Answers.Body: <p>I'm posting a sample answer to my question to give others an idea about what I'm thinking about.  </p>
  
  <p>First, you have to define what you mean by best. For example, does best mean you are the most dominant player for your era? Or does it mean that the quality of your player is superior to all other players. And if quality is what you mean, then how do you define quality?</p>
  
  <p>Paul Morphy was probably the most dominant player. For example, when he was 12 years old he defeated a top ten player (Lowenthal) in a match 3-0. According to Edo and chessmetrics he was probably already one of the best players in the world at the age of 12! At the age of 21, he played against a simultaneous against 5 top ten players (Bird, Barnes, Boden, De Reviere, and Lowenthal) and scored 3-2. </p>
  
  <p>However, most would argue that dominance is a poor indicator of who is best. After all, Morphy has been described as the first modern chess player. His competition was weak compared with subsequent champions. </p>
  
  <p>Another definition that has been used is quality of play. However, this definition also has a lot of problems. In the 1900 hundreds , a number individuals argued that Steinitz or Lasker were the best players of all time arguing that their knowledge of opening and modern theory would make them superior to players from the past. However, Louis Paulsen made some very clever arguments against this hypothesis. He argued that Morphy (who had a photographic memory and memorized the Louisana bar code by the age of 19) if brought back to life would learn openings and modern theory within a year and be able to compete successfully against modern chess players. </p>
  
  <p>The mathematician Kenneth Regan argues that modern chess players who have access to chess computers and modern training methods play more like computers than players of the past. That’s no surprise because they were trained by computers but does that mean that modern players are really better? This begs the question what would Fischer or Capablanca do if they had access to modern computers?   The problem with computer comparisons is they don’t take the historical factor into account.</p>
  
  <p>You need an error weighting system that doesn’t just calculate the percentage of errors per 100 moves (which is basically what Regan and Guid and Bratko did ). Instead, you need to calculate the difference between your error rate and your opponents error rate. After all, chess is about committing fewer errors than your opponent. Putting pressure on your opponent to induce more errors is considered a good quality.
  If innovation leads to dominance within a specific chess era over time and it becomes increasingly difficult to innovate over time as the strength of the competition increases you can’t measure true dominance by just looking at the match records of the top 30 players. That is, it’s a lot harder for Magnus Carlsen to dominate his opponents than it was for past champions.
  Can the problem of increasing quality of play overtime be corrected by looking at back ratings? I prefer the Edo back rating system <a href="http://www.edochess.ca/" rel="nofollow noreferrer">http://www.edochess.ca/</a> because the statistical assumptions are better. According to Chessmetrics, Zukertort, Steinitz, Tarrasch, Lasker, Pillsbury, Maroczy, Marshall, Janowsky, Chigorin, Schlechter, Blackburne, Duras, Teichmann, Neumann, Vidmar, Gunsberg, Rubinstein and Burn were better than Morphy.   That doesn’t ring true for me.
  If you look at Edo or Chessmetrics back ratings it’s easy to see that the magnitude of the difference between the top players’ ratings has been decreasing over time. So I believe an Edo type statistical model that takes into consideration the difficulty to dominate over time would be a better approach than what has been tried previously. 
  So my dream analysis is that you use Edo ratings based on a database that only includes the top 20 or 30 players from each five year period. After you complete this analysis you reweight your results by a dominance factor. That is, more recent players get a bonus factor that is calculated by estimating the trajectory of difficulty of dominating over time (the decrease in rating disparities between top 30 players over time). Next, you would validate this analysis by comparing players percentage of chess computer calculated blunders their opponents make minus their own blunders. If this invalidates the above, then you need to reweight according to the computer error checking analysis if it shows there is a tendency for more recent top players to play more accurately even after my dominance factor is taken into consideration. 
  My guess based on my eyeballing this, is that Kasparov would do very well. But that’s just a guess.</p>
  
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Answers.Text: I think there's a gradual rise in ability over time across players of all classes simply due to the availability of books/DVDs/Computers. John Nunn did a serious analysis of how good (bad?) old masters were and his conclusion was that their play was pretty weak by modern GM standards. I can't remember where it was published though. Chessbase maybe? If you dropped a modern 2600 GM into the 19th century he'd be the strongest player in the world by a mile.
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Answers.UserDisplayName: ToddM
Answers.Body: <p>This is an endless discussion . The best way to predict the player is based upon whose games you would like to see again &amp; again . The games from whom you learn the most . The style of players that you become fascinated with , I mean you would like to copy . </p>
  
  <p>From the above what I mean is let's say I want to play Sicilian as Black then Fischer &amp; Kasparov have the best Games.</p>
  
  <p>I want to make my Endgame strong then Magnus I should choose .</p>
  
  <p>I like Tactics &amp; imaginative Sacrifices then Mikhail 
  Tal , Shirov , Speilmann are my Idols .</p>
  
  <p>Positional play then Botvinnik , Karpov etc.</p>
  
  <p>From a popular perspective my vote goes to Bobby Fischer and Kasparov . Now from a Country perspective Russsia may deny Fischer &amp; Americans may not like Kasparov . Indian security may say Anand .</p>
  
  <p>So everyone has a different opinion .</p>
  
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Answers.Body: <p>The ++<strong>only and only way</strong>++ objectively determine the best player is to make the candidates play games against each other.</p>
  
  <p>There is no way to perfectly answer your question, because:</p>
  
  <ul>
  <li>Anyone who comes up with a new paper will argue the statistical assumptions in the paper are more solid and reliable than anything else</li>
  <li>There will be always someone arguing how the best player should be judged. For example, Kasparov lost a match to Kramnik in a world-championship match, but... Kasparov was still considered a better player until he retired.</li>
  </ul>
  
  <p>There're lots of ways to determine the "best" player without making them to play chess:</p>
  
  <ul>
  <li>Use the change in principal variation across depth (the paper cited in the question)</li>
  <li>Use a computer algorithm to simulate the player</li>
  <li>Estimate the strength by comparing accuracy to a computer</li>
  <li>Use weighted average of past performance (Chessmetrics)</li>
  </ul>
  
  <p>There is no perfect method.</p>
  
  <ul>
  <li>Change in principal variation assumes the change is a good indicator.</li>
  <li>Accuracy may not be reliable. In chess, the winner only needs to play better chess than the opponent.</li>
  <li>Weighted average can't be used for comparing players from different eras.</li>
  </ul>
  
  <p>I should share my personal opinion.</p>
  
  <p><strong>Best by dominance</strong></p>
  
  <p>Someone in other answer suggests Paul Morphy. But... Philidor was able to beat everybody else. He would even win with a pawn odd. I'd argue Philidor is the best player ever in terms of dominance.</p>
  
  <p><strong>Best by playing strength</strong></p>
  
  <p>Hard to believe anyone before the computer era can play chess better than modern elite players. Thus, we should only consider modern players. Carlsen and Kasparov are clearly the best players.</p>
  
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Answers.UserDisplayName: SmallChess
Answers.Body: <p>You need to define "best". I agree with Todd's answer above that Morphy was the most dominant. He was probably the strongest in the world when he was only 12 years old (before puberty). No player in history can compare with that. Tal and Capablanca were the best in the world when they were about 18. In terms of chess knowledge and problem solving capability it would be Kasparov. Kasparov was not as talented as Tal or Capablanca and others, but he was much, much more disciplined and hard working. In terms of what human penetrated most deeply into the secrets of chess and knew it the best, it would be Kasparov.</p>
  
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Answers.UserDisplayName: Cecil De Vere
Answers.Body: <p>The only way to do this, IMO, is to assume &quot;authority&quot; in the form of best engine we have today (currently Stockfish, with estimated ELO 3600, far stronger than any human player ever) and then to compare Stockfish' s evaluations of its best move and move actually played by a human player.</p>
  <p>E.g., if Stockfish's best move has evaluation of +0.60 and move played by a human has  evaluation +0.40 then the strength of human move is 0.20 (closer to 0 is better). Then by using this method on a large sample of games (say 500 or 1000 games) you can calculate how much human moves differ on average from the best move for particular player.</p>
  <p>Note, you should start to evaluate, say from the move 10 or even from the move 15 for modern era players to compensate for development of opening theory (otherwise players from the past would be in disadvantage).</p>
  
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Answers.Text: This is still not objective and fair, given that players today have access to engines and can model their play in the opening and beyond based on engine-play and further advanced theory. It is not necessarily the greatness of the players that enables them to play like an engine, but the very engine that they use and that will be used to evaluate their play.
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Answers.Text: Agreed, it is not perfect, by any means, but I don't see any other way to compare players from different eras objectively. Yes, general understanding of chess and opening theory has advanced over time, that's why you should start evaluation of moves after opening phase. Once player is confronted with the new position he is on his own and forced to play with his own strength. There is still plenty of room for players of the past to shine. I've seen some Lasker games where he played 90% of top engine choice, quite remarkable and pretty hard for modern players to accomplish.
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Answers.Body: <p>NO!</p>
  
  <p>Trying would be comparing kumquats and kummerbunds and be meaningless.
  Chess playing strength has improved steadily over the past few centuries.   </p>
  
  <p>So an objective test is impossible as so many players are dead.  It is hard enough to know who is the best player today and that will likely change next year or so, just like it has done in the past. </p>
  
  <p>You would need to get all the players in the same tournament at the same time and have enough games to come up with a winner who could reasonably be called best.  And that might depend on the time control as well as luck and who got W/B when against who as you would need a swiss to be able to run the tournament in a reasonable amount of time.  The days of have 16 let alone 64 or 256 GMs in a double round robin are long gone.  And with fewer players there will be arguments that somebody good got left out who would have won. </p>
  
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Body: <p>There have been a number of statistical attempts (e.g., <a href="http://www.chessmetrics.com/cm/CM2/HistoricalRatings.asp" rel="noreferrer">chessmetrics</a> and <a href="http://www.edochess.ca/" rel="noreferrer">edo</a>)  or <a href="https://en.chessbase.com/post/computers-choose-who-was-the-strongest-player-" rel="noreferrer">computerized attempts</a> to determine who was the best chess player of all time.  </p>
  
  <p>The statistical approaches attempt to back rate all top chess players through time in order to make meaningful rating comparisons.  You can't just compare Elo ratings because many great players played before the Elo system was implemented.</p>
  
  <p>A second approach is to use computer analysis of the games of great players and determine who blundered the least.</p>
  
  <p>However, I see some problems with these approaches as implemented to date.  Here are my thoughts on this.  I would like to hear others thoughts.</p>
  
  <p>A computer comparison blunder analysis by professors <a href="https://en.chessbase.com/post/computers-choose-who-was-the-strongest-player-" rel="noreferrer">Matej Guid and Ivan Bratko</a> found that Capablanca played more like a computer than modern players! . However, Guid and Bratko noted that Capablanca's rather sedate style and lower quality of competition than modern players led to fewer positions where he was likely to blunder. Perhaps, an aggressive player like Kasparov may make more tactical errors because he sought complex positions but his opponents made even more errors under his pressure! </p>
  
  <p>Perhaps, you need an error weighting system that doesn’t just calculate the percentage of errors per 100 moves but estimates the difference between your error rate and your opponents error rate. </p>
  
  <p>Because computer comparison analyses don’t take into consideration the strength of your opponent back ratings have been used to adjust for increasing quality of play over time.  These approaches make some hidden assumptions as well. For example, Chessmetrics assumes a player’s peak rating occurs when they are 40 years old which probably isn't true in all cases. </p>
  
  <p>According to Edo, Capablanca and Morphy are rated the two highest players from the pre 1920s era.  According to Chessmetrics, Capablanca and Lasker were the two best players (Morphy doesn’t even make the top ten.). There are many other discrepancies between these two back rating systems.</p>
  
  <p>Can one derive a better system based on more solid assumptions to accurately estimate who was the best chess player?</p>
  
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Comments.Text: Related: [Are Elo ratings comparable across history?](https://chess.stackexchange.com/q/43142/26335)
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Tags: <rating><world-championship><famous-players><computer-chess><best-practice>
Title: Can you objectively determine who was the best chess player of all time?
ThreadText: # Can you objectively determine who was the best chess player of all time?
  
  (Asked by: username_0 on 2017-02-14)
  
  There have been a number of statistical attempts (e.g., [chessmetrics](http://www.chessmetrics.com/cm/CM2/HistoricalRatings.asp) and [edo](http://www.edochess.ca/)) or [computerized attempts](https://en.chessbase.com/post/computers-choose-who-was-the-strongest-player-) to determine who was the best chess player of all time.
  
  The statistical approaches attempt to back rate all top chess players through time in order to make meaningful rating comparisons. You can't just compare Elo ratings because many great players played before the Elo system was implemented.
  
  A second approach is to use computer analysis of the games of great players and determine who blundered the least.
  
  However, I see some problems with these approaches as implemented to date. Here are my thoughts on this. I would like to hear others thoughts.
  
  A computer comparison blunder analysis by professors [Matej Guid and Ivan Bratko](https://en.chessbase.com/post/computers-choose-who-was-the-strongest-player-) found that Capablanca played more like a computer than modern players! . However, Guid and Bratko noted that Capablanca's rather sedate style and lower quality of competition than modern players led to fewer positions where he was likely to blunder. Perhaps, an aggressive player like Kasparov may make more tactical errors because he sought complex positions but his opponents made even more errors under his pressure!
  
  Perhaps, you need an error weighting system that doesn’t just calculate the percentage of errors per 100 moves but estimates the difference between your error rate and your opponents error rate.
  
  Because computer comparison analyses don’t take into consideration the strength of your opponent back ratings have been used to adjust for increasing quality of play over time. These approaches make some hidden assumptions as well. For example, Chessmetrics assumes a player’s peak rating occurs when they are 40 years old which probably isn't true in all cases.
  
  According to Edo, Capablanca and Morphy are rated the two highest players from the pre 1920s era. According to Chessmetrics, Capablanca and Lasker were the two best players (Morphy doesn’t even make the top ten.). There are many other discrepancies between these two back rating systems.
  
  Can one derive a better system based on more solid assumptions to accurately estimate who was the best chess player?
  
  **Tags:** rating, world-championship, famous-players, computer-chess, best-practice
  
  > **Comments:**
  > **username_1**: Related: [Are Elo ratings comparable across history?](https://chess.stackexchange.com/q/43142/26335)  
  
  ---
  
  ## 6 answers
  
  ### Answer by username_0 on 2017-02-14. Score: 5
  
  I'm posting a sample answer to my question to give others an idea about what I'm thinking about.
  
  First, you have to define what you mean by best. For example, does best mean you are the most dominant player for your era? Or does it mean that the quality of your player is superior to all other players. And if quality is what you mean, then how do you define quality?
  
  Paul Morphy was probably the most dominant player. For example, when he was 12 years old he defeated a top ten player (Lowenthal) in a match 3-0. According to Edo and chessmetrics he was probably already one of the best players in the world at the age of 12! At the age of 21, he played against a simultaneous against 5 top ten players (Bird, Barnes, Boden, De Reviere, and Lowenthal) and scored 3-2.
  
  However, most would argue that dominance is a poor indicator of who is best. After all, Morphy has been described as the first modern chess player. His competition was weak compared with subsequent champions.
  
  Another definition that has been used is quality of play. However, this definition also has a lot of problems. In the 1900 hundreds , a number individuals argued that Steinitz or Lasker were the best players of all time arguing that their knowledge of opening and modern theory would make them superior to players from the past. However, Louis Paulsen made some very clever arguments against this hypothesis. He argued that Morphy (who had a photographic memory and memorized the Louisana bar code by the age of 19) if brought back to life would learn openings and modern theory within a year and be able to compete successfully against modern chess players.
  
  The mathematician Kenneth Regan argues that modern chess players who have access to chess computers and modern training methods play more like computers than players of the past. That’s no surprise because they were trained by computers but does that mean that modern players are really better? This begs the question what would Fischer or Capablanca do if they had access to modern computers? The problem with computer comparisons is they don’t take the historical factor into account.
  
  You need an error weighting system that doesn’t just calculate the percentage of errors per 100 moves (which is basically what Regan and Guid and Bratko did ). Instead, you need to calculate the difference between your error rate and your opponents error rate. After all, chess is about committing fewer errors than your opponent. Putting pressure on your opponent to induce more errors is considered a good quality.
  If innovation leads to dominance within a specific chess era over time and it becomes increasingly difficult to innovate over time as the strength of the competition increases you can’t measure true dominance by just looking at the match records of the top 30 players. That is, it’s a lot harder for Magnus Carlsen to dominate his opponents than it was for past champions.
  Can the problem of increasing quality of play overtime be corrected by looking at back ratings? I prefer the Edo back rating system <http://www.edochess.ca/> because the statistical assumptions are better. According to Chessmetrics, Zukertort, Steinitz, Tarrasch, Lasker, Pillsbury, Maroczy, Marshall, Janowsky, Chigorin, Schlechter, Blackburne, Duras, Teichmann, Neumann, Vidmar, Gunsberg, Rubinstein and Burn were better than Morphy. That doesn’t ring true for me.
  If you look at Edo or Chessmetrics back ratings it’s easy to see that the magnitude of the difference between the top players’ ratings has been decreasing over time. So I believe an Edo type statistical model that takes into consideration the difficulty to dominate over time would be a better approach than what has been tried previously.
  So my dream analysis is that you use Edo ratings based on a database that only includes the top 20 or 30 players from each five year period. After you complete this analysis you reweight your results by a dominance factor. That is, more recent players get a bonus factor that is calculated by estimating the trajectory of difficulty of dominating over time (the decrease in rating disparities between top 30 players over time). Next, you would validate this analysis by comparing players percentage of chess computer calculated blunders their opponents make minus their own blunders. If this invalidates the above, then you need to reweight according to the computer error checking analysis if it shows there is a tendency for more recent top players to play more accurately even after my dominance factor is taken into consideration.
  My guess based on my eyeballing this, is that Kasparov would do very well. But that’s just a guess.
  
  > **Comments:**
  > **username_2**: I think there's a gradual rise in ability over time across players of all classes simply due to the availability of books/DVDs/Computers. John Nunn did a serious analysis of how good (bad?) old masters were and his conclusion was that their play was pretty weak by modern GM standards. I can't remember where it was published though. Chessbase maybe? If you dropped a modern 2600 GM into the 19th century he'd be the strongest player in the world by a mile.  
  
  ---
  
  ### Answer by username_3 on 2017-02-14. Score: 1
  
  This is an endless discussion . The best way to predict the player is based upon whose games you would like to see again & again . The games from whom you learn the most . The style of players that you become fascinated with , I mean you would like to copy .
  
  From the above what I mean is let's say I want to play Sicilian as Black then Fischer & Kasparov have the best Games.
  
  I want to make my Endgame strong then Magnus I should choose .
  
  I like Tactics & imaginative Sacrifices then Mikhail
  Tal , Shirov , Speilmann are my Idols .
  
  Positional play then Botvinnik , Karpov etc.
  
  From a popular perspective my vote goes to Bobby Fischer and Kasparov . Now from a Country perspective Russsia may deny Fischer & Americans may not like Kasparov . Indian security may say Anand .
  
  So everyone has a different opinion .
  
  
  ---
  
  ### Answer by username_4 on 2017-02-16. Score: 1
  
  The ++**only and only way**++ objectively determine the best player is to make the candidates play games against each other.
  
  There is no way to perfectly answer your question, because:
  
  * Anyone who comes up with a new paper will argue the statistical assumptions in the paper are more solid and reliable than anything else
  * There will be always someone arguing how the best player should be judged. For example, Kasparov lost a match to Kramnik in a world-championship match, but... Kasparov was still considered a better player until he retired.
  
  There're lots of ways to determine the "best" player without making them to play chess:
  
  * Use the change in principal variation across depth (the paper cited in the question)
  * Use a computer algorithm to simulate the player
  * Estimate the strength by comparing accuracy to a computer
  * Use weighted average of past performance (Chessmetrics)
  
  There is no perfect method.
  
  * Change in principal variation assumes the change is a good indicator.
  * Accuracy may not be reliable. In chess, the winner only needs to play better chess than the opponent.
  * Weighted average can't be used for comparing players from different eras.
  
  I should share my personal opinion.
  
  **Best by dominance**
  
  Someone in other answer suggests Paul Morphy. But... Philidor was able to beat everybody else. He would even win with a pawn odd. I'd argue Philidor is the best player ever in terms of dominance.
  
  **Best by playing strength**
  
  Hard to believe anyone before the computer era can play chess better than modern elite players. Thus, we should only consider modern players. Carlsen and Kasparov are clearly the best players.
  
  
  ---
  
  ### Answer by username_5 on 2017-02-15. Score: 1
  
  You need to define "best". I agree with Todd's answer above that Morphy was the most dominant. He was probably the strongest in the world when he was only 12 years old (before puberty). No player in history can compare with that. Tal and Capablanca were the best in the world when they were about 18. In terms of chess knowledge and problem solving capability it would be Kasparov. Kasparov was not as talented as Tal or Capablanca and others, but he was much, much more disciplined and hard working. In terms of what human penetrated most deeply into the secrets of chess and knew it the best, it would be Kasparov.
  
  
  ---
  
  ### Answer by username_6 on 2022-07-07. Score: 1
  
  The only way to do this, IMO, is to assume "authority" in the form of best engine we have today (currently Stockfish, with estimated ELO 3600, far stronger than any human player ever) and then to compare Stockfish' s evaluations of its best move and move actually played by a human player.
  
  E.g., if Stockfish's best move has evaluation of +0.60 and move played by a human has evaluation +0.40 then the strength of human move is 0.20 (closer to 0 is better). Then by using this method on a large sample of games (say 500 or 1000 games) you can calculate how much human moves differ on average from the best move for particular player.
  
  Note, you should start to evaluate, say from the move 10 or even from the move 15 for modern era players to compensate for development of opening theory (otherwise players from the past would be in disadvantage).
  
  > **Comments:**
  > **username_7**: This is still not objective and fair, given that players today have access to engines and can model their play in the opening and beyond based on engine-play and further advanced theory. It is not necessarily the greatness of the players that enables them to play like an engine, but the very engine that they use and that will be used to evaluate their play.  
  > **username_6**: Agreed, it is not perfect, by any means, but I don't see any other way to compare players from different eras objectively. Yes, general understanding of chess and opening theory has advanced over time, that's why you should start evaluation of moves after opening phase. Once player is confronted with the new position he is on his own and forced to play with his own strength. There is still plenty of room for players of the past to shine. I've seen some Lasker games where he played 90% of top engine choice, quite remarkable and pretty hard for modern players to accomplish.  
  
  ---
  
  ### Answer by username_8 on 2020-01-11. Score: 0
  
  NO!
  
  Trying would be comparing kumquats and kummerbunds and be meaningless.
  Chess playing strength has improved steadily over the past few centuries.
  
  So an objective test is impossible as so many players are dead. It is hard enough to know who is the best player today and that will likely change next year or so, just like it has done in the past.
  
  You would need to get all the players in the same tournament at the same time and have enough games to come up with a winner who could reasonably be called best. And that might depend on the time control as well as luck and who got W/B when against who as you would need a swiss to be able to run the tournament in a reasonable amount of time. The days of have 16 let alone 64 or 256 GMs in a double round robin are long gone. And with fewer players there will be arguments that somebody good got left out who would have won.
  
  
  ---
  
  