('''1970'''). ''[https://www.jstor.org/stable/2283595 On Extending the Bradley-Terry Model to Accommodate Ties in Paired Comparison Experiments]''. [https://en.wikipedia.org/wiki/Journal_of_the_American_Statistical_Association Journal of the American Statistical Association], Vol. 64, No. 329
 +
* <span id="Bloss"></span>[http://what-when-how.com/earth-scientists/bloss-f-donald-earth-scientist/ F. Donald Bloss] ('''1973'''). ''[https://www.amazon.de/Rate-Your-Chess-F-Donald-Bloss/dp/0442008295 Rate your own Chess]''. Van Nostrand Reinhold Inc.
 
* [[Tony Marsland]], [[Paul Rushton]] ('''1973'''). ''[http://dl.acm.org/citation.cfm?id=805703 Mechanisms for Comparing Chess Programs].'' [[ACM 1973|ACM Annual Conference]], [http://webdocs.cs.ualberta.ca/~tony/OldPapers/Marsland-Rushton-ACM73 pdf]
 
* [[Tony Marsland]], [[Paul Rushton]] ('''1973'''). ''[http://dl.acm.org/citation.cfm?id=805703 Mechanisms for Comparing Chess Programs].'' [[ACM 1973|ACM Annual Conference]], [http://webdocs.cs.ualberta.ca/~tony/OldPapers/Marsland-Rushton-ACM73 pdf]
 
* [[James Gillogly]] ('''1978'''). ''Performance Analysis of the Technology Chess Program''. Ph.D. Thesis. Tech. Report CMU-CS-78-189, [[Carnegie Mellon University]], [http://reports-archive.adm.cs.cmu.edu/anon/anon/usr/ftp/scan/CMU-CS-77-gillogly.pdf CMU-CS-77 pdf] » [[Tech]]
 
* [[James Gillogly]] ('''1978'''). ''Performance Analysis of the Technology Chess Program''. Ph.D. Thesis. Tech. Report CMU-CS-78-189, [[Carnegie Mellon University]], [http://reports-archive.adm.cs.cmu.edu/anon/anon/usr/ftp/scan/CMU-CS-77-gillogly.pdf CMU-CS-77 pdf] » [[Tech]]
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* [[David Cahlander]] ('''1979'''). ''Strength of a Chess Playing Computer''. [[ICGA Journal#2_1|ICCA Newsletter, Vol. 2, No. 1]]
 
* [[David Cahlander]] ('''1979'''). ''Strength of a Chess Playing Computer''. [[ICGA Journal#2_1|ICCA Newsletter, Vol. 2, No. 1]]
 
* [[Jack Good]] ('''1979'''). ''On the Grading of Chess Players''. [[Personal Computing#3_3|Personal Computing, Vol. 3, No. 3]], pp. 47
 
* [[Jack Good]] ('''1979'''). ''On the Grading of Chess Players''. [[Personal Computing#3_3|Personal Computing, Vol. 3, No. 3]], pp. 47
 +
* <span id="Ratliff"></span>[[Gary L. Ratliff]] ('''1979'''). ''Practical Rating Program''. [[Personal Computing#3_9|Personal Computing, Vol. 3, No. 9]], pp. 62  » [[#Bloss|Bloss]]
 +
* [[Frieder Schwenkel]] ('''1979'''). ''Berating the ratings system''. [[Personal Computing#3_11|Personal Computing, Vol. 3, No. 11]], pp. 77 » [[#Ratliff|Ratliff]], [[#Bloss|Bloss]]
 +
* [[John Shaposka]] ('''1979'''). ''"JS" Takes the Bloss Test''. [[Personal Computing#3_12|Personal Computing, Vol. 3, No. 12]], pp. 75 » [[#Ratliff|Ratliff]], [[#Bloss|Bloss]]
 
==1980 ...==  
 
==1980 ...==  
 +
* Floyd R. Kirk ('''1980'''). ''Bloss Flunks Test''. [[Personal Computing#4_8|Personal Computing, Vol. 4, No. 8]], pp. 72  » [[#Ratliff|Ratliff]], [[#Bloss|Bloss]]
 
* [[John F. White]] ('''1981'''). ''[http://yourcomputeronline.wordpress.com/2010/12/10/survey-chess-games/ Survey-Chess Games]''. [[Your Computer]], [http://yourcomputeronline.wordpress.com/2010/10/31/augustseptember-1981-contents-and-editorial/ August/September 1981] <ref>[https://en.wikipedia.org/wiki/The_Master_Game The Master Game from Wikipedia]</ref>
 
* [[John F. White]] ('''1981'''). ''[http://yourcomputeronline.wordpress.com/2010/12/10/survey-chess-games/ Survey-Chess Games]''. [[Your Computer]], [http://yourcomputeronline.wordpress.com/2010/10/31/augustseptember-1981-contents-and-editorial/ August/September 1981] <ref>[https://en.wikipedia.org/wiki/The_Master_Game The Master Game from Wikipedia]</ref>
 
* [[Ken Thompson]] ('''1982'''). ''Computer Chess Strength''. [[Advances in Computer Chess 3]]
 
* [[Ken Thompson]] ('''1982'''). ''Computer Chess Strength''. [[Advances in Computer Chess 3]]
Line 341: Line 353:
 
==1990 ...==
 
==1990 ...==
 
* [[Hans Berliner]], [[Gordon Goetsch]], [[Murray Campbell]], [[Carl Ebeling]] ('''1990'''). ''Measuring the Performance Potential of Chess Programs.'' [https://en.wikipedia.org/wiki/Artificial_Intelligence_%28journal%29 Artificial Intelligence], Vol. 43, No. 1
 
* [[Hans Berliner]], [[Gordon Goetsch]], [[Murray Campbell]], [[Carl Ebeling]] ('''1990'''). ''Measuring the Performance Potential of Chess Programs.'' [https://en.wikipedia.org/wiki/Artificial_Intelligence_%28journal%29 Artificial Intelligence], Vol. 43, No. 1
* [http://www.ics.uci.edu/~sternh/ Hal Stern] ('''1990'''). ''Are all Linear Paired Comparison Models Equivalent''. [http://www.dtic.mil/dtic/tr/fulltext/u2/a236856.pdf pdf]
+
* [[Mathematician#HSStern|Hal Stern]] ('''1990'''). ''Are all Linear Paired Comparison Models Equivalent''. [http://www.dtic.mil/dtic/tr/fulltext/u2/a236856.pdf pdf]
 
* [[Eric Hallsworth]] ('''1990'''). ''Speed, Processors and Ratings''. [[Selective Search|Computer Chess News Sheet]] 25, pp 6, [http://www.chesscomputeruk.com/SS_25.pdf pdf] hosted by [[Mike Watters]]
 
* [[Eric Hallsworth]] ('''1990'''). ''Speed, Processors and Ratings''. [[Selective Search|Computer Chess News Sheet]] 25, pp 6, [http://www.chesscomputeruk.com/SS_25.pdf pdf] hosted by [[Mike Watters]]
 
* [[Hans Berliner]], [[Danny Kopec]], [[Ed Northam]] ('''1991'''). ''A taxonomy of concepts for evaluating chess strength: examples from two difficult categories''. [[Advances in Computer Chess 6]], [http://www.sci.brooklyn.cuny.edu/%7Ekopec/Publications/Publications/O_20_C.pdf pdf]
 
* [[Hans Berliner]], [[Danny Kopec]], [[Ed Northam]] ('''1991'''). ''A taxonomy of concepts for evaluating chess strength: examples from two difficult categories''. [[Advances in Computer Chess 6]], [http://www.sci.brooklyn.cuny.edu/%7Ekopec/Publications/Publications/O_20_C.pdf pdf]
 
* [[Steve Maughan]] ('''1992'''). ''Are You Sure It's Better?'' [[Selective Search]] 40, pp. 21, [http://www.chesscomputeruk.com/SS_40.pdf pdf] hosted by [[Mike Watters]]
 
* [[Steve Maughan]] ('''1992'''). ''Are You Sure It's Better?'' [[Selective Search]] 40, pp. 21, [http://www.chesscomputeruk.com/SS_40.pdf pdf] hosted by [[Mike Watters]]
 
* [[Warren D. Smith]] ('''1993'''). ''Rating Systems for Gameplayers, and Learning''. [http://scorevoting.net/WarrenSmithPages/homepage/ratingspap.ps ps]
 
* [[Warren D. Smith]] ('''1993'''). ''Rating Systems for Gameplayers, and Learning''. [http://scorevoting.net/WarrenSmithPages/homepage/ratingspap.ps ps]
 +
* [[Mark E. Glickman]] ('''1993'''). ''Paired Comparison Models with Time Varying Parameters''. Ph.D. thesis, [[Harvard University]], advisor [[Mathematician#HSStern|Hal Stern]], [http://www.glicko.net/research/thesis.pdf pdf]
 +
* [[Mark E. Glickman]] ('''1995'''). ''A Comprehensive Guide To Chess Ratings''. [http://www.glicko.net/research/acjpaper.pdf pdf]
 +
* [[Mark E. Glickman]], [[Christopher Chabris]] ('''1996'''). ''Using Chess Ratings as Data in Psychological Research''. [https://pdfs.semanticscholar.org/1ffd/3432f56476f0047426b37f7f433f5a6575b0.pdf pdf]
 
* [[Robert Hyatt]], [[Monroe Newborn]] ('''1997'''). ''CRAFTY Goes Deep''. [[ICGA Journal#20_2|ICCA Journal, Vol. 20, No. 2]] » [[Crafty]]
 
* [[Robert Hyatt]], [[Monroe Newborn]] ('''1997'''). ''CRAFTY Goes Deep''. [[ICGA Journal#20_2|ICCA Journal, Vol. 20, No. 2]] » [[Crafty]]
 +
* [[Mark E. Glickman]], [[Mathematician#ACJones|Albyn C. Jones]] ('''1999'''). ''Rating the Chess Rating System''. [http://www.glicko.net/research/chance.pdf pdf]
 
==2000 ...==  
 
==2000 ...==  
 
* [[Ernst A. Heinz]] ('''2000'''). ''[http://link.springer.com/chapter/10.1007/3-540-45579-5_18 New Self-Play Results in Computer Chess]''. [[CG 2000]]
 
* [[Ernst A. Heinz]] ('''2000'''). ''[http://link.springer.com/chapter/10.1007/3-540-45579-5_18 New Self-Play Results in Computer Chess]''. [[CG 2000]]
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==2005 ...==
 
==2005 ...==
 
* [[Jan Renze Steenhuisen]] ('''2005'''). ''New Results in Deep-Search Behaviour''. [[ICGA Journal#28_4|ICGA Journal, Vol. 28, No. 4]], [http://www.st.ewi.tudelft.nl/%7Erenze/doc/ICGA_2005_4_DeepSearch.pdf pdf]
 
* [[Jan Renze Steenhuisen]] ('''2005'''). ''New Results in Deep-Search Behaviour''. [[ICGA Journal#28_4|ICGA Journal, Vol. 28, No. 4]], [http://www.st.ewi.tudelft.nl/%7Erenze/doc/ICGA_2005_4_DeepSearch.pdf pdf]
 +
* [[Mark Levene]], [[Judit Bar-Ilan]] ('''2005'''). ''[https://www.researchgate.net/publication/220174440_Comparing_Move_Choices_of_Chess_Search_Engines Comparing Move Choices of Chess Search Engines]''. [[ICGA Journal#28_2|ICGA Journal, Vol. 28, No. 2]], [http://www.dcs.bbk.ac.uk/~mark/download/fritz_junior_icga.pdf pdf] » [[Fritz]], [[Junior]]
 +
* [[Mark Levene]], [[Judit Bar-Ilan]] ('''2006'''). ''Comparing Typical Opening Move Choices Made by Humans and Chess Engines''. [https://arxiv.org/abs/cs/0610060 arXiv:cs/0610060]
 +
* [[Mark Levene]], [[Judit Bar-Ilan]] ('''2007'''). ''Comparing Typical Opening Move Choices Made by Humans and Chess Engines''. [https://en.wikipedia.org/wiki/The_Computer_Journal The Computer Journal], Vol. 50, No. 5
 
* [[Matej Guid]], [[Ivan Bratko]] ('''2007'''). ''Factors affecting diminishing returns for searching deeper''. [[CGW 2007]] » [[Crafty]], [[Rybka]], [[Shredder]], [[Depth#DiminishingReturns|Diminishing Returns]]
 
* [[Matej Guid]], [[Ivan Bratko]] ('''2007'''). ''Factors affecting diminishing returns for searching deeper''. [[CGW 2007]] » [[Crafty]], [[Rybka]], [[Shredder]], [[Depth#DiminishingReturns|Diminishing Returns]]
 
* [[Jeff Rollason]] ('''2007'''). ''[http://www.aifactory.co.uk/newsletter/2007_04_stat_minefields.htm Statistical Minefields with Version Testing]''. [[AI Factory]], Winter 2007 » [[Engine Testing]]
 
* [[Jeff Rollason]] ('''2007'''). ''[http://www.aifactory.co.uk/newsletter/2007_04_stat_minefields.htm Statistical Minefields with Version Testing]''. [[AI Factory]], Winter 2007 » [[Engine Testing]]
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* [[Kenneth W. Regan]], [[Guy Haworth]] ('''2011'''). ''[http://www.aaai.org/ocs/index.php/AAAI/AAAI11/paper/view/3779 Intrinsic Chess Ratings]''. [http://www.informatik.uni-trier.de/%7Eley/db/conf/aaai/aaai2011.html#ReganH11 AAAI 2011], [http://www.aaai.org/ocs/index.php/AAAI/AAAI11/paper/view/3779/3962 pdf], [http://www.cse.buffalo.edu/%7Eregan/Talks/IntrinsicRatings.pdf slides as pdf] <ref> [http://www.talkchess.com/forum/viewtopic.php?t=65772 "Intrinsic Chess Ratings" by Regan, Haworth -- seq] by Kai Middleton, [[CCC]], November 19, 2017</ref>
 
* [[Kenneth W. Regan]], [[Guy Haworth]] ('''2011'''). ''[http://www.aaai.org/ocs/index.php/AAAI/AAAI11/paper/view/3779 Intrinsic Chess Ratings]''. [http://www.informatik.uni-trier.de/%7Eley/db/conf/aaai/aaai2011.html#ReganH11 AAAI 2011], [http://www.aaai.org/ocs/index.php/AAAI/AAAI11/paper/view/3779/3962 pdf], [http://www.cse.buffalo.edu/%7Eregan/Talks/IntrinsicRatings.pdf slides as pdf] <ref> [http://www.talkchess.com/forum/viewtopic.php?t=65772 "Intrinsic Chess Ratings" by Regan, Haworth -- seq] by Kai Middleton, [[CCC]], November 19, 2017</ref>
 
* [[Kenneth W. Regan]], [[Bartłomiej Macieja]], [[Guy Haworth|Guy McCrossan Haworth]] ('''2011'''). ''[http://centaur.reading.ac.uk/23800/ Understanding Distributions of Chess Performances]''. [[Advances in Computer Games 13]], [http://www.cse.buffalo.edu/~regan/papers/pdf/RMH11.pdf pdf]
 
* [[Kenneth W. Regan]], [[Bartłomiej Macieja]], [[Guy Haworth|Guy McCrossan Haworth]] ('''2011'''). ''[http://centaur.reading.ac.uk/23800/ Understanding Distributions of Chess Performances]''. [[Advances in Computer Games 13]], [http://www.cse.buffalo.edu/~regan/papers/pdf/RMH11.pdf pdf]
* [[Trevor Fenner]], [[Mark Levene]], [[Mathematician#GLoizou|George Loizou]] ('''2011'''). ''A Discrete Evolutionary Model for Chess Players' Ratings''. [http://arxiv.org/list/physics.soc-ph/recent Physics and Society], [http://arxiv.org/abs/1103.1530v2 arXiv:1103.1530v2]
+
* [[Trevor Fenner]], [[Mark Levene]], [[Mathematician#GLoizou|George Loizou]] ('''2011'''). ''A Discrete Evolutionary Model for Chess Players' Ratings''. [https://arxiv.org/abs/1103.1530 arXiv:1103.1530]
* [[Rémi Coulom]] ('''2012'''). ''Paired Comparisons with Ties: Modeling Game Outcomes in Chess''. [http://www.grappa.univ-lille3.fr/~coulom/ChessOutcomes.pdf pdf preprint] <ref>[http://www.talkchess.com/forum/viewtopic.php?topic_view=threads&p=471004&t=44180 Re: EloStat, Bayeselo and Ordo] by [[Rémi Coulom]], [[CCC]], June 25, 2012</ref>
 
 
* [[Diogo R. Ferreira]] ('''2012'''). ''Determining the Strength of Chess Players based on actual Play''. [[ICGA Journal#35_1|ICGA Journal, Vol. 35, No. 1]]
 
* [[Diogo R. Ferreira]] ('''2012'''). ''Determining the Strength of Chess Players based on actual Play''. [[ICGA Journal#35_1|ICGA Journal, Vol. 35, No. 1]]
 +
* [[Daniel Shawul]], [[Rémi Coulom]] ('''2013'''). ''Paired Comparisons with Ties: Modeling Game Outcomes in Chess''.  <ref>[http://www.talkchess.com/forum/viewtopic.php?topic_view=threads&p=471004&t=44180 Re: EloStat, Bayeselo and Ordo] by [[Rémi Coulom]], [[CCC]], June 25, 2012</ref> <ref>[http://www.talkchess.com/forum3/viewtopic.php?f=7&t=72087&start=3 Re: Understanding and Pushing the Limits of the Elo Rating Algorithm] by [[Daniel Shawul]], [[CCC]], October 15, 2019</ref>
 
* [[Diogo R. Ferreira]] ('''2013'''). ''The Impact of the Search Depth on Chess Playing Strength''. [[ICGA Journal#36_2|ICGA Journal, Vol. 36, No. 2]]
 
* [[Diogo R. Ferreira]] ('''2013'''). ''The Impact of the Search Depth on Chess Playing Strength''. [[ICGA Journal#36_2|ICGA Journal, Vol. 36, No. 2]]
 
* [[Miguel A. Ballicora]] ('''2014'''). ''ORDO v0.9.6 Ratings for chess and other games''. September 2014, [https://docs.google.com/viewer?a=v&pid=sites&srcid=ZGVmYXVsdGRvbWFpbnxnYXZpb3RhY2hlc3NlbmdpbmV8Z3g6NmQ0NmNhNGM4YjA3YTc5ZQ pdf] » [[Ordo]] <ref>[https://sites.google.com/site/gaviotachessengine/ordo Ordo] by [[Miguel A. Ballicora]]</ref>
 
* [[Miguel A. Ballicora]] ('''2014'''). ''ORDO v0.9.6 Ratings for chess and other games''. September 2014, [https://docs.google.com/viewer?a=v&pid=sites&srcid=ZGVmYXVsdGRvbWFpbnxnYXZpb3RhY2hlc3NlbmdpbmV8Z3g6NmQ0NmNhNGM4YjA3YTc5ZQ pdf] » [[Ordo]] <ref>[https://sites.google.com/site/gaviotachessengine/ordo Ordo] by [[Miguel A. Ballicora]]</ref>
* [[Don Dailey]], [[Adam Hair]], [[Mark Watkins]] ('''2014'''). ''[http://www.sciencedirect.com/science/article/pii/S1875952113000177 Move Similarity Analysis in Chess Programs]''. [http://www.journals.elsevier.com/entertainment-computing/ Entertainment Computing], Vol. 5, No. 3, [http://magma.maths.usyd.edu.au/~watkins/papers/DHW.pdf preprint as pdf] <ref>[http://www.top-5000.nl/clone.htm A Pairwise Comparison of Chess Engine Move Selections] by [[Adam Hair]], hosted by [[Ed Schroder|Ed Schröder]]</ref>
+
* [[Don Dailey]], [[Adam Hair]], [[Mark Watkins]] ('''2014'''). ''[http://www.sciencedirect.com/science/article/pii/S1875952113000177 Move Similarity Analysis in Chess Programs]''. [http://www.journals.elsevier.com/entertainment-computing/ Entertainment Computing], Vol. 5, No. 3, [http://magma.maths.usyd.edu.au/~watkins/papers/DHW.pdf preprint as pdf] <ref>[http://www.talkchess.com/forum/viewtopic.php?t=38772 Pairwise Analysis of Chess Engine Move Selections] by [[Adam Hair]], [[CCC]], April 17, 2011</ref>
 
* [[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]
 
* [[Erik Varend]] ('''2014'''). ''Quality of play in chess and methods for measuring''. [http://www.chessanalysis.ee/Quality%20of%20play%20in%20chess%20and%20methods%20for%20measuring.pdf pdf] <ref>[http://www.talkchess.com/forum/viewtopic.php?t=54571 Questions regarding rating systems of humans and engines] by [[Erik Varend]], [[CCC]], December 06, 2014</ref> <ref>[http://www.talkchess.com/forum/viewtopic.php?t=60721 chess statistics scientific article] by Nuno Sousa, [[CCC]], July 06, 2016</ref>
 
* [[Erik Varend]] ('''2014'''). ''Quality of play in chess and methods for measuring''. [http://www.chessanalysis.ee/Quality%20of%20play%20in%20chess%20and%20methods%20for%20measuring.pdf pdf] <ref>[http://www.talkchess.com/forum/viewtopic.php?t=54571 Questions regarding rating systems of humans and engines] by [[Erik Varend]], [[CCC]], December 06, 2014</ref> <ref>[http://www.talkchess.com/forum/viewtopic.php?t=60721 chess statistics scientific article] by Nuno Sousa, [[CCC]], July 06, 2016</ref>
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* [[Jean-Marc Alliot]] ('''2017'''). ''Who is the Master''? [[ICGA Journal#39_1|ICGA Journal, Vol. 39, No. 1]], [http://www.alliot.fr/CHESS/draft-icga-39-1.pdf draft as pdf] » [[Stockfish]], [[Jean-Marc Alliot#WhoistheMaster|Who is the Master?]]
 
* [[Jean-Marc Alliot]] ('''2017'''). ''Who is the Master''? [[ICGA Journal#39_1|ICGA Journal, Vol. 39, No. 1]], [http://www.alliot.fr/CHESS/draft-icga-39-1.pdf draft as pdf] » [[Stockfish]], [[Jean-Marc Alliot#WhoistheMaster|Who is the Master?]]
 
* [[Mathematician#IAdler|Ilan Adler]], [[Mathematician#YangCao|Yang Cao]], [[Richard Karp]], [[Mathematician#EAPekoz|Erol A. Peköz]], [[Mathematician#SMRoss|Sheldon M. Ross]] ('''2017'''). ''[https://pubsonline.informs.org/doi/10.1287/opre.2017.1657 Random Knockout Tournaments]''. [https://en.wikipedia.org/wiki/Operations_Research_(journal) Operations Research], Vol. 65, No. 6, [https://arxiv.org/abs/1612.04448 arXiv:1612.04448]
 
* [[Mathematician#IAdler|Ilan Adler]], [[Mathematician#YangCao|Yang Cao]], [[Richard Karp]], [[Mathematician#EAPekoz|Erol A. Peköz]], [[Mathematician#SMRoss|Sheldon M. Ross]] ('''2017'''). ''[https://pubsonline.informs.org/doi/10.1287/opre.2017.1657 Random Knockout Tournaments]''. [https://en.wikipedia.org/wiki/Operations_Research_(journal) Operations Research], Vol. 65, No. 6, [https://arxiv.org/abs/1612.04448 arXiv:1612.04448]
 +
* [[Leszek Szczecinski]], [[Aymen Djebbi]] ('''2019'''). ''Understanding and Pushing the Limits of the Elo Rating Algorithm''. [https://arxiv.org/abs/1910.06081 arXiv:1910.06081] <ref>[http://www.talkchess.com/forum3/viewtopic.php?f=7&t=72087 Understanding and Pushing the Limits of the Elo Rating Algorithm] by [[Michel Van den Bergh]], [[CCC]], October 15, 2019</ref>
  
 
=Forum & Blog Postings=  
 
=Forum & Blog Postings=  
Line 388: Line 408:
 
* [https://groups.google.com/d/msg/rec.games.chess.computer/GkgFc3jOl84/vWn-SG8kVboJ Theoretical chess rating question...] by Cyber Linguist, [[Computer Chess Forums|rgcc]], April 17, 1996
 
* [https://groups.google.com/d/msg/rec.games.chess.computer/GkgFc3jOl84/vWn-SG8kVboJ Theoretical chess rating question...] by Cyber Linguist, [[Computer Chess Forums|rgcc]], April 17, 1996
 
* [http://groups.google.com/group/rec.games.chess.computer/browse_frm/thread/3014e4ea570dbf38 Statistical validity of medium-length match results] by [[Bruce Moreland]], [[Computer Chess Forums|rgcc]], February 15, 1997
 
* [http://groups.google.com/group/rec.games.chess.computer/browse_frm/thread/3014e4ea570dbf38 Statistical validity of medium-length match results] by [[Bruce Moreland]], [[Computer Chess Forums|rgcc]], February 15, 1997
 +
* [https://www.stmintz.com/ccc/index.php?id=24669 Small number statistics and small differences] by [[Daniel Homan]], [[CCC]], August 14, 1998
 +
* [https://www.stmintz.com/ccc/index.php?id=24978 Re: Waltzing Matilda (was: statistics, 10 events tell us what ?] by [[Daniel Homan]], [[CCC]], August 17, 1998
 
* [https://www.stmintz.com/ccc/index.php?id=52542 ELO performance?] by [[Stefan Meyer-Kahlen]], [[CCC]], May 22, 1999 » [[Pawn Advantage, Win Percentage, and Elo]], [[Playing Strength]]
 
* [https://www.stmintz.com/ccc/index.php?id=52542 ELO performance?] by [[Stefan Meyer-Kahlen]], [[CCC]], May 22, 1999 » [[Pawn Advantage, Win Percentage, and Elo]], [[Playing Strength]]
 
==2000 ...==  
 
==2000 ...==  
Line 417: Line 439:
 
* [http://www.talkchess.com/forum/viewtopic.php?t=37056 SPRT and Engine testing] by [[Adam Hair]], [[CCC]], December 13, 2010 » [[Match Statistics#SPRT|SPRT]]
 
* [http://www.talkchess.com/forum/viewtopic.php?t=37056 SPRT and Engine testing] by [[Adam Hair]], [[CCC]], December 13, 2010 » [[Match Statistics#SPRT|SPRT]]
 
'''2011'''
 
'''2011'''
 +
* [http://www.talkchess.com/forum/viewtopic.php?t=38772 Pairwise Analysis of Chess Engine Move Selections] by [[Adam Hair]], [[CCC]], April 17, 2011
 
* [http://www.talkchess.com/forum/viewtopic.php?t=39511 Ply vs ELO] by Andriy Dzyben, [[CCC]], June 28, 2011
 
* [http://www.talkchess.com/forum/viewtopic.php?t=39511 Ply vs ELO] by Andriy Dzyben, [[CCC]], June 28, 2011
 
* [http://www.talkchess.com/forum/viewtopic.php?t=40193 One billion random games] by [[Steven Edwards]], [[CCC]], August 27, 2011
 
* [http://www.talkchess.com/forum/viewtopic.php?t=40193 One billion random games] by [[Steven Edwards]], [[CCC]], August 27, 2011
Line 422: Line 445:
 
'''2012'''
 
'''2012'''
 
* [http://www.talkchess.com/forum/viewtopic.php?t=42729 Advantage for White; Bayeselo (to Rémi Coulom)] by [[Edmund Moshammer]], [[CCC]], March 03, 2012
 
* [http://www.talkchess.com/forum/viewtopic.php?t=42729 Advantage for White; Bayeselo (to Rémi Coulom)] by [[Edmund Moshammer]], [[CCC]], March 03, 2012
 +
* [http://www.talkchess.com/forum/viewtopic.php?t=42737 Pairwise Analysis of Chess Engine Move Selections Revisited] by [[Adam Hair]], [[CCC]], March 04, 2012
 
* [http://www.talkchess.com/forum/viewtopic.php?t=44219 Human Elo ratings: averages and standard deviations] by [[Jesús Muñoz]], [[CCC]], March 18, 2012 <ref>[http://en.chessbase.com/post/arpad-elo-and-the-elo-rating-system Arpad Elo and the Elo Rating System] by [[Dan Ross]], [[ChessBase|ChessBase News]], December 16, 2007</ref>
 
* [http://www.talkchess.com/forum/viewtopic.php?t=44219 Human Elo ratings: averages and standard deviations] by [[Jesús Muñoz]], [[CCC]], March 18, 2012 <ref>[http://en.chessbase.com/post/arpad-elo-and-the-elo-rating-system Arpad Elo and the Elo Rating System] by [[Dan Ross]], [[ChessBase|ChessBase News]], December 16, 2007</ref>
 
* [http://www.talkchess.com/forum/viewtopic.php?t=42998 Elo uncertainties calculator] by [[Jesús Muñoz]], [[CCC]], March 24, 2012
 
* [http://www.talkchess.com/forum/viewtopic.php?t=42998 Elo uncertainties calculator] by [[Jesús Muñoz]], [[CCC]], March 24, 2012
 
* [http://www.talkchess.com/forum/viewtopic.php?t=43134 Elo versus speed] by [[Peter Österlund]], [[CCC]], April 02, 2012
 
* [http://www.talkchess.com/forum/viewtopic.php?t=43134 Elo versus speed] by [[Peter Österlund]], [[CCC]], April 02, 2012
 +
* [http://www.talkchess.com/forum/viewtopic.php?t=43323 Pawn Advantage, Win Percentage, and Elo] by [[Adam Hair]], [[CCC]], April 15, 2012 » [[Pawn Advantage, Win Percentage, and Elo]]
 +
* [http://www.talkchess.com/forum/viewtopic.php?t=43598 Elo Increase per Doubling] by [[Adam Hair]], [[CCC]], May 07, 2012
 
* [http://www.talkchess.com/forum/viewtopic.php?t=44003 Rybka odds matches and the strength of engines] by [[Kai Laskos]], [[CCC]], June 09, 2012 » [[Rybka]]
 
* [http://www.talkchess.com/forum/viewtopic.php?t=44003 Rybka odds matches and the strength of engines] by [[Kai Laskos]], [[CCC]], June 09, 2012 » [[Rybka]]
 
* [http://www.talkchess.com/forum/viewtopic.php?t=44147 A new way to compare chess programs] by [[Larry Kaufman]], [[CCC]], June 21, 2012 » [[Komodo]]
 
* [http://www.talkchess.com/forum/viewtopic.php?t=44147 A new way to compare chess programs] by [[Larry Kaufman]], [[CCC]], June 21, 2012 » [[Komodo]]
Line 440: Line 466:
 
* [http://www.talkchess.com/forum/viewtopic.php?t=46572 A word for casual testers] by [[Don Dailey]], [[CCC]], December 25, 2012
 
* [http://www.talkchess.com/forum/viewtopic.php?t=46572 A word for casual testers] by [[Don Dailey]], [[CCC]], December 25, 2012
 
'''2013'''
 
'''2013'''
* [http://www.talkchess.com/forum/viewtopic.php?t=46759 A poor man's testing environment] by [[Ed Schroder|Ed Schröder]], [[CCC]], January 04, 2013 <ref>[http://www.top-5000.nl/tuning.htm Testing a chess engine from the ground up] from [http://www.top-5000.nl/ Home of the Dutch Rebel] by [[Ed Schroder|Ed Schröder]]</ref> » [[Engine Testing]]
+
* [http://www.talkchess.com/forum/viewtopic.php?t=46759 A poor man's testing environment] by [[Ed Schroder|Ed Schröder]], [[CCC]], January 04, 2013 » [[Engine Testing]]
 
* [http://www.talkchess.com/forum/viewtopic.php?t=46786 Noise in ELO estimators: a quantitative approach] by [[Marco Costalba]], [[CCC]], January 06, 2013
 
* [http://www.talkchess.com/forum/viewtopic.php?t=46786 Noise in ELO estimators: a quantitative approach] by [[Marco Costalba]], [[CCC]], January 06, 2013
 
* [http://www.talkchess.com/forum/viewtopic.php?t=47086 Updated Dendrogram] by [[Kai Laskos]], [[CCC]], February 02, 2013
 
* [http://www.talkchess.com/forum/viewtopic.php?t=47086 Updated Dendrogram] by [[Kai Laskos]], [[CCC]], February 02, 2013
Line 472: Line 498:
 
* [http://www.talkchess.com/forum/viewtopic.php?t=56095 Getting SPRT right] by [[Alexandru Mosoi]], [[CCC]], April 22, 2015 » [[Match Statistics#SPRT|SPRT]]
 
* [http://www.talkchess.com/forum/viewtopic.php?t=56095 Getting SPRT right] by [[Alexandru Mosoi]], [[CCC]], April 22, 2015 » [[Match Statistics#SPRT|SPRT]]
 
* [http://www.talkchess.com/forum/viewtopic.php?t=56358 SPRT questions] by [[Uri Blass]], [[CCC]], May 15, 2015 » [[Match Statistics#SPRT|SPRT]]
 
* [http://www.talkchess.com/forum/viewtopic.php?t=56358 SPRT questions] by [[Uri Blass]], [[CCC]], May 15, 2015 » [[Match Statistics#SPRT|SPRT]]
* [http://www.talkchess.com/forum/viewtopic.php?t=56426 Adam Hair's article on Pairwise comparison of engines] by [[Charles Roberson]], [[CCC]], May 19, 2015 <ref>[http://www.top-5000.nl/clone.htm A Pairwise Comparison of Chess Engine Move Selections] by [[Adam Hair]], hosted by [[Ed Schroder|Ed Schröder]]</ref>
+
* [http://www.talkchess.com/forum/viewtopic.php?t=56426 Adam Hair's article on Pairwise comparison of engines] by [[Charles Roberson]], [[CCC]], May 19, 2015  
 
* [http://www.talkchess.com/forum/viewtopic.php?t=57223 computing elo of multiple chess engines] by [[Alexandru Mosoi]], [[CCC]], August 09, 2015
 
* [http://www.talkchess.com/forum/viewtopic.php?t=57223 computing elo of multiple chess engines] by [[Alexandru Mosoi]], [[CCC]], August 09, 2015
 
* [http://www.talkchess.com/forum/viewtopic.php?t=57270 Some musings about search] by [[Ed Schroder|Ed Schröder]], [[CCC]], August 14, 2015 » [[Automated Tuning]], [[Search]]
 
* [http://www.talkchess.com/forum/viewtopic.php?t=57270 Some musings about search] by [[Ed Schroder|Ed Schröder]], [[CCC]], August 14, 2015 » [[Automated Tuning]], [[Search]]
Line 525: Line 551:
 
* [http://www.talkchess.com/forum/viewtopic.php?t=63875 Wilo rating properties from FGRL rating lists] by [[Kai Laskos]], [[CCC]], May 01, 2017 » [[FGRL]]
 
* [http://www.talkchess.com/forum/viewtopic.php?t=63875 Wilo rating properties from FGRL rating lists] by [[Kai Laskos]], [[CCC]], May 01, 2017 » [[FGRL]]
 
* [http://www.talkchess.com/forum/viewtopic.php?t=63888 MATCH sanity] by [[Ed Schroder]], [[CCC]], May 03, 2017 » [[Portable Game Notation]]
 
* [http://www.talkchess.com/forum/viewtopic.php?t=63888 MATCH sanity] by [[Ed Schroder]], [[CCC]], May 03, 2017 » [[Portable Game Notation]]
 +
: [http://www.talkchess.com/forum3/viewtopic.php?f=7&t=63888&start=2 Re: MATCH sanity] by [[Salvatore Giannotti]], [[CCC]], May 03, 2017
 
* [http://www.talkchess.com/forum/viewtopic.php?t=63903 Symmetric multiprocessing (SMP) scaling - SF8 and K10.4] by [[Andreas Strangmüller]], [[CCC]], May 05, 2017 » [[Lazy SMP]], [[Komodo]], [[Stockfish]]
 
* [http://www.talkchess.com/forum/viewtopic.php?t=63903 Symmetric multiprocessing (SMP) scaling - SF8 and K10.4] by [[Andreas Strangmüller]], [[CCC]], May 05, 2017 » [[Lazy SMP]], [[Komodo]], [[Stockfish]]
 
* [http://www.talkchess.com/forum/viewtopic.php?t=63955 Symmetric multiprocessing (SMP) scaling - K10.4 Contempt=0] by [[Andreas Strangmüller]], [[CCC]], May 11, 2017 » [[SMP]], [[Komodo]], [[Contempt Factor]]
 
* [http://www.talkchess.com/forum/viewtopic.php?t=63955 Symmetric multiprocessing (SMP) scaling - K10.4 Contempt=0] by [[Andreas Strangmüller]], [[CCC]], May 11, 2017 » [[SMP]], [[Komodo]], [[Contempt Factor]]
Line 552: Line 579:
 
* [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]], [[Pawn Advantage, Win Percentage, and Elo]]
 
* [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]], [[Pawn Advantage, Win Percentage, and Elo]]
 
* [http://www.talkchess.com/forum3/viewtopic.php?f=7&t=69069 Are draws hard to predict?] by [[Daniel Shawul]], [[CCC]], November 27, 2018 » [[Draw]], [[Neural Networks]]
 
* [http://www.talkchess.com/forum3/viewtopic.php?f=7&t=69069 Are draws hard to predict?] by [[Daniel Shawul]], [[CCC]], November 27, 2018 » [[Draw]], [[Neural Networks]]
 +
* [http://www.talkchess.com/forum3/viewtopic.php?f=7&t=69284 testing consistency] by [[Jon Dart]], [[CCC]], December 16, 2018
 +
* [http://www.talkchess.com/forum3/viewtopic.php?f=7&t=69407 Fixed nodes games and the pentanomial model] by [[Michel Van den Bergh]], [[CCC]], December 29, 2018
 +
'''2019'''
 +
* [http://www.talkchess.com/forum3/viewtopic.php?f=2&t=69672 Schizophrenic rating model for Leela] by [[Kai Laskos]], [[CCC]], January 21, 2019 » [[Leela Chess Zero]]
 +
* [http://www.talkchess.com/forum3/viewtopic.php?f=7&t=71419 best way to determine elos of a group] by [[Daniel Shawul]], [[CCC]], July 30, 2019
  
 
=External Links=  
 
=External Links=  
* [http://www.top-5000.nl/tuning.htm Testing a chess engine from the ground up] from [http://www.top-5000.nl/ Home of the Dutch Rebel] by [[Ed Schroder|Ed Schröder]] <ref>[http://www.talkchess.com/forum/viewtopic.php?t=46759 A poor man's testing environment] by [[Ed Schroder|Ed Schröder]], [[CCC]], January 04, 2013</ref> » [[Engine Testing]]
 
* [http://www.top-5000.nl/match.htm MATCH - eng-eng utility] by [[Ed Schroder|Ed Schröder]]
 
* [http://walkofmind.com/programming/chess/mat_stats.html Statistics of material imbalances in chess games] by [[Alessandro Scotti]] » [[Material]]
 
 
==Rating Systems==  
 
==Rating Systems==  
 
* [https://en.wikipedia.org/wiki/Chessmetrics Chessmetrics from Wikipedia]
 
* [https://en.wikipedia.org/wiki/Chessmetrics Chessmetrics from Wikipedia]
Line 562: Line 591:
 
* [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://en.chessbase.com/post/arpad-elo-and-the-elo-rating-system Arpad Elo and the Elo Rating System] by [[Dan Ross]], [[ChessBase|ChessBase News]], December 16, 2007
 
* [http://en.chessbase.com/post/arpad-elo-and-the-elo-rating-system Arpad Elo and the Elo Rating System] by [[Dan Ross]], [[ChessBase|ChessBase News]], December 16, 2007
 +
* [https://www.kaggle.com/c/chess Chess ratings - Elo versus the Rest of the World] | [https://en.wikipedia.org/wiki/Kaggle Kaggle]
 
* [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]]
 
* [http://www.husvankempen.de/nunn/rating/tablejoseph.htm LOS Table] by [[Joseph Ciarrochi]] from [[CEGT]] <ref>[https://www.stmintz.com/ccc/index.php?id=484357 table for detecting significant difference between two engines] by [[Joseph Ciarrochi]], [[CCC]], February 03, 2006</ref>
 
* [http://www.husvankempen.de/nunn/rating/tablejoseph.htm LOS Table] by [[Joseph Ciarrochi]] from [[CEGT]] <ref>[https://www.stmintz.com/ccc/index.php?id=484357 table for detecting significant difference between two engines] by [[Joseph Ciarrochi]], [[CCC]], February 03, 2006</ref>
Line 604: Line 634:
 
* [https://www.khanacademy.org/math/probability/statistics-inferential/hypothesis-testing/v/type-1-errors Type 1 Errors | Hypothesis testing with one sample] | [https://en.wikipedia.org/wiki/Khan_Academy Khan Academy]
 
* [https://www.khanacademy.org/math/probability/statistics-inferential/hypothesis-testing/v/type-1-errors Type 1 Errors | Hypothesis testing with one sample] | [https://en.wikipedia.org/wiki/Khan_Academy Khan Academy]
 
==Data Visualization==
 
==Data Visualization==
* [http://www.top-5000.nl/clone.htm A Pairwise Comparison of Chess Engine Move Selections] by [[Adam Hair]], hosted by [[Ed Schroder|Ed Schröder]] <ref>[https://en.wikipedia.org/wiki/UPGMA UPGMA from Wikipedia]</ref> <ref>[http://www.southampton.ac.uk/~re1u06/teaching/upgma/ UPGMA Worked Example] by [http://www.southampton.ac.uk/biosci/about/staff/re1u06.page? Richard Edwards]</ref> <ref>[http://www.talkchess.com/forum/viewtopic.php?t=56426 Adam Hair's article on Pairwise comparison of engines] by [[Charles Roberson]], [[CCC]], May 19, 2015</ref> <ref>[[Don Dailey]], [[Adam Hair]], [[Mark Watkins]] ('''2014'''). ''[http://www.sciencedirect.com/science/article/pii/S1875952113000177 Move Similarity Analysis in Chess Programs]''. [http://www.journals.elsevier.com/entertainment-computing/ Entertainment Computing], Vol. 5, No. 3, [http://magma.maths.usyd.edu.au/~watkins/papers/DHW.pdf preprint as pdf]</ref>
 
 
* [https://blog.ebemunk.com/a-visual-look-at-2-million-chess-games/ A Visual Look at 2 Million Chess Games - Thinking Through the Party] by [[Buğra Fırat]], March 02, 2016 <ref>[http://www.talkchess.com/forum/viewtopic.php?t=65610 A Visual Look at 2 Million Chess Games] by Brahim Hamadicharef, [[CCC]], November 02, 2017</ref>
 
* [https://blog.ebemunk.com/a-visual-look-at-2-million-chess-games/ A Visual Look at 2 Million Chess Games - Thinking Through the Party] by [[Buğra Fırat]], March 02, 2016 <ref>[http://www.talkchess.com/forum/viewtopic.php?t=65610 A Visual Look at 2 Million Chess Games] by Brahim Hamadicharef, [[CCC]], November 02, 2017</ref>
 
* [https://github.com/ebemunk/chess-dataviz GitHub - ebemunk/chess-dataviz: chess visualization library written for d3.js] by [[Buğra Fırat]] » [[JavaScript]]
 
* [https://github.com/ebemunk/chess-dataviz GitHub - ebemunk/chess-dataviz: chess visualization library written for d3.js] by [[Buğra Fırat]] » [[JavaScript]]

Latest revision as of 11:53, 17 October 2019

Home * Engine Testing * Match Statistics

Match Statistics [1]

Match Statistics,
the statistics of chess tournaments and matches, that is a collection of chess games and the presentation, analysis, and interpretation of game related data, most common game results to determine the relative playing strength of chess playing entities, here with focus on chess engines. To apply match statistics, beside considering statistical population, it is conventional to hypothesize a statistical model describing a set of probability distributions.

Ratios / Operating Figures

Common tools, ratios and figures to illustrate a tournament outcome and provide a base for its interpretation.

Number of games

The total number of games played by an engine in a tournament.

N = wins + draws + losses

Score

The score is a representation of the tournament-outcome from the viewpoint of a certain engine.

score_difference = wins - losses
score = wins + draws/2

Win & Draw Ratio

win_ratio  = score/N
draw_ratio = draws/N

These two ratios depend on the strength difference between the competitors, the average strength level, the color and the drawishness of the opening book-line. Due to the second reason given, these ratios are very much influenced by the timecontrol, what is also confirmed by the published statistics of the testing orgnisations CCRL and CEGT, showing an increase of the draw rate at longer time controls. This correlation was also shown by Kirill Kryukov, who was analyzing statistics of his test-games [2] . The program playing white seems to be more supported by the additional level of strength. So, although one would expect with increasing draw rates the win ratio to approach 50%, in fact it is remaining about equal.

Timecontrol Draw Ratio Win Ratio (white) Source
40/4 30.9% 55.0% CEGT
40/20 35.6% 54.6% CEGT
40/120 41.3% 55.4% CEGT
40/120 (4cpu) 45.2% 55.9% CEGT
Timecontrol Draw Ratio Win Ratio (white) Source
40/4 31.0% 54.1% CCRL
40/40 37.2% 54.6% CCRL

Doubling Time Control As posted in October 2016 [3] , Andreas Strangmüller conducted an experiment with Komodo 9.3, time control doubling matches under Cutechess-cli, playing 3000 games with 1500 opening positions each, without pondering, learning, and tablebases, Intel i5-750 @ 3.5 GHz, 1 Core, 128 MB Hash [4] , see also Kai Laskos' 2013 results with Houdini 3 [5] and Diminishing Returns:

Time Control 2
vs 1
20+0.2
10+0.1
40+0.4
20+0.2
80+0.8
40+0.4
160+1.6
80+0.8
320+3.2
160+1.6
640+6.4
320+3.2
1280+12.8
640+6.4
2560+25.6
1280+12.8
Elo 144 133 112 101 93 73 59 51
Win 44.97% 41.27% 36.67% 32.67% 30.47% 25.17% 21.77% 18.97%
Draw 49.20% 54.00% 57.93% 63.03% 65.33% 70.47% 73.17% 76.63%
Loss 5.83% 4.73% 5.40% 4.30% 4.20% 4.37% 5.07% 4.40%

Elo-Rating & Win-Probability

see Pawn Advantage, Win Percentage, and Elo

Expected win_ratio, win_probability (E)
Elo Rating Difference (Δ) = Elo_Player1 - Elo_Player2
E = 1 / ( 1 + 10-Δ/400)
Δ = 400 log10(E / (1 - E))

Generalization of the Elo-Formula: win_probability of player i in a tournament with n players

Ei = 10Eloi / (10Elo1 + 10Elo2 + ... + 10Elon-1 + 10Elon)

Likelihood of Superiority

See LOS Table

The likelihood of superiority (LOS) denotes how likely it would be for two players of the same strength to reach a certain result - in other fields called a p-value, a measure of statistical significance of a departure from the null hypothesis [6]. Doing this analysis after the tournament one has to differentiate between the case where one knows that a certain engine is either stronger or equally strong (directional or one-tailed test) or the case where one has no information of whether the other engine is stronger or weaker (non-directional or two-tailed test). The latter due to the reduced information results in larger confidence intervals.

Two-tailed Test
Null- and alternative hypothesis:

H0 : Elo_Player1 = Elo_Player2 

H1 : Elo_Player1 ≠ Elo_Player2 
LOS = P(Score > score of 2 programs with equal strength)

The probability of the null hypothesis being true can be calculated given the tournament outcome. In other words, how likely would it be for two players of the same strength to reach a certain result. The LOS would then be the inverse, 1 - the resulting probability.

For this type of analysis the trinomial distribution, a generalization of the binomial distribution, is needed. Whilest the binomial distribution can only calculate the probability to reach a certain outcome with two possible events, the trinominal distribution can account for all three possible events (win, draw, loss).

The following functions gives the probability of a certain game outcome assuming both players were of equal strength:

win_probability = (1 - draw_ratio) / 2
P(wins,draws,losses) = N!/(wins! draws! losses!) win_probabilitywins draw_ratiodrwas win_probabilitylosses

This calculation becomes very inefficient for larger number of games. In this case the standard normal distribution can give a good approximation:

N(N/2, N(1-draw_ratio))

where N(1 - draw_ratio) is the sum of wins and losses:

N(N/2, wins + losses)

To calculate the LOS one needs the cumulative distribution function of the given normal distribution. However, as pointed out by Rémi Coulom, calculation can be done cleverly, and the normal approximation is not really required [7] . As further emphasized by Kai Laskos [8] and Rémi Coulom [9] [10] , draws do not count in LOS calculation and don't make a difference whether the game results were obtained when playing Black or White. It is a good approximation when the two players played the same number of games with each color:

LOS = ϕ((wins - losses)/√(wins + losses))

LOS = ½[1 + erf((wins - losses)/√(2wins + 2losses))]

[11] [12] [13]

One-tailed Test
Null- and alternative hypothesis:

H0 : Elo_Player1 ≤ Elo_Player2 

H1 : Elo_Player1 > Elo_Player2 

Sample Program
A tiny C++11 program to compute Elo difference and LOS from W/L/D counts was given by Álvaro Begué [14] :

#include <cstdio>
#include <cstdlib>
#include <cmath>

int main(int argc, char **argv) {
  if (argc != 4) {
    std::printf("Wrong number of arguments.\n\nUsage:%s <wins> <losses> <draws>\n", argv[0]);
    return 1;
  }
  int wins = std::atoi(argv[1]);
  int losses = std::atoi(argv[2]);
  int draws = std::atoi(argv[3]);

  double games = wins + losses + draws;
  std::printf("Number of games: %g\n", games);
  double winning_fraction = (wins + 0.5*draws) / games;
  std::printf("Winning fraction: %g\n", winning_fraction);
  double elo_difference = -std::log(1.0/winning_fraction-1.0)*400.0/std::log(10.0);
  std::printf("Elo difference: %+g\n", elo_difference);
  double los = .5 + .5 * std::erf((wins-losses)/std::sqrt(2.0*(wins+losses)));
  std::printf("LOS: %g\n", los);
}

Statistical Analysis

The trinomial versus the 5-nomial model

As indicated above a match between two engines is usually modeled as a sequence of independent trials taken from a trinomial distribution with probabilities (win_ratio,draw_ratio,loss_ratio). This model is appropriate for a match with randomly selected opening positions and randomly assigned colors (to maintain fairness). However one may show that under reasonable elo models the trinomial model is not correct in case games are played in pairs with reversed colors (as is commonly the case) and unbalanced opening positions are used.

This was also empirically observed by Kai Laskos [15] . He noted that the statistical predictions of the trinomial model do not match reality very well in the case of paired games. In particular he observed that for some data sets the variance of the match score as predicted by the trinomial model greatly exceeds the variance as calculated by the jackknife estimator. The jackknife estimator is a non-parametric estimator, so it does not depend on any particular statistical model. It appears the mismatch may even occur for balanced opening positions, an effect which can only be explained by the existence of correlations between paired games - something not considered by any elo model.

Over estimating the variance of the match score implies that derived quantities such as the number of games required to establish the superiority of one engine over another with a given level of significance are also over estimated. To obtain agreement between statistical predictions and actual measurements one may adopt the more general 5-nomial model. In the 5-nomial model the outcome of paired games is assumed to follow a 5-nomial distribution with probabilities

(p0, p1/2, p1, p3/2, p2)

These unknown probabilities may be estimated from the outcome frequencies of the paired games and then subsequently be used to compute an estimate for the variance of the match score. Summarizing: in the case of paired games the 5-nomial model handles the following effects correctly which the trinomial model does not:

  • Unbalanced openings
  • Correlations between paired games

For further discussion on the potential use of unbalanced opening positions in engine testing see the posting by Kai Laskos [16] .

SPRT

The sequential probability ratio test (SPRT) is a specific sequential hypothesis test - a statistical analysis where the sample size is not fixed in advance - developed by Abraham Wald [17] . While originally developed for use in quality control studies in the realm of manufacturing, SPRT has been formulated for use in the computerized testing of human examinees as a termination criterion [18]. As mentioned by Arthur Guez in this 2015 Ph.D. thesis Sample-based Search Methods for Bayes-Adaptive Planning [19], Alan Turing assisted by Jack Good used a similar sequential testing technique to help decipher enigma codes at Bletchley Park [20]. SPRT is applied in Stockfish testing to terminate self-testing series early if the result is likely outside a given elo-window [21] . In August 2016, Michel Van den Bergh posted following Python code in CCC to implement the SPRT a la Cutechess-cli or Fishtest: [22] [23]

from __future__ import division

import math

def LL(x):
    return 1/(1+10**(-x/400))

def LLR(W,D,L,elo0,elo1):
    """
This function computes the log likelihood ratio of H0:elo_diff=elo0 versus
H1:elo_diff=elo1 under the logistic elo model

expected_score=1/(1+10**(-elo_diff/400)).

W/D/L are respectively the Win/Draw/Loss count. It is assumed that the outcomes of
the games follow a trinomial distribution with probabilities (w,d,l). Technically
this is not quite an SPRT but a so-called GSPRT as the full set of parameters (w,d,l)
cannot be derived from elo_diff, only w+(1/2)d. For a description and properties of
the GSPRT (which are very similar to those of the SPRT) see

http://stat.columbia.edu/~jcliu/paper/GSPRT_SQA3.pdf

This function uses the convenient approximation for log likelihood
ratios derived here:

http://hardy.uhasselt.be/Toga/GSPRT_approximation.pdf

The previous link also discusses how to adapt the code to the 5-nomial model
discussed above.
"""
# avoid division by zero
    if W==0 or D==0 or  L==0:
        return 0.0
    N=W+D+L
    w,d,l=W/N,D/N,L/N
    s=w+d/2
    m2=w+d/4
    var=m2-s**2
    var_s=var/N
    s0=LL(elo0)
    s1=LL(elo1)
    return (s1-s0)*(2*s-s0-s1)/var_s/2.0

def SPRT(W,D,L,elo0,elo1,alpha,beta):
    """
This function sequentially tests the hypothesis H0:elo_diff=elo0 versus
the hypothesis H1:elo_diff=elo1 for elo0<elo1. It should be called after
each game until it returns either 'H0' or 'H1' in which case the test stops
and the returned hypothesis is accepted.

alpha is the probability that H1 is accepted while H0 is true
(a false positive) and beta is the probability that H0 is accepted
while H1 is true (a false negative). W/D/L are the current win/draw/loss
counts, as before.
"""
    LLR_=LLR(W,D,L,elo0,elo1)
    LA=math.log(beta/(1-alpha))
    LB=math.log((1-beta)/alpha)
    if LLR_>LB:
        return 'H1'
    elif LLR_<LA:
        return 'H0'
    else:
        return ''

Tournaments

See also

Publications

1920 ...

1940 ...

1950 ...

1960 ...

1970 ...

1980 ...

1990 ...

2000 ...

2005 ...

2010 ...

2015 ...

Forum & Blog Postings

1996 ...

2000 ...

2005 ...

2010 ...

Re: Engine Testing - Statistics by John Major, CCC, January 14, 2010

2011

2012

2013

2014

2015 ...

Re: The SPRT without draw model, elo model or whatever.. by Michel Van den Bergh, CCC, August 18, 2016

2016

About expected scores and draw ratios by Jesús Muñoz, CCC, September 17, 2016

2017

Re: MATCH sanity by Salvatore Giannotti, CCC, May 03, 2017
ELO measurements by Peter Österlund, CCC, August 06, 2017 » Playing Strength
Re: "Intrinsic Chess Ratings" by Regan, Haworth -- by Kenneth Regan, CCC, November 20, 2017 » Who is the Master?

2018

2019

External Links

Rating Systems

Tools

Statistics

Data Visualization

Misc

ARMS Charity Concert, Madison Square Garden, December 08, 1983

References

  1. Image based on Standard deviation diagram by Mwtoews, April 7, 2007 with R code given, CC BY 2.5, Wikimedia Commons, Normal distribution from Wikipedia
  2. Kirr's Chess Engine Comparison KCEC - Draw rate » KCEC
  3. Doubling of time control by Andreas Strangmüller, CCC, October 21, 2016
  4. K93-Doubling-TC.pdf
  5. Scaling at 2x nodes (or doubling time control) by Kai Laskos, CCC, July 23, 2013
  6. Re: Likelihood Of Success (LOS) in the real world by Álvaro Begué, CCC, May 26, 2017
  7. Re: Calculating the LOS (likelihood of superiority) from results by Rémi Coulom, CCC, January 23, 2014
  8. Re: Calculating the LOS (likelihood of superiority) from results by Kai Laskos, CCC, January 22, 2014
  9. Re: Likelihood of superiority by Rémi Coulom, CCC, November 15, 2009
  10. Re: Likelihood of superiority by Rémi Coulom, CCC, November 15, 2009
  11. Error function from Wikipedia
  12. The Open Group Base Specifications Issue 6IEEE Std 1003.1, 2004 Edition: erf
  13. erf(x) and math.h by user76293, Stack Overflow, March 10, 2009
  14. Re: Calculating the LOS (likelihood of superiority) from results by Álvaro Begué, CCC, January 22, 2014
  15. Error margins via resampling (jackknifing) by Kai Laskos, CCC, August 12, 2016
  16. Properties of unbalanced openings using Bayeselo model by Kai Laskos, CCC, August 27, 2016
  17. Abraham Wald (1945). Sequential Tests of Statistical Hypotheses. Annals of Mathematical Statistics, Vol. 16, No. 2, doi: 10.1214/aoms/1177731118
  18. Sequential probability ratio test from Wikipedia
  19. Arthur Guez (2015). Sample-based Search Methods for Bayes-Adaptive Planning. Ph.D. thesis, Gatsby Computational Neuroscience Unit, University College London, pdf
  20. Jack Good (1979). Studies in the history of probability and statistics. XXXVII AM Turing’s statistical work in World War II. Biometrika, Vol. 66, No. 2
  21. How (not) to use SPRT ? by BB+, OpenChess Forum, October 19, 2013
  22. Re: The SPRT without draw model, elo model or whatever.. by Michel Van den Bergh, CCC, August 18, 2016
  23. GSPRT approximation (pdf) by Michel Van den Bergh
  24. Law of comparative judgment - Wikipedia
  25. Elo's Book: The Rating of Chess Players by Sam Sloan
  26. The Master Game from Wikipedia
  27. Handwritten Notes on the 2004 David R. Hunter Paper 'MM Algorithms for Generalized Bradley-Terry Models' by Rémi Coulom
  28. Derivation of bayeselo formula by Rémi Coulom, CCC, August 07, 2012
  29. Mm algorithm from Wikipedia
  30. Pairwise comparison from Wikipedia
  31. Bayesian inference from Wikipedia
  32. How I did it: Diogo Ferreira on 4th place in Elo chess ratings competition | no free hunch
  33. "Intrinsic Chess Ratings" by Regan, Haworth -- seq by Kai Middleton, CCC, November 19, 2017
  34. Re: EloStat, Bayeselo and Ordo by Rémi Coulom, CCC, June 25, 2012
  35. Re: Understanding and Pushing the Limits of the Elo Rating Algorithm by Daniel Shawul, CCC, October 15, 2019
  36. Ordo by Miguel A. Ballicora
  37. Pairwise Analysis of Chess Engine Move Selections by Adam Hair, CCC, April 17, 2011
  38. Questions regarding rating systems of humans and engines by Erik Varend, CCC, December 06, 2014
  39. chess statistics scientific article by Nuno Sousa, CCC, July 06, 2016
  40. Understanding and Pushing the Limits of the Elo Rating Algorithm by Michel Van den Bergh, CCC, October 15, 2019
  41. LOS Table by Joseph Ciarrochi from CEGT
  42. Arpad Elo and the Elo Rating System by Dan Ross, ChessBase News, December 16, 2007
  43. David R. Hunter (2004). MM Algorithms for Generalized Bradley-Terry Models. The Annals of Statistics, Vol. 32, No. 1, 384–406, pdf
  44. Type I and type II errors from Wikipedia
  45. Arpad Elo - Wikipedia
  46. Regan's latest: Depth of Satisficing by Carl Lumma, CCC, October 09, 2015
  47. Resampling (statistics) from Wikipedia
  48. Jackknife resampling from WIkipedia
  49. Delphil 3.3b2 (2334) - Stockfish 030916 (3228), TCEC Season 9 - Rapid, Round 11, September 16, 2016
  50. World Chess Championship 2016 from Wikipedia
  51. Normalized Elo (pdf) by Michel Van den Bergh
  52. table for detecting significant difference between two engines by Joseph Ciarrochi, CCC, February 03, 2006
  53. an interesting study from Erik Varend by scandien, Hiarcs Forum, August 13, 2017
  54. A Visual Look at 2 Million Chess Games by Brahim Hamadicharef, CCC, November 02, 2017

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