7 ms·

Who is the most accurate world chess champion?

169 points by piotrgrudzien 5y ago

KingOfCoders 5y ago
Yes "Alan Turing, was the first recorded to have tried, creating a programme called Turochamp in 1948." But also "Since 1941 Zuse worked on chess playing algorithms and formulated program routines in Plankalkül in 1945." https://www.chessprogramming.org/Konrad_Zuse https://www.chessprogramming.org/Konrad_Zuse
mjw1007 5y ago
Is there a risk that this measure is telling us as much about how likely a match was to contain difficult positions as about how skilled the players were? For example, Karpov and Kasparov sometimes agreed short draws. I wonder if that is flattering their figures.
- jeremyjh 5y ago
  Definitely - if there are lots of good moves to be found accuracy will be higher. This is why when you analyze games for suspicion of cheating you cannot look only at the accuracy figure - you have to take into account how challenging the positions are. Lichess and chess.com both do this but they do not tell us how, for obvious reasons.
  - freediver 5y ago
    > Lichess and chess.com both do this but they do not tell us how, for obvious reasons. Isn't lichess open source?
    - shric 5y ago
      Yes, but the cheat detection isn't.
tromp 5y ago
I'm most impressed by Capablanca's jump in highly accurate play back in 1921, that would not be surpassed for another 60 years.
- marvel_boy 5y ago
  Capablanca without any doubt. Also Morphy.
- LudwigNagasena 5y ago
  In part high accuracy means that the opponents are approximately of equal strength. The way people win games in chess is by complicating the position so much that it forces your opponent to make a mistake while you are able to handle it. If the accuracy is high, not only it means that the players are good, it also means that they don’t ask each other serious questions. Put any human against Stockfish and, I am sure, their ACPL will increase dramatically.
- pk2200 5y ago
  Capablanca preferred playing quiet, positional chess, often patiently nursing tiny endgame advantages into a win. It's generally much easier to play accurately in simple endgames than complex middlegames, and that's a big factor in his low ACPL score. (I don't mean to take anything away from him - he was probably the best ever at that style of play.)
LudwigNagasena 5y ago
Precision is a murky concept in chess because it is not a solved game. First, if the move doesn’t change the best play result, can it really be called imprecise? Only in terms of practical chances. And if we are talking about practical chances, why should we rely on computer-centric evaluation? If a human has to choose between a move that leads to the win but they have to find 40 best moves or they will lose and a move that is a theoretical draw but now the opponent has to find 40 moves or they will lose, what should a human choose? What is even the ACPL of a move from a tablebase? There is no value, it is either a win, a draw or a loss. So while the whole idea behind this exercise is intuitively appealing and certainly captures some sense behind the idea of accuracy, it should be taken with a grain of salt.
- thom 5y ago
  Yep, agree with this. It was surprising to me to find out how large the error bars were in computer evaluations of their own games. In the last TCEC superfinal, for example, the majority of the draws saw at least one position with an evaluation higher than +/-1.0, and 3 of the 26 decisive games came after a 0.0 evaluation. I assume that margin should be even bigger in human games, so it’s hard to see what there is to learn (outside some fun lines) from looking at these numbers outside of opening prep. As for the tablebase question, it would be nice to see win/forced-draw probabilities from engines instead of the increasingly artificial material evaluation.
- Barrin92 5y ago
  >Precision is a murky concept in chess because it is not a solved game it's ironically also a murky concept for the opposite reason. In some openings the analysis of GM's goes so deep that they can fairly often play almost exclusively computer-aided prep. There's a big difference between a 40-move game in that kind of theoretical position vs off-beat games. So you might have a very precise, narrow, theoretical repertoire but that's not the same as playing strength because your opponents can prepare. What really matters is more something like precision under uncertainty.
pgcj_poster 5y ago
I would have liked to see this go back far enough to include Morphy, whom Fischer considered "the most accurate player who ever lived." I would be surprised if Stockfish agreed, but it would be interesting to see.
- dfan 5y ago
  Kenneth Regan's work on Intrinsic Performance Ratings includes estimated ratings for Morphy, which vary widely from event to event but average around 2300, which I think matches the intuitive perception of his strength that modern strong players have. https://cse.buffalo.edu/~regan/papers/pdf/Reg12IPRs.pdf https://cse.buffalo.edu/~regan/papers/pdf/Reg12IPRs.pdf (Of course, as with all historical players, he would be stronger if he were re-animated today and exposed to modern principles and openings.)
nomilk 5y ago
Centipawn loss (or simply the engine's evaluation of a position) doesn't take into account how realistically a human could hold a position. During yesterday's WCC Game 6 the computer evaluation meant little when players were in time trouble. Anything could have happened going into the first time control, despite the game being dead drawn for the first 3.5 hours. In the final stages the computer again evaluated the game as drawn, but presumed Nepo could defend perfectly for tens of moves without a single inaccuracy. Super GMs can't do that given hours or days, let alone minutes. Last thought: did anyone else assume this was written in R/ggplot2 at first glance? Seaborn and/or matplotlib look strikingly like ggplot2 now days!
- polytely 5y ago
  and exhaustion also starts to play a role after playing for like 7 hours, at some point mistakes will start to slip in.
- jeremyjh 5y ago
  You are definitely right about the evaluation; I switched between several streams and I don't think there was anyone saying that they didn't prefer white after around move 39, despite a 0.0 eval for a lot of those positions. But part of the reason the eval is misleading is because it might be reflecting a sequence of "only moves" - where only one move can hold that evaluation and it may be very hard to find some of those moves for black, while white has lots of good moves in each position. While that is a problem with human interpretation of eval, I do not see how it invalidates use of ACPL which is an average across the entire game.
- eckesicle 5y ago
  I was thinking a bit about this during the game too. Perhaps alongside centipawn loss (a measure of how many hundredths of a pawn a player loses by making the non-optimal move as determined by a chess AI engine) we could also measure the difficulty of any position. Stockfish (a popular chess engine) roughly works by constructing a tree of possible moves and evaluating the score according to some heuristic at its maximum depth. The best result at depth n (25 I believe) is considered the best move and incurs 0 centipawn loss. Perhaps we can define the difficulty of a position by the relative centipawn loss at each preceeding depth in the tree? The difficulty of a position is then determined by the depth at which the best move no longer changes.
umutisik 5y ago
If “accuracy” measures how well a player matches computer chess, then as players continue to study more and more with chess programs, you would expect their play to match the programs more and more. Personally I find it odd to measure how well the players match the computer program and call it accuracy. The computers do not open the game tree exhaustively so they give only one prediction of true min-max accuracy. When Lee Sedol made move 78 in game 4 against AlphaGo, it reduced his accuracy but won him the game.
- thepete2 5y ago
  I don't know if this is a thing, but chess players might also steer the game in a direction/position which their opponent hasn't studied much, but they have. There's a "social" side to this seemingly "mathematical" game, no?
  - JulianWasTaken 5y ago
    This is more so in the opening (the beginning of the game, and separately where engines tend to be a bit less informative) but yes it is definitely part of the chess metagame, and you'll often see commentators talk about whether someone is "still in prep" or has gotten out of it. It often can lead to time advantages if one gets an opponent out of prep.
  - thom 5y ago
    Fabiano Caruana (previous World Championship challenger) has said that he’s happy to find lines where the machines have you slightly behind, purely because they’re less like to have been studied in detail by your opponent. Even with perfect recall of the first 20/30 moves in various lines, players are still going to steer away from some lines based on their and their opponent’s strengths (tough against super GMs with few weaknesses though). So you’re definitely right, I think there’s a lot of game theory here, albeit much of it settled by your team ahead of the actual match.
- chki 5y ago
  This is addressed in the article by the way.
deleted 5y ago
[deleted]
marcodiego 5y ago
Why not use something similar to alphago zero to carefully analyze chess games of a deceased player until it is able to mimic its decisions? It could bring many players "back to life". It would be even possible to watch "impossible matches" like Kasparov vs Capablanca!
- thom 5y ago
  You’d be training purely on games with outdated theory, in which case the engine would lose to those trained from more modern repertoires. Or you’d let it learn through self play after initially showing it the human games, in which case it would probably quickly lose the identifiable stylistic aspects of its initial training.
  - csee 5y ago
    The point isn't to make an unbeatable chess player, it's to 'bring them back to life'.
    - thom 5y ago
      But what I mean is Kasparov would destroy Capablanca. Even outside of what one might consider ‘raw chess talent’, he was drawing on decades of better theory and would deploy that knowledge. It would be hard to simulate Kasparov as if he were taught chess in Capablanca’s time (maybe not impossible and a fascinating project, I just don’t see how you’d do it).
      - msbarnett 5y ago
        > It would be hard to simulate Kasparov as if he were taught chess in Capablanca’s time (maybe not impossible and a fascinating project, I just don’t see how you’d do it). I don't think they were suggesting that's the result they wanted - if you could somehow magically reanimate Capablanca in real life and pit him against peak Kasparov, he might lose badly. A neural net having the same outcome is essentially what's being asked for. Kasparov raised on Capablanca's era chess or vice versa would be unrecognizably different players, and I don't think anybody expects an AI to simulate their soul.
thom 5y ago
I think it would be worth looking at a player’s accuracy in terms of their cohort’s standard deviation, given that theory is more or less shared across all players. Even then, the best players now have the best teams and computers, so a lot of Magnus’s accuracy in this game is a credit to Jan Gustafsson et al. I’ve been thinking how you might capture the player’s accuracy out of their prep, that seems a better measure, but even then you’re so often choosing between five +0.0 moves by the middle-game, and you could easily play many totally accurate moves if you didn’t feel like agreeing a draw. I know some have looked at Markov models of a player’s likelihood of a blunder to analyse this instead. Personally I’ve never felt Magnus enjoyed the modern game with as much opening preparation as we have now. It seems like he’s only in the last few years invested the time in this, instead of relying on his technique to win even from losing positions. I hope AlphaZero proving that fun positional ideas like pawn sacrifices and h4 everywhere reinvigorated him somewhat during his dominant first half of 2019, so there’s still hope the machines haven’t just drained the romance from the game, even if their ideas remain dominant.
blt 5y ago
> If we’d used a different chess engine, even a weaker version of the same one — such as Stockfish 12 — it may have found the 2018 World Championship the most accurate in history (assuming both players prepared and trained using Stockfish 12 in 2018). This would be a really good follow-up experiment. If the theorized result really happens, we would have strong evidence that players are "overfitting" to their training chess engine. It would also be interesting to see how stable the historical figures look between different engines.
BlanketLogic 5y ago
> At the time of publishing, the last decisive game in the World Championship was game 10 of the World Championships 2016 — 1835 days ago, or 5 years and 9 days. Is the singularity being reached, with man and machine minds melding towards inevitable monochromatic matches? Very very unfortunate timing but still a valid question.
ItsMonkk 5y ago
One of the reasons that Poker players prefer tournaments is because it induces them to move away from perfect Nash equilibrium play and into being exploitable, as someone who plays unexploitable play simply doesn't make it to the money as someone who does. Winning 51% of the time means nothing when you need to be in the top 10% to earn anything back. It seems like just looking at ACPL isn't looking at this correctly. If someone makes a mistake, and loses some centi-pawn, but it induces an even larger mistake in their competitor, that wasn't a mistake, it was a risk.
hippodamos 5y ago
Sorry i am highjacking this thread. I am on a quest to find the rules of the chess variant finesse by GM walter Browne. If anyone knows them : https://lookingforfinesse.github.io/lookingforfinessevariant/ https://lookingforfinesse.github.io/lookingforfinessevariant...
raymondh 5y ago
For historical human-to-human games, it would be more interesting to see how well players targeted with weaknesses of their opponents. That skill likely mattered more than absolute accuracy as measured by computers.
oh_my_goodness 5y ago
It's strange how many times the article says 'chess software' has improved since (Turing's day, the 1990s, whenever). Sure, the software is better, but six orders of magnitude in hardware performance haven't hurt either.
- ummonk 5y ago
  The hardware improvement has been huge, but on the other hand if you pit Stockfish NNUE against top 1990s software on equal modern hardware, Stockfish would win handily. It's really been both hardware and software improving.
  - deleted 5y ago
    [deleted]
lisper 5y ago
Just in case you, like me, were wondering what the word "accurate" means in this context: https://support.chess.com/article/1135-what-is-accuracy-in-analysis-how-is-it-measured https://support.chess.com/article/1135-what-is-accuracy-in-a...
ummonk 5y ago
I'm not sure how meaningful these numbers are. I get around 40-50 ACPL in my games, and I certainly wouldn't have been anywhere near a match for Botvinnik.
bjourne 5y ago
In chess ACPL roughly works like goals scored (conceded) in football. Goals are made when the defending team makes mistakes. A team that is a master of defense will concede few goals. But will also score few goals since defending well requires playing cautiously. Its the same with attacking, aggressive teams. They both score and concede more goals than the average.

169 points by piotrgrudzien 5y ago

Yes "Alan Turing, was the first recorded to have tried, creating a programme called Turochamp in 1948." But also "Since 1941 Zuse worked on chess playing algorithms and formulated program routines in Plankalkül in 1945." https://www.chessprogramming.org/Konrad_Zuse https://www.chessprogramming.org/Konrad_Zuse

mjw1007 5y ago

Is there a risk that this measure is telling us as much about how likely a match was to contain difficult positions as about how skilled the players were? For example, Karpov and Kasparov sometimes agreed short draws. I wonder if that is flattering their figures.

jeremyjh 5y ago
Definitely - if there are lots of good moves to be found accuracy will be higher. This is why when you analyze games for suspicion of cheating you cannot look only at the accuracy figure - you have to take into account how challenging the positions are. Lichess and chess.com both do this but they do not tell us how, for obvious reasons.
- freediver 5y ago
  > Lichess and chess.com both do this but they do not tell us how, for obvious reasons. Isn't lichess open source?
  - shric 5y ago
    Yes, but the cheat detection isn't.

tromp 5y ago

I'm most impressed by Capablanca's jump in highly accurate play back in 1921, that would not be surpassed for another 60 years.

marvel_boy 5y ago
Capablanca without any doubt. Also Morphy.
LudwigNagasena 5y ago
In part high accuracy means that the opponents are approximately of equal strength. The way people win games in chess is by complicating the position so much that it forces your opponent to make a mistake while you are able to handle it. If the accuracy is high, not only it means that the players are good, it also means that they don’t ask each other serious questions. Put any human against Stockfish and, I am sure, their ACPL will increase dramatically.
pk2200 5y ago
Capablanca preferred playing quiet, positional chess, often patiently nursing tiny endgame advantages into a win. It's generally much easier to play accurately in simple endgames than complex middlegames, and that's a big factor in his low ACPL score. (I don't mean to take anything away from him - he was probably the best ever at that style of play.)

LudwigNagasena 5y ago

Precision is a murky concept in chess because it is not a solved game. First, if the move doesn’t change the best play result, can it really be called imprecise? Only in terms of practical chances. And if we are talking about practical chances, why should we rely on computer-centric evaluation? If a human has to choose between a move that leads to the win but they have to find 40 best moves or they will lose and a move that is a theoretical draw but now the opponent has to find 40 moves or they will lose, what should a human choose? What is even the ACPL of a move from a tablebase? There is no value, it is either a win, a draw or a loss. So while the whole idea behind this exercise is intuitively appealing and certainly captures some sense behind the idea of accuracy, it should be taken with a grain of salt.

thom 5y ago
Yep, agree with this. It was surprising to me to find out how large the error bars were in computer evaluations of their own games. In the last TCEC superfinal, for example, the majority of the draws saw at least one position with an evaluation higher than +/-1.0, and 3 of the 26 decisive games came after a 0.0 evaluation. I assume that margin should be even bigger in human games, so it’s hard to see what there is to learn (outside some fun lines) from looking at these numbers outside of opening prep. As for the tablebase question, it would be nice to see win/forced-draw probabilities from engines instead of the increasingly artificial material evaluation.
Barrin92 5y ago
>Precision is a murky concept in chess because it is not a solved game it's ironically also a murky concept for the opposite reason. In some openings the analysis of GM's goes so deep that they can fairly often play almost exclusively computer-aided prep. There's a big difference between a 40-move game in that kind of theoretical position vs off-beat games. So you might have a very precise, narrow, theoretical repertoire but that's not the same as playing strength because your opponents can prepare. What really matters is more something like precision under uncertainty.

pgcj_poster 5y ago

I would have liked to see this go back far enough to include Morphy, whom Fischer considered "the most accurate player who ever lived." I would be surprised if Stockfish agreed, but it would be interesting to see.

dfan 5y ago
Kenneth Regan's work on Intrinsic Performance Ratings includes estimated ratings for Morphy, which vary widely from event to event but average around 2300, which I think matches the intuitive perception of his strength that modern strong players have. https://cse.buffalo.edu/~regan/papers/pdf/Reg12IPRs.pdf https://cse.buffalo.edu/~regan/papers/pdf/Reg12IPRs.pdf (Of course, as with all historical players, he would be stronger if he were re-animated today and exposed to modern principles and openings.)

nomilk 5y ago

Centipawn loss (or simply the engine's evaluation of a position) doesn't take into account how realistically a human could hold a position. During yesterday's WCC Game 6 the computer evaluation meant little when players were in time trouble. Anything could have happened going into the first time control, despite the game being dead drawn for the first 3.5 hours. In the final stages the computer again evaluated the game as drawn, but presumed Nepo could defend perfectly for tens of moves without a single inaccuracy. Super GMs can't do that given hours or days, let alone minutes. Last thought: did anyone else assume this was written in R/ggplot2 at first glance? Seaborn and/or matplotlib look strikingly like ggplot2 now days!

polytely 5y ago
and exhaustion also starts to play a role after playing for like 7 hours, at some point mistakes will start to slip in.
jeremyjh 5y ago
You are definitely right about the evaluation; I switched between several streams and I don't think there was anyone saying that they didn't prefer white after around move 39, despite a 0.0 eval for a lot of those positions. But part of the reason the eval is misleading is because it might be reflecting a sequence of "only moves" - where only one move can hold that evaluation and it may be very hard to find some of those moves for black, while white has lots of good moves in each position. While that is a problem with human interpretation of eval, I do not see how it invalidates use of ACPL which is an average across the entire game.
eckesicle 5y ago
I was thinking a bit about this during the game too. Perhaps alongside centipawn loss (a measure of how many hundredths of a pawn a player loses by making the non-optimal move as determined by a chess AI engine) we could also measure the difficulty of any position. Stockfish (a popular chess engine) roughly works by constructing a tree of possible moves and evaluating the score according to some heuristic at its maximum depth. The best result at depth n (25 I believe) is considered the best move and incurs 0 centipawn loss. Perhaps we can define the difficulty of a position by the relative centipawn loss at each preceeding depth in the tree? The difficulty of a position is then determined by the depth at which the best move no longer changes.

umutisik 5y ago

If “accuracy” measures how well a player matches computer chess, then as players continue to study more and more with chess programs, you would expect their play to match the programs more and more. Personally I find it odd to measure how well the players match the computer program and call it accuracy. The computers do not open the game tree exhaustively so they give only one prediction of true min-max accuracy. When Lee Sedol made move 78 in game 4 against AlphaGo, it reduced his accuracy but won him the game.

thepete2 5y ago
I don't know if this is a thing, but chess players might also steer the game in a direction/position which their opponent hasn't studied much, but they have. There's a "social" side to this seemingly "mathematical" game, no?
- JulianWasTaken 5y ago
  This is more so in the opening (the beginning of the game, and separately where engines tend to be a bit less informative) but yes it is definitely part of the chess metagame, and you'll often see commentators talk about whether someone is "still in prep" or has gotten out of it. It often can lead to time advantages if one gets an opponent out of prep.
- thom 5y ago
  Fabiano Caruana (previous World Championship challenger) has said that he’s happy to find lines where the machines have you slightly behind, purely because they’re less like to have been studied in detail by your opponent. Even with perfect recall of the first 20/30 moves in various lines, players are still going to steer away from some lines based on their and their opponent’s strengths (tough against super GMs with few weaknesses though). So you’re definitely right, I think there’s a lot of game theory here, albeit much of it settled by your team ahead of the actual match.
chki 5y ago
This is addressed in the article by the way.

deleted 5y ago

[deleted]

marcodiego 5y ago

Why not use something similar to alphago zero to carefully analyze chess games of a deceased player until it is able to mimic its decisions? It could bring many players "back to life". It would be even possible to watch "impossible matches" like Kasparov vs Capablanca!

thom 5y ago
You’d be training purely on games with outdated theory, in which case the engine would lose to those trained from more modern repertoires. Or you’d let it learn through self play after initially showing it the human games, in which case it would probably quickly lose the identifiable stylistic aspects of its initial training.
- csee 5y ago
  The point isn't to make an unbeatable chess player, it's to 'bring them back to life'.
  - thom 5y ago
    But what I mean is Kasparov would destroy Capablanca. Even outside of what one might consider ‘raw chess talent’, he was drawing on decades of better theory and would deploy that knowledge. It would be hard to simulate Kasparov as if he were taught chess in Capablanca’s time (maybe not impossible and a fascinating project, I just don’t see how you’d do it).
    - msbarnett 5y ago
      > It would be hard to simulate Kasparov as if he were taught chess in Capablanca’s time (maybe not impossible and a fascinating project, I just don’t see how you’d do it). I don't think they were suggesting that's the result they wanted - if you could somehow magically reanimate Capablanca in real life and pit him against peak Kasparov, he might lose badly. A neural net having the same outcome is essentially what's being asked for. Kasparov raised on Capablanca's era chess or vice versa would be unrecognizably different players, and I don't think anybody expects an AI to simulate their soul.

thom 5y ago

I think it would be worth looking at a player’s accuracy in terms of their cohort’s standard deviation, given that theory is more or less shared across all players. Even then, the best players now have the best teams and computers, so a lot of Magnus’s accuracy in this game is a credit to Jan Gustafsson et al. I’ve been thinking how you might capture the player’s accuracy out of their prep, that seems a better measure, but even then you’re so often choosing between five +0.0 moves by the middle-game, and you could easily play many totally accurate moves if you didn’t feel like agreeing a draw. I know some have looked at Markov models of a player’s likelihood of a blunder to analyse this instead. Personally I’ve never felt Magnus enjoyed the modern game with as much opening preparation as we have now. It seems like he’s only in the last few years invested the time in this, instead of relying on his technique to win even from losing positions. I hope AlphaZero proving that fun positional ideas like pawn sacrifices and h4 everywhere reinvigorated him somewhat during his dominant first half of 2019, so there’s still hope the machines haven’t just drained the romance from the game, even if their ideas remain dominant.

blt 5y ago

> If we’d used a different chess engine, even a weaker version of the same one — such as Stockfish 12 — it may have found the 2018 World Championship the most accurate in history (assuming both players prepared and trained using Stockfish 12 in 2018). This would be a really good follow-up experiment. If the theorized result really happens, we would have strong evidence that players are "overfitting" to their training chess engine. It would also be interesting to see how stable the historical figures look between different engines.

BlanketLogic 5y ago

> At the time of publishing, the last decisive game in the World Championship was game 10 of the World Championships 2016 — 1835 days ago, or 5 years and 9 days. Is the singularity being reached, with man and machine minds melding towards inevitable monochromatic matches? Very very unfortunate timing but still a valid question.

ItsMonkk 5y ago

One of the reasons that Poker players prefer tournaments is because it induces them to move away from perfect Nash equilibrium play and into being exploitable, as someone who plays unexploitable play simply doesn't make it to the money as someone who does. Winning 51% of the time means nothing when you need to be in the top 10% to earn anything back. It seems like just looking at ACPL isn't looking at this correctly. If someone makes a mistake, and loses some centi-pawn, but it induces an even larger mistake in their competitor, that wasn't a mistake, it was a risk.

hippodamos 5y ago

Sorry i am highjacking this thread. I am on a quest to find the rules of the chess variant finesse by GM walter Browne. If anyone knows them : https://lookingforfinesse.github.io/lookingforfinessevariant/ https://lookingforfinesse.github.io/lookingforfinessevariant...

raymondh 5y ago

For historical human-to-human games, it would be more interesting to see how well players targeted with weaknesses of their opponents. That skill likely mattered more than absolute accuracy as measured by computers.

oh_my_goodness 5y ago

It's strange how many times the article says 'chess software' has improved since (Turing's day, the 1990s, whenever). Sure, the software is better, but six orders of magnitude in hardware performance haven't hurt either.

ummonk 5y ago
The hardware improvement has been huge, but on the other hand if you pit Stockfish NNUE against top 1990s software on equal modern hardware, Stockfish would win handily. It's really been both hardware and software improving.
- deleted 5y ago
  [deleted]

lisper 5y ago

Just in case you, like me, were wondering what the word "accurate" means in this context: https://support.chess.com/article/1135-what-is-accuracy-in-analysis-how-is-it-measured https://support.chess.com/article/1135-what-is-accuracy-in-a...

ummonk 5y ago

I'm not sure how meaningful these numbers are. I get around 40-50 ACPL in my games, and I certainly wouldn't have been anywhere near a match for Botvinnik.

bjourne 5y ago

In chess ACPL roughly works like goals scored (conceded) in football. Goals are made when the defending team makes mistakes. A team that is a master of defense will concede few goals. But will also score few goals since defending well requires playing cautiously. Its the same with attacking, aggressive teams. They both score and concede more goals than the average.