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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.

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  • 3
    There are players called "opening experts". Geller, Fischer, Kasparov or Giri were/are feared for their opening preparations even more than their fellow grandmasters.
    – Evargalo
    Oct 13, 2021 at 7:59
  • If "hard" statistical measures are things like accuracy scores then the "soft" may be more reliable
    – David
    Jan 16 at 9:13

1 Answer 1

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1

Did an experiment finding a top player playing against a top player on games that reaches an ending. I took some top tournaments 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
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