Answers.Body: <p>Did an experiment finding a top player playing against a top player on games that reaches an ending. I took some <a href="https://en.chessbase.com/post/what-was-the-strongest-tournament-of-all-time-" rel="nofollow noreferrer">top tournaments</a> according to Jeff Jonas and analyze those games.</p>
  <p>I define an ending position as those positions where the total piece (excluding pawns and kings) values are 2 queens or less. Q=10, R=5, B=N=3. Example for KQKQ, piecevalue = 20 is an ending. KRRKRR, piecevalue = 20 is also an ending. So the condition is: if piecevalue &lt;= 20 it is an ending.</p>
  <p>For each tournament check all games, if a piece value of the position reaches 20 or less, analyze it with stockfish 14.1 with 2 threads for 30s. If this position is not winning or losing (score &gt;= -50cp and score &lt;= 50cp), then consider it in the calculation.</p>
  <h3>AVRO 1938 Result</h3>
  <pre><code>                    players  games   rate
  0              Fine, Reuben      1  1.000
  1  Reshevsky, Samuel Herman      4  0.500
  2     Capablanca, Jose Raul      3  0.500
  3                 Euwe, Max      3  0.500
  4        Botvinnik, Mikhail      2  0.500
  5               Keres, Paul      1  0.500
  6       Alekhine, Alexander      4  0.375
  </code></pre>
  <p>Fine had 1 game and won it. The others got 50% and Alekhine got 37.5% from 4 games.</p>
  <p>The game where Fine won from equal ending position.</p>
  <pre><code>[Event &quot;AVRO&quot;]
  [Site &quot;Holland&quot;]
  [Date &quot;1938.??.??&quot;]
  [Round &quot;?&quot;]
  [White &quot;Alekhine, Alexander&quot;]
  [Black &quot;Fine, Reuben&quot;]
  [Result &quot;0-1&quot;]
  [BlackElo &quot;&quot;]
  [ECO &quot;C83&quot;]
  [WhiteElo &quot;&quot;]
  
  1. e4 e5 2. Nf3 Nc6 3. Bb5 a6 4. Ba4 Nf6 5. O-O Nxe4 6. d4 b5 7. Bb3 d5 8. dxe5 Be6 9. c3 Be7 10. Nd4 Nxe5 11. f3 Nf6 12. Qe2 Nc4 13. Bc2 Qd7 14. b3 Nb6 15. Re1 O-O 16. Bg5 Rfe8 17. Nd2 Nh5 18. Bxe7 Rxe7 19. Qe5 g6 20. g4 Ng7 21. b4 Rae8 22. Qf4 Na4 23. Re3 Qd6 24. Qxd6 cxd6 25. Rae1 Rc7 26. Nb1 Bd7 27. Rxe8+ Bxe8 28. Bb3 Nb6 29. Kf2 Kf8 30. Rd1 Ne6 31. Ne2 Bc6 32. Na3 Ke7 33. Nc2 Nc4 34. Ne3 h6 35. h4 Nb6 36. Bxd5 Bxd5 37. Nxd5+ Nxd5 38. Rxd5 Rc4 39. Ke3 Kd7 40. f4 Kc6 41. Rd1 Kd7 42. Rf1 Ke7 43. Kd3 g5 44. hxg5 hxg5 45. f5 Nf8 46. f6+ Kd7 47. a4 Ng6 48. axb5 Ne5+ 49. Kd2 axb5 50. Nd4 Nxg4 51. Nxb5 Ne5 52. Nd4 g4 53. Kc2 Rc8 54. Nf5 Rg8 55. Ng3 Rh8 56. Rf2 Nf3 57. Re2 Rh3 58. Nf5 Ne5 59. b5 Rf3 60. Nd4 Rxf6 61. b6 Kc8 62. Nb5 g3 63. Kb3 Rg6 64. Rg2 f5 65. Ra2 Kb7 66. Rd2 f4 67. Nxd6+ Rxd6 68. Rxd6 g2 0-1
  </code></pre>
  <p>The ending position with stockfish 14.1 analysis:</p>
  <pre><code>8/2r1kp2/p2pn1pp/1p1n4/1P4PP/2P2P2/P3NK2/3R4 w - - 0 38 acd 45; acs 30; ce 0; Ae Stockfish 14.1;
  </code></pre>
  <ul>
  <li>acd is the analysis depth</li>
  <li>acs is the analysis time in seconds</li>
  <li>ce is the evaluation in centipawn</li>
  <li>Ae is the analyzing engine name</li>
  </ul>
  <h3>St. Petersburg 1895</h3>
  <pre><code>                   players  games   rate
  0  Pillsbury, Harry Nelson      5  0.600
  1        Steinitz, William      2  0.500
  2        Chigorin, Mikhail      1  0.500
  3          Lasker, Emanuel      4  0.375
  </code></pre>
  <h3>Budapest 1950 Candidates</h3>
  <p>The first candidates.</p>
  <pre><code>         players  games      rate
  0    Bronstein D      2  0.750000
  1        Kotov A      2  0.750000
  2      Smyslov V      3  0.666667
  3        Keres P      4  0.625000
  4  Boleslavsky I      3  0.500000
  5        Flohr S      1  0.500000
  6      Najdorf M      5  0.400000
  7    Stahlberg G      5  0.400000
  8        Szabo L      2  0.250000
  9   Lilienthal A      1  0.000000
  </code></pre>
  <h3>Zurich 1953</h3>
  <pre><code>          players  games      rate
  0        Geller E      3  0.666667
  1         Kotov A      3  0.666667
  2     Stahlberg A      3  0.666667
  3       Najdorf M      7  0.571429
  4         Keres P      7  0.500000
  5         Szabo L      6  0.500000
  6       Smyslov V      5  0.500000
  7     Bronstein D      3  0.500000
  8     Petrosian T      3  0.500000
  9      Taimanov M      3  0.500000
  10  Boleslavsky I      2  0.500000
  11     Averbakh Y      7  0.428571
  12         Euwe M      6  0.416667
  13     Gligoric S      4  0.375000
  14    Reshevsky S      2  0.250000
  </code></pre>
  <h3>Reggio Emilia 1991</h3>
  <pre><code>                   players  games      rate
  0   Beliavsky, Alexander G      4  0.750000
  1             Kamsky, Gata      5  0.500000
  2        Gurevich, Mikhail      4  0.500000
  3           Andersson, Ulf      3  0.500000
  4            Ehlvest, Jaan      2  0.500000
  5           Gulko, Boris F      2  0.500000
  6         Polugaevsky, Lev      2  0.500000
  7       Vaganian, Rafael A      2  0.500000
  8        Epishin, Vladimir      1  0.500000
  9          Karpov, Anatoly      1  0.500000
  10    Ljubojevic, Ljubomir      1  0.500000
  11           Ribli, Zoltan      1  0.500000
  12         Portisch, Lajos      3  0.333333
  13      Romanishin, Oleg M      1  0.000000
  </code></pre>
  <h3>Las Palmas 1996</h3>
  <pre><code>              players  games   rate
  0      Kasparov, Gary      5  0.600
  1     Karpov, Anatoly      4  0.500
  2  Anand, Viswanathan      2  0.500
  3   Kramnik, Vladimir      2  0.500
  4   Ivanchuk, Vassily      1  0.500
  5    Topalov, Veselin      4  0.375
  </code></pre>
  <p>Gary is superior got 60% in 5 games. He defeated Veselin.</p>
  <h3>Linares 1998</h3>
  <pre><code>              players  games      rate
  0   Ivanchuk, Vassily      6  0.583333
  1   Kramnik, Vladimir      5  0.500000
  2      Kasparov, Gary      4  0.500000
  3    Topalov, Veselin      3  0.500000
  4  Anand, Viswanathan      2  0.500000
  5      Shirov, Alexei      2  0.500000
  6      Svidler, Peter      2  0.250000
  </code></pre>
  <h3>Linares 1999</h3>
  <pre><code>              players  games      rate
  0      Kasparov, Gary      3  0.666667
  1         Leko, Peter      5  0.500000
  2   Ivanchuk, Vassily      4  0.500000
  3  Anand, Viswanathan      3  0.500000
  4   Kramnik, Vladimir      3  0.500000
  5      Adams, Michael      1  0.500000
  6      Svidler, Peter      1  0.500000
  7    Topalov, Veselin      4  0.375000
  </code></pre>
  <h3>Dortmund 2001</h3>
  <pre><code>        players  games      rate
  0     Kramnik,V      3  0.666667
  1     Topalov,V      2  0.500000
  2      Adams,Mi      1  0.500000
  3        Leko,P      1  0.500000
  4  Morozevich,A      1  0.500000
  5       Anand,V      2  0.250000
  </code></pre>
  <h3>Corus A, WijkaanZee 2008</h3>
  <pre><code>         players  games      rate
  0      Aronian,L      3  0.666667
  1      Kramnik,V      5  0.500000
  2   Mamedyarov,S      5  0.500000
  3      Polgar,Ju      5  0.500000
  4      Carlsen,M      4  0.500000
  5       Adams,Mi      3  0.500000
  6     Ivanchuk,V      3  0.500000
  7         Leko,P      3  0.500000
  8     Radjabov,T      3  0.500000
  9     Van Wely,L      3  0.500000
  10       Anand,V      2  0.500000
  11     Eljanov,P      2  0.500000
  12     Gelfand,B      2  0.500000
  13     Topalov,V      3  0.333333
  Average Rating: 2742
  </code></pre>
  <h3>Bilbao 2008</h3>
  <pre><code>      players  games      rate
  0   Aronian,L      2  0.750000
  1  Radjabov,T      4  0.500000
  2   Topalov,V      4  0.500000
  3   Carlsen,M      2  0.500000
  4  Ivanchuk,V      2  0.500000
  5     Anand,V      6  0.416667
  Average Rating: 2768
  </code></pre>
  <h3>Tal Memorial 2009</h3>
  <pre><code>        players  games   rate
  0     Carlsen,M      4  0.625
  1  Morozevich,A      6  0.500
  2     Aronian,L      5  0.500
  3     Kramnik,V      5  0.500
  4  Ponomariov,R      5  0.500
  5     Svidler,P      5  0.500
  6       Anand,V      4  0.500
  7     Gelfand,B      4  0.500
  8    Ivanchuk,V      3  0.500
  9        Leko,P      5  0.400
  </code></pre>
  <h2>Other tournament not in Jeff's list</h2>
  <h3>Palma de Mallorca Interzonal 1970</h3>
  <pre><code>               players  games      rate
  0          Reshevsky S      1  1.000000
  1             Larsen B      5  0.700000
  2              Minic D      4  0.625000
  3            Uhlmann W      4  0.625000
  4            Fischer R      5  0.600000
  5           Portisch L      7  0.500000
  6             Geller E      5  0.500000
  7              Panno O      5  0.500000
  8            Huebner R      4  0.500000
  9            Mecking H      4  0.500000
  10           Smyslov V      4  0.500000
  11           Naranja R      3  0.500000
  12           Suttles D      3  0.500000
  13           Addison W      2  0.500000
  14          Gligoric S      2  0.500000
  15       Polugaevsky L      2  0.500000
  16          Taimanov M      2  0.500000
  17              Hort V      1  0.500000
  18             Ivkov B      6  0.416667
  19             Filip M      4  0.375000
  20  Jimenez Zerquera E      4  0.375000
  21         Matulovic M      4  0.375000
  22           Ujtumen T      3  0.333333
  23         Rubinetti J      2  0.250000
  </code></pre>
  <h3>WijkaanZee 2010</h3>
  <pre><code>              players  games  rate
  0          Van Wely,L      1  1.00
  1            Shirov,A      2  0.75
  2             Short,N      5  0.50
  3              Leko,P      4  0.50
  4             Anand,V      3  0.50
  5           Kramnik,V      3  0.50
  6         Nakamura,Hi      3  0.50
  7           Carlsen,M      2  0.50
  8          Ivanchuk,V      2  0.50
  9     Karjakin,Sergey      2  0.50
  10  Dominguez Perez,L      1  0.50
  11          Caruana,F      5  0.40
  12         Tiviakov,S      1  0.00
  </code></pre>
  <h3>London 2013 Candidates</h3>
  <pre><code>      players  games      rate
  0  Ivanchuk,V      3  0.666667
  1   Kramnik,V      7  0.642857
  2   Carlsen,M      7  0.500000
  3   Aronian,L      5  0.500000
  4   Gelfand,B      5  0.500000
  5  Grischuk,A      5  0.400000
  6   Svidler,P      5  0.400000
  7  Radjabov,T      3  0.333333
  </code></pre>
  <h3>WijkaanZee 2013</h3>
  <pre><code>                 players  games      rate
  0         Aronian, Levon      5  0.600000
  1   Harikrishna, Pentala      8  0.562500
  2       Caruana, Fabiano      5  0.500000
  3              Wang, Hao      5  0.500000
  4        Carlsen, Magnus      4  0.500000
  5       Karjakin, Sergey      4  0.500000
  6           L'Ami, Erwin      4  0.500000
  7       Nakamura, Hikaru      3  0.500000
  8          Sokolov, Ivan      3  0.500000
  9         Van Wely, Loek      3  0.500000
  10            Hou, Yifan      2  0.500000
  11    Anand, Viswanathan      1  0.500000
  12           Giri, Anish      7  0.428571
  13           Leko, Peter      6  0.416667
  </code></pre>
  <h3>WijkaanZee 2015</h3>
  <pre><code>              players  games   rate
  0          Ding Liren      2  0.750
  1          Ivanchuk,V      5  0.600
  2          Radjabov,T      5  0.500
  3           Aronian,L      4  0.500
  4           Hou Yifan      4  0.500
  5            Saric,Iv      4  0.500
  6           Carlsen,M      3  0.500
  7                So,W      3  0.500
  8   Vachier Lagrave,M      3  0.500
  9           Caruana,F      2  0.500
  10             Giri,A      2  0.500
  11         Van Wely,L      2  0.500
  12        Wojtaszek,R      4  0.375
  13          Jobava,Ba      1  0.000
  Average Rating: 2746
  </code></pre>
  <h3>London 2016</h3>
  <pre><code>                   players  games  rate
  0               So, Wesley      5   0.5
  1        Kramnik, Vladimir      4   0.5
  2           Aronian, Levon      3   0.5
  3         Caruana, Fabiano      3   0.5
  4              Giri, Anish      3   0.5
  5  Vachier-Lagrave, Maxime      3   0.5
  6           Adams, Michael      2   0.5
  7       Anand, Viswanathan      2   0.5
  8         Nakamura, Hikaru      2   0.5
  9         Topalov, Veselin      1   0.5
  Average Rating: 2785
  </code></pre>
  <h3>Moscow 2016 Candidates</h3>
  <pre><code>           players  games  rate
  0        Aronian,L      6   0.5
  1           Giri,A      6   0.5
  2        Caruana,F      4   0.5
  3        Svidler,P      4   0.5
  4  Karjakin,Sergey      3   0.5
  5          Anand,V      2   0.5
  6        Topalov,V      2   0.5
  7      Nakamura,Hi      1   0.5
  </code></pre>
  <h3>WijkaanZee 2016</h3>
  <pre><code>            players  games      rate
  0         Carlsen,M      6  0.583333
  1          Navara,D      7  0.571429
  2              So,W      7  0.500000
  3          Adams,Mi      6  0.500000
  4            Giri,A      5  0.500000
  5        Ding Liren      4  0.500000
  6      Mamedyarov,S      4  0.500000
  7     Tomashevsky,E      4  0.500000
  8            Wei Yi      4  0.500000
  9   Karjakin,Sergey      3  0.500000
  10        Eljanov,P      2  0.500000
  11       Van Wely,L      1  0.500000
  12        Hou Yifan      8  0.437500
  13        Caruana,F      3  0.333333
  Average Rating: 2747
  </code></pre>
  <h3>WijkaanZee 2017</h3>
  <pre><code>                 players  games      rate
  0      Adhiban, Baskaran      3  0.666667
  1             So, Wesley      6  0.500000
  2        Carlsen, Magnus      5  0.500000
  3            Giri, Anish      5  0.500000
  4   Harikrishna, Pentala      5  0.500000
  5    Nepomniachtchi, Ian      4  0.500000
  6         Aronian, Levon      3  0.500000
  7      Andreikin, Dmitry      2  0.500000
  8         Eljanov, Pavel      2  0.500000
  9       Rapport, Richard      2  0.500000
  10               Wei, Yi      2  0.500000
  11      Karjakin, Sergey      1  0.500000
  12        Van Wely, Loek      1  0.500000
  13   Wojtaszek, Radoslaw      3  0.333333
  Average Rating: 2751
  </code></pre>
  <h3>Stavanger 2018</h3>
  <pre><code>             players  games  rate
  0          Aronian,L      5   0.5
  1            Anand,V      4   0.5
  2          Carlsen,M      4   0.5
  3    Karjakin,Sergey      3   0.5
  4        Nakamura,Hi      3   0.5
  5               So,W      3   0.5
  6          Caruana,F      2   0.5
  7       Mamedyarov,S      2   0.5
  8  Vachier Lagrave,M      2   0.5
  Average Rating: 2790
  </code></pre>
  <h3>Stavanger 2019</h3>
  <pre><code>             players  games      rate
  0          Caruana,F      3  0.666667
  1               So,W      7  0.571429
  2            Anand,V      6  0.500000
  3          Aronian,L      5  0.500000
  4          Carlsen,M      5  0.500000
  5         Ding Liren      5  0.500000
  6          Yu Yangyi      5  0.500000
  7       Mamedyarov,S      3  0.500000
  8  Vachier Lagrave,M      7  0.428571
  9         Grischuk,A      4  0.375000
  Average Rating: 2784
  </code></pre>
  <h3>Saint Louis 2019</h3>
  <pre><code>              players  games   rate
  0   Dominguez Perez,L      4  0.625
  1                So,W      4  0.625
  2           Caruana,F      5  0.600
  3           Akobian,V      6  0.500
  4         Shankland,S      6  0.500
  5         Lenderman,A      5  0.500
  6            Robson,R      4  0.500
  7       Xiong,Jeffery      4  0.500
  8       Liang,Awonder      3  0.500
  9         Nakamura,Hi      2  0.500
  10      Sevian,Samuel      4  0.375
  11           Gareev,T      5  0.300
  Average Rating: 2682
  </code></pre>
  <h3>Shamkir 2019</h3>
  <pre><code>           players  games      rate
  0         Navara,D      3  0.666667
  1        Carlsen,M      5  0.600000
  2       Radjabov,T      9  0.500000
  3       Ding Liren      6  0.500000
  4       Grischuk,A      3  0.500000
  5  Karjakin,Sergey      3  0.500000
  6     Mamedyarov,S      3  0.500000
  7           Giri,A      2  0.500000
  8          Anand,V      3  0.333333
  9        Topalov,V      3  0.333333
  Average Rating: 2778
  </code></pre>
  <h3>WijkaanZee 2020</h3>
  <pre><code>               players  games      rate
  0        Xiong,Jeffery      3  0.666667
  1     Firouzja,Alireza      4  0.625000
  2               Duda,J      5  0.600000
  3   Van Foreest,Jorden      5  0.600000
  4               Giri,A      8  0.500000
  5                 So,W      8  0.500000
  6            Carlsen,M      6  0.500000
  7            Caruana,F      4  0.500000
  8           Vitiugov,N      3  0.500000
  9              Anand,V      2  0.500000
  10        Dubov,Daniil      1  0.500000
  11          Artemiev,V      4  0.375000
  12           Yu Yangyi      6  0.333333
  13          Kovalev,Vl      3  0.333333
  Average Rating: 2740
  </code></pre>
  <h3>Stavanger 2020</h3>
  <pre><code>            players  games      rate
  0  Firouzja,Alireza      7  0.642857
  1         Carlsen,M      4  0.625000
  2         Caruana,F      3  0.500000
  3         Aronian,L      7  0.428571
  4            Duda,J      4  0.375000
  5            Tari,A      3  0.333333
  Average Rating: 2762
  </code></pre>
  <h3>WijkaanZee 2021</h3>
  <pre><code>               players  games      rate
  0     Firouzja,Alireza      3  0.666667
  1         Grandelius,N      3  0.666667
  2    Vachier Lagrave,M      5  0.600000
  3   Van Foreest,Jorden      6  0.583333
  4            Caruana,F      8  0.500000
  5     Anton Guijarro,D      7  0.500000
  6            Carlsen,M      7  0.500000
  7          Wojtaszek,R      6  0.500000
  8        Harikrishna,P      5  0.500000
  9               Tari,A      4  0.500000
  10     Esipenko,Andrey      3  0.500000
  11              Giri,A      7  0.428571
  12              Duda,J      5  0.400000
  13     Donchenko,Alexa      7  0.357143
  Average Rating: 2724
  </code></pre>
  <h3>Stavanger 2021</h3>
  <pre><code>            players  games      rate
  0         Carlsen,M      3  0.666667
  1   Karjakin,Sergey      4  0.625000
  2  Firouzja,Alireza      2  0.500000
  3  Nepomniachtchi,I      5  0.400000
  4         Rapport,R      4  0.375000
  Average Rating: 2760
  </code></pre>
  <h3>WijkaanZee 2022</h3>
  <pre><code>                    players  games      rate
  0    Mamedyarov, Shakhriyar      2  0.750000
  1          Karjakin, Sergey      5  0.700000
  2               Giri, Anish      3  0.666667
  3          Rapport, Richard      5  0.600000
  4           Carlsen, Magnus      4  0.500000
  5          Caruana, Fabiano      4  0.500000
  6   Vidit, Santosh Gujrathi      4  0.500000
  7             Dubov, Daniil      3  0.500000
  8          Grandelius, Nils      3  0.500000
  9          Esipenko, Andrey      2  0.500000
  10      Duda, Jan-Krzysztof      4  0.375000
  11           Shankland, Sam      5  0.300000
  12        Praggnanandhaa, R      2  0.250000
  13      Van Foreest, Jorden      2  0.250000
  Average Rating: 2736
  </code></pre>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2022-04-02T14:03:05.183Z
Answers.LastActivityDate: 2022-04-03T14:10:07.000Z
Answers.LastEditDate: 2022-04-03T14:10:07.000Z
Answers.UserDisplayName: ferdy
Body: <p>There are famous players who are <em>called</em> endgame experts (&quot;opening expert&quot; IMHO is less used), e.g. Rubinstein. Now obviously, to be a GM, you have to know a bit of all game phases, and a mere &quot;calling&quot; is judgmental and not suited for CSE. One has to back it up.</p>
  <p>Question: Do (various possible) &quot;hard&quot; statistical measurements agree with the &quot;soft&quot; assessments found in chess press and literature? (An obvious &quot;soft&quot; recent example would be Carlsen, reknowned endgame torturer.)</p>
  <p>My suggested statistical approach (other are possible, see comments, like average game length or centipawn loss): Arbitrarily split a game into the parts &lt;20 moves (&quot;opening&quot;), &gt;40 (&quot;endgame&quot;) and &quot;middlegame&quot;. (This is not true - see Berlin Wall - but should suffice for the crude approach.) Assume the percentages of wins by an average player scored in these phases are o+m+e=100%. Now I expect o to be rather small in GM play (when does a novelty totally pwn the opponent), and thus let e/(o+m) be a proxy for the endgame strength of a player. Thus, can anybody, for starters (I would do it myself if I had the tools), compute these numbers a) for a global average set, b) for Carlsen?</p>
  <p>Any metholodogy used here is open to criticism, e.g. the longer the game, the higher the probability the weaker player cracks.</p>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2021-10-13T07:59:48.017Z
Comments.Text: There are players called "opening experts". Geller, Fischer, Kasparov or Giri  were/are feared for their opening preparations even more than their fellow grandmasters.
Comments.UserDisplayName: Evargalo
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2023-01-16T09:13:29.773Z
Comments.Text: If "hard" statistical measures are things like accuracy scores then the "soft" may be more reliable
Comments.UserDisplayName: David
Tags: <endgame><statistics><style>
Title: Opening and endgame experts in chess
ThreadText: # Opening and endgame experts in chess
  
  (Asked by: username_0 on 2021-10-13)
  
  There are famous players who are *called* endgame experts ("opening expert" IMHO is less used), e.g. Rubinstein. Now obviously, to be a GM, you have to know a bit of all game phases, and a mere "calling" is judgmental and not suited for CSE. One has to back it up.
  
  Question: Do (various possible) "hard" statistical measurements agree with the "soft" assessments found in chess press and literature? (An obvious "soft" recent example would be Carlsen, reknowned endgame torturer.)
  
  My suggested statistical approach (other are possible, see comments, like average game length or centipawn loss): Arbitrarily split a game into the parts <20 moves ("opening"), >40 ("endgame") and "middlegame". (This is not true - see Berlin Wall - but should suffice for the crude approach.) Assume the percentages of wins by an average player scored in these phases are o+m+e=100%. Now I expect o to be rather small in GM play (when does a novelty totally pwn the opponent), and thus let e/(o+m) be a proxy for the endgame strength of a player. Thus, can anybody, for starters (I would do it myself if I had the tools), compute these numbers a) for a global average set, b) for Carlsen?
  
  Any metholodogy used here is open to criticism, e.g. the longer the game, the higher the probability the weaker player cracks.
  
  **Tags:** endgame, statistics, style
  
  > **Comments:**
  > **username_1**: There are players called "opening experts". Geller, Fischer, Kasparov or Giri  were/are feared for their opening preparations even more than their fellow grandmasters.  
  > **username_2**: If "hard" statistical measures are things like accuracy scores then the "soft" may be more reliable  
  
  ---
  
  ## 1 answers
  
  ### Answer by username_3 on 2022-04-02. Score: 1
  
  Did an experiment finding a top player playing against a top player on games that reaches an ending. I took some [top tournaments](https://en.chessbase.com/post/what-was-the-strongest-tournament-of-all-time-) according to Jeff Jonas and analyze those games.
  
  I define an ending position as those positions where the total piece (excluding pawns and kings) values are 2 queens or less. Q=10, R=5, B=N=3. Example for KQKQ, piecevalue = 20 is an ending. KRRKRR, piecevalue = 20 is also an ending. So the condition is: if piecevalue <= 20 it is an ending.
  
  For each tournament check all games, if a piece value of the position reaches 20 or less, analyze it with stockfish 14.1 with 2 threads for 30s. If this position is not winning or losing (score >= -50cp and score <= 50cp), then consider it in the calculation.
  
  ### AVRO 1938 Result
  
  ```
                      players  games   rate
  0              Fine, Reuben      1  1.000
  1  Reshevsky, Samuel Herman      4  0.500
  2     Capablanca, Jose Raul      3  0.500
  3                 Euwe, Max      3  0.500
  4        Botvinnik, Mikhail      2  0.500
  5               Keres, Paul      1  0.500
  6       Alekhine, Alexander      4  0.375
  
  ```
  
  Fine had 1 game and won it. The others got 50% and Alekhine got 37.5% from 4 games.
  
  The game where Fine won from equal ending position.
  
  ```
  [Event "AVRO"]
  [Site "Holland"]
  [Date "1938.??.??"]
  [Round "?"]
  [White "Alekhine, Alexander"]
  [Black "Fine, Reuben"]
  [Result "0-1"]
  [BlackElo ""]
  [ECO "C83"]
  [WhiteElo ""]
  
  1. e4 e5 2. Nf3 Nc6 3. Bb5 a6 4. Ba4 Nf6 5. O-O Nxe4 6. d4 b5 7. Bb3 d5 8. dxe5 Be6 9. c3 Be7 10. Nd4 Nxe5 11. f3 Nf6 12. Qe2 Nc4 13. Bc2 Qd7 14. b3 Nb6 15. Re1 O-O 16. Bg5 Rfe8 17. Nd2 Nh5 18. Bxe7 Rxe7 19. Qe5 g6 20. g4 Ng7 21. b4 Rae8 22. Qf4 Na4 23. Re3 Qd6 24. Qxd6 cxd6 25. Rae1 Rc7 26. Nb1 Bd7 27. Rxe8+ Bxe8 28. Bb3 Nb6 29. Kf2 Kf8 30. Rd1 Ne6 31. Ne2 Bc6 32. Na3 Ke7 33. Nc2 Nc4 34. Ne3 h6 35. h4 Nb6 36. Bxd5 Bxd5 37. Nxd5+ Nxd5 38. Rxd5 Rc4 39. Ke3 Kd7 40. f4 Kc6 41. Rd1 Kd7 42. Rf1 Ke7 43. Kd3 g5 44. hxg5 hxg5 45. f5 Nf8 46. f6+ Kd7 47. a4 Ng6 48. axb5 Ne5+ 49. Kd2 axb5 50. Nd4 Nxg4 51. Nxb5 Ne5 52. Nd4 g4 53. Kc2 Rc8 54. Nf5 Rg8 55. Ng3 Rh8 56. Rf2 Nf3 57. Re2 Rh3 58. Nf5 Ne5 59. b5 Rf3 60. Nd4 Rxf6 61. b6 Kc8 62. Nb5 g3 63. Kb3 Rg6 64. Rg2 f5 65. Ra2 Kb7 66. Rd2 f4 67. Nxd6+ Rxd6 68. Rxd6 g2 0-1
  
  ```
  
  The ending position with stockfish 14.1 analysis:
  
  ```
  8/2r1kp2/p2pn1pp/1p1n4/1P4PP/2P2P2/P3NK2/3R4 w - - 0 38 acd 45; acs 30; ce 0; Ae Stockfish 14.1;
  
  ```
  
  * acd is the analysis depth
  * acs is the analysis time in seconds
  * ce is the evaluation in centipawn
  * Ae is the analyzing engine name
  
  ### St. Petersburg 1895
  
  ```
                     players  games   rate
  0  Pillsbury, Harry Nelson      5  0.600
  1        Steinitz, William      2  0.500
  2        Chigorin, Mikhail      1  0.500
  3          Lasker, Emanuel      4  0.375
  
  ```
  
  ### Budapest 1950 Candidates
  
  The first candidates.
  
  ```
           players  games      rate
  0    Bronstein D      2  0.750000
  1        Kotov A      2  0.750000
  2      Smyslov V      3  0.666667
  3        Keres P      4  0.625000
  4  Boleslavsky I      3  0.500000
  5        Flohr S      1  0.500000
  6      Najdorf M      5  0.400000
  7    Stahlberg G      5  0.400000
  8        Szabo L      2  0.250000
  9   Lilienthal A      1  0.000000
  
  ```
  
  ### Zurich 1953
  
  ```
            players  games      rate
  0        Geller E      3  0.666667
  1         Kotov A      3  0.666667
  2     Stahlberg A      3  0.666667
  3       Najdorf M      7  0.571429
  4         Keres P      7  0.500000
  5         Szabo L      6  0.500000
  6       Smyslov V      5  0.500000
  7     Bronstein D      3  0.500000
  8     Petrosian T      3  0.500000
  9      Taimanov M      3  0.500000
  10  Boleslavsky I      2  0.500000
  11     Averbakh Y      7  0.428571
  12         Euwe M      6  0.416667
  13     Gligoric S      4  0.375000
  14    Reshevsky S      2  0.250000
  
  ```
  
  ### Reggio Emilia 1991
  
  ```
                     players  games      rate
  0   Beliavsky, Alexander G      4  0.750000
  1             Kamsky, Gata      5  0.500000
  2        Gurevich, Mikhail      4  0.500000
  3           Andersson, Ulf      3  0.500000
  4            Ehlvest, Jaan      2  0.500000
  5           Gulko, Boris F      2  0.500000
  6         Polugaevsky, Lev      2  0.500000
  7       Vaganian, Rafael A      2  0.500000
  8        Epishin, Vladimir      1  0.500000
  9          Karpov, Anatoly      1  0.500000
  10    Ljubojevic, Ljubomir      1  0.500000
  11           Ribli, Zoltan      1  0.500000
  12         Portisch, Lajos      3  0.333333
  13      Romanishin, Oleg M      1  0.000000
  
  ```
  
  ### Las Palmas 1996
  
  ```
                players  games   rate
  0      Kasparov, Gary      5  0.600
  1     Karpov, Anatoly      4  0.500
  2  Anand, Viswanathan      2  0.500
  3   Kramnik, Vladimir      2  0.500
  4   Ivanchuk, Vassily      1  0.500
  5    Topalov, Veselin      4  0.375
  
  ```
  
  Gary is superior got 60% in 5 games. He defeated Veselin.
  
  ### Linares 1998
  
  ```
                players  games      rate
  0   Ivanchuk, Vassily      6  0.583333
  1   Kramnik, Vladimir      5  0.500000
  2      Kasparov, Gary      4  0.500000
  3    Topalov, Veselin      3  0.500000
  4  Anand, Viswanathan      2  0.500000
  5      Shirov, Alexei      2  0.500000
  6      Svidler, Peter      2  0.250000
  
  ```
  
  ### Linares 1999
  
  ```
                players  games      rate
  0      Kasparov, Gary      3  0.666667
  1         Leko, Peter      5  0.500000
  2   Ivanchuk, Vassily      4  0.500000
  3  Anand, Viswanathan      3  0.500000
  4   Kramnik, Vladimir      3  0.500000
  5      Adams, Michael      1  0.500000
  6      Svidler, Peter      1  0.500000
  7    Topalov, Veselin      4  0.375000
  
  ```
  
  ### Dortmund 2001
  
  ```
          players  games      rate
  0     Kramnik,V      3  0.666667
  1     Topalov,V      2  0.500000
  2      Adams,Mi      1  0.500000
  3        Leko,P      1  0.500000
  4  Morozevich,A      1  0.500000
  5       Anand,V      2  0.250000
  
  ```
  
  ### Corus A, WijkaanZee 2008
  
  ```
           players  games      rate
  0      Aronian,L      3  0.666667
  1      Kramnik,V      5  0.500000
  2   Mamedyarov,S      5  0.500000
  3      Polgar,Ju      5  0.500000
  4      Carlsen,M      4  0.500000
  5       Adams,Mi      3  0.500000
  6     Ivanchuk,V      3  0.500000
  7         Leko,P      3  0.500000
  8     Radjabov,T      3  0.500000
  9     Van Wely,L      3  0.500000
  10       Anand,V      2  0.500000
  11     Eljanov,P      2  0.500000
  12     Gelfand,B      2  0.500000
  13     Topalov,V      3  0.333333
  Average Rating: 2742
  
  ```
  
  ### Bilbao 2008
  
  ```
        players  games      rate
  0   Aronian,L      2  0.750000
  1  Radjabov,T      4  0.500000
  2   Topalov,V      4  0.500000
  3   Carlsen,M      2  0.500000
  4  Ivanchuk,V      2  0.500000
  5     Anand,V      6  0.416667
  Average Rating: 2768
  
  ```
  
  ### Tal Memorial 2009
  
  ```
          players  games   rate
  0     Carlsen,M      4  0.625
  1  Morozevich,A      6  0.500
  2     Aronian,L      5  0.500
  3     Kramnik,V      5  0.500
  4  Ponomariov,R      5  0.500
  5     Svidler,P      5  0.500
  6       Anand,V      4  0.500
  7     Gelfand,B      4  0.500
  8    Ivanchuk,V      3  0.500
  9        Leko,P      5  0.400
  
  ```
  
  ## Other tournament not in Jeff's list
  
  ### Palma de Mallorca Interzonal 1970
  
  ```
                 players  games      rate
  0          Reshevsky S      1  1.000000
  1             Larsen B      5  0.700000
  2              Minic D      4  0.625000
  3            Uhlmann W      4  0.625000
  4            Fischer R      5  0.600000
  5           Portisch L      7  0.500000
  6             Geller E      5  0.500000
  7              Panno O      5  0.500000
  8            Huebner R      4  0.500000
  9            Mecking H      4  0.500000
  10           Smyslov V      4  0.500000
  11           Naranja R      3  0.500000
  12           Suttles D      3  0.500000
  13           Addison W      2  0.500000
  14          Gligoric S      2  0.500000
  15       Polugaevsky L      2  0.500000
  16          Taimanov M      2  0.500000
  17              Hort V      1  0.500000
  18             Ivkov B      6  0.416667
  19             Filip M      4  0.375000
  20  Jimenez Zerquera E      4  0.375000
  21         Matulovic M      4  0.375000
  22           Ujtumen T      3  0.333333
  23         Rubinetti J      2  0.250000
  
  ```
  
  ### WijkaanZee 2010
  
  ```
                players  games  rate
  0          Van Wely,L      1  1.00
  1            Shirov,A      2  0.75
  2             Short,N      5  0.50
  3              Leko,P      4  0.50
  4             Anand,V      3  0.50
  5           Kramnik,V      3  0.50
  6         Nakamura,Hi      3  0.50
  7           Carlsen,M      2  0.50
  8          Ivanchuk,V      2  0.50
  9     Karjakin,Sergey      2  0.50
  10  Dominguez Perez,L      1  0.50
  11          Caruana,F      5  0.40
  12         Tiviakov,S      1  0.00
  
  ```
  
  ### London 2013 Candidates
  
  ```
        players  games      rate
  0  Ivanchuk,V      3  0.666667
  1   Kramnik,V      7  0.642857
  2   Carlsen,M      7  0.500000
  3   Aronian,L      5  0.500000
  4   Gelfand,B      5  0.500000
  5  Grischuk,A      5  0.400000
  6   Svidler,P      5  0.400000
  7  Radjabov,T      3  0.333333
  
  ```
  
  ### WijkaanZee 2013
  
  ```
                   players  games      rate
  0         Aronian, Levon      5  0.600000
  1   Harikrishna, Pentala      8  0.562500
  2       Caruana, Fabiano      5  0.500000
  3              Wang, Hao      5  0.500000
  4        Carlsen, Magnus      4  0.500000
  5       Karjakin, Sergey      4  0.500000
  6           L'Ami, Erwin      4  0.500000
  7       Nakamura, Hikaru      3  0.500000
  8          Sokolov, Ivan      3  0.500000
  9         Van Wely, Loek      3  0.500000
  10            Hou, Yifan      2  0.500000
  11    Anand, Viswanathan      1  0.500000
  12           Giri, Anish      7  0.428571
  13           Leko, Peter      6  0.416667
  
  ```
  
  ### WijkaanZee 2015
  
  ```
                players  games   rate
  0          Ding Liren      2  0.750
  1          Ivanchuk,V      5  0.600
  2          Radjabov,T      5  0.500
  3           Aronian,L      4  0.500
  4           Hou Yifan      4  0.500
  5            Saric,Iv      4  0.500
  6           Carlsen,M      3  0.500
  7                So,W      3  0.500
  8   Vachier Lagrave,M      3  0.500
  9           Caruana,F      2  0.500
  10             Giri,A      2  0.500
  11         Van Wely,L      2  0.500
  12        Wojtaszek,R      4  0.375
  13          Jobava,Ba      1  0.000
  Average Rating: 2746
  
  ```
  
  ### London 2016
  
  ```
                     players  games  rate
  0               So, Wesley      5   0.5
  1        Kramnik, Vladimir      4   0.5
  2           Aronian, Levon      3   0.5
  3         Caruana, Fabiano      3   0.5
  4              Giri, Anish      3   0.5
  5  Vachier-Lagrave, Maxime      3   0.5
  6           Adams, Michael      2   0.5
  7       Anand, Viswanathan      2   0.5
  8         Nakamura, Hikaru      2   0.5
  9         Topalov, Veselin      1   0.5
  Average Rating: 2785
  
  ```
  
  ### Moscow 2016 Candidates
  
  ```
             players  games  rate
  0        Aronian,L      6   0.5
  1           Giri,A      6   0.5
  2        Caruana,F      4   0.5
  3        Svidler,P      4   0.5
  4  Karjakin,Sergey      3   0.5
  5          Anand,V      2   0.5
  6        Topalov,V      2   0.5
  7      Nakamura,Hi      1   0.5
  
  ```
  
  ### WijkaanZee 2016
  
  ```
              players  games      rate
  0         Carlsen,M      6  0.583333
  1          Navara,D      7  0.571429
  2              So,W      7  0.500000
  3          Adams,Mi      6  0.500000
  4            Giri,A      5  0.500000
  5        Ding Liren      4  0.500000
  6      Mamedyarov,S      4  0.500000
  7     Tomashevsky,E      4  0.500000
  8            Wei Yi      4  0.500000
  9   Karjakin,Sergey      3  0.500000
  10        Eljanov,P      2  0.500000
  11       Van Wely,L      1  0.500000
  12        Hou Yifan      8  0.437500
  13        Caruana,F      3  0.333333
  Average Rating: 2747
  
  ```
  
  ### WijkaanZee 2017
  
  ```
                   players  games      rate
  0      Adhiban, Baskaran      3  0.666667
  1             So, Wesley      6  0.500000
  2        Carlsen, Magnus      5  0.500000
  3            Giri, Anish      5  0.500000
  4   Harikrishna, Pentala      5  0.500000
  5    Nepomniachtchi, Ian      4  0.500000
  6         Aronian, Levon      3  0.500000
  7      Andreikin, Dmitry      2  0.500000
  8         Eljanov, Pavel      2  0.500000
  9       Rapport, Richard      2  0.500000
  10               Wei, Yi      2  0.500000
  11      Karjakin, Sergey      1  0.500000
  12        Van Wely, Loek      1  0.500000
  13   Wojtaszek, Radoslaw      3  0.333333
  Average Rating: 2751
  
  ```
  
  ### Stavanger 2018
  
  ```
               players  games  rate
  0          Aronian,L      5   0.5
  1            Anand,V      4   0.5
  2          Carlsen,M      4   0.5
  3    Karjakin,Sergey      3   0.5
  4        Nakamura,Hi      3   0.5
  5               So,W      3   0.5
  6          Caruana,F      2   0.5
  7       Mamedyarov,S      2   0.5
  8  Vachier Lagrave,M      2   0.5
  Average Rating: 2790
  
  ```
  
  ### Stavanger 2019
  
  ```
               players  games      rate
  0          Caruana,F      3  0.666667
  1               So,W      7  0.571429
  2            Anand,V      6  0.500000
  3          Aronian,L      5  0.500000
  4          Carlsen,M      5  0.500000
  5         Ding Liren      5  0.500000
  6          Yu Yangyi      5  0.500000
  7       Mamedyarov,S      3  0.500000
  8  Vachier Lagrave,M      7  0.428571
  9         Grischuk,A      4  0.375000
  Average Rating: 2784
  
  ```
  
  ### Saint Louis 2019
  
  ```
                players  games   rate
  0   Dominguez Perez,L      4  0.625
  1                So,W      4  0.625
  2           Caruana,F      5  0.600
  3           Akobian,V      6  0.500
  4         Shankland,S      6  0.500
  5         Lenderman,A      5  0.500
  6            Robson,R      4  0.500
  7       Xiong,Jeffery      4  0.500
  8       Liang,Awonder      3  0.500
  9         Nakamura,Hi      2  0.500
  10      Sevian,Samuel      4  0.375
  11           Gareev,T      5  0.300
  Average Rating: 2682
  
  ```
  
  ### Shamkir 2019
  
  ```
             players  games      rate
  0         Navara,D      3  0.666667
  1        Carlsen,M      5  0.600000
  2       Radjabov,T      9  0.500000
  3       Ding Liren      6  0.500000
  4       Grischuk,A      3  0.500000
  5  Karjakin,Sergey      3  0.500000
  6     Mamedyarov,S      3  0.500000
  7           Giri,A      2  0.500000
  8          Anand,V      3  0.333333
  9        Topalov,V      3  0.333333
  Average Rating: 2778
  
  ```
  
  ### WijkaanZee 2020
  
  ```
                 players  games      rate
  0        Xiong,Jeffery      3  0.666667
  1     Firouzja,Alireza      4  0.625000
  2               Duda,J      5  0.600000
  3   Van Foreest,Jorden      5  0.600000
  4               Giri,A      8  0.500000
  5                 So,W      8  0.500000
  6            Carlsen,M      6  0.500000
  7            Caruana,F      4  0.500000
  8           Vitiugov,N      3  0.500000
  9              Anand,V      2  0.500000
  10        Dubov,Daniil      1  0.500000
  11          Artemiev,V      4  0.375000
  12           Yu Yangyi      6  0.333333
  13          Kovalev,Vl      3  0.333333
  Average Rating: 2740
  
  ```
  
  ### Stavanger 2020
  
  ```
              players  games      rate
  0  Firouzja,Alireza      7  0.642857
  1         Carlsen,M      4  0.625000
  2         Caruana,F      3  0.500000
  3         Aronian,L      7  0.428571
  4            Duda,J      4  0.375000
  5            Tari,A      3  0.333333
  Average Rating: 2762
  
  ```
  
  ### WijkaanZee 2021
  
  ```
                 players  games      rate
  0     Firouzja,Alireza      3  0.666667
  1         Grandelius,N      3  0.666667
  2    Vachier Lagrave,M      5  0.600000
  3   Van Foreest,Jorden      6  0.583333
  4            Caruana,F      8  0.500000
  5     Anton Guijarro,D      7  0.500000
  6            Carlsen,M      7  0.500000
  7          Wojtaszek,R      6  0.500000
  8        Harikrishna,P      5  0.500000
  9               Tari,A      4  0.500000
  10     Esipenko,Andrey      3  0.500000
  11              Giri,A      7  0.428571
  12              Duda,J      5  0.400000
  13     Donchenko,Alexa      7  0.357143
  Average Rating: 2724
  
  ```
  
  ### Stavanger 2021
  
  ```
              players  games      rate
  0         Carlsen,M      3  0.666667
  1   Karjakin,Sergey      4  0.625000
  2  Firouzja,Alireza      2  0.500000
  3  Nepomniachtchi,I      5  0.400000
  4         Rapport,R      4  0.375000
  Average Rating: 2760
  
  ```
  
  ### WijkaanZee 2022
  
  ```
                      players  games      rate
  0    Mamedyarov, Shakhriyar      2  0.750000
  1          Karjakin, Sergey      5  0.700000
  2               Giri, Anish      3  0.666667
  3          Rapport, Richard      5  0.600000
  4           Carlsen, Magnus      4  0.500000
  5          Caruana, Fabiano      4  0.500000
  6   Vidit, Santosh Gujrathi      4  0.500000
  7             Dubov, Daniil      3  0.500000
  8          Grandelius, Nils      3  0.500000
  9          Esipenko, Andrey      2  0.500000
  10      Duda, Jan-Krzysztof      4  0.375000
  11           Shankland, Sam      5  0.300000
  12        Praggnanandhaa, R      2  0.250000
  13      Van Foreest, Jorden      2  0.250000
  Average Rating: 2736
  
  ```
  
  
  ---
  
  