Answers.Body: <p>Yes, there are such studies. You can check <a href="https://content.iospress.com/articles/icga-journal/icg0012" rel="noreferrer">this recent paper</a> and references therein for the older ones. Various ideas have indeed been tried in order to quantify the "complexity" of position (e. g., in terms of complexity of search tree or dynamics of the evaluation function as the depth grows), but I think you better read the papers if you are interested in details. </p>
  
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Answers.CreationDate: 2019-12-31T11:58:10.800Z
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Answers.UserDisplayName: Kostya_I
Answers.Body: <p>Not that I know of. You could do this yourself for each world champion, taking a sample size of something like 20-30 games for each. That may give you fairly good statistics, since as the sample size goes above that there won't be any dramatic changes.</p>
  
  <p>It's a good point to mention the bias, but in who's favour this works isn't clear. If world champions get in tougher positions, there tend to be fewer acceptable moves (meaning the number of choices to match with the engine's best choice is smaller). But in a solid position, there are often many acceptable moves (and you need to find the one the engine likes best).</p>
  
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Answers.CreationDate: 2019-12-31T04:42:44.883Z
Answers.Text: It is true that in solid positions there are a variety of moves which are available while in very sharp positions the best move needs to be found however solid positions are also very intuitive and in sharp positions a lot of calculation is needed.
Answers.UserDisplayName: SubhanKhan
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Answers.Text: @SubhanKhan Yes, that's why I don't know which way the bias goes (although there is definitely some bias).
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Answers.UserDisplayName: Inertial Ignorance
Body: <p>Is there an analysis of World Champion games, with the help of engines, that shows statistics like percentage of best moves played, blunders made, creative moves which computers can only see at high depths, and etc? There might be some bias in this analysis since solid players, at least to me, will play objectively better moves since the positions that arise are simpler.</p>
  
Tags: <analysis><statistics><master-games>
Title: Is there an analysis of World Champions' games that shows the statistics of their game?
ThreadText: # Is there an analysis of World Champions' games that shows the statistics of their game?
  
  (Asked by: username_0 on 2019-12-31)
  
  Is there an analysis of World Champion games, with the help of engines, that shows statistics like percentage of best moves played, blunders made, creative moves which computers can only see at high depths, and etc? There might be some bias in this analysis since solid players, at least to me, will play objectively better moves since the positions that arise are simpler.
  
  **Tags:** analysis, statistics, master-games
  
  
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  ## 2 answers
  
  ### Answer by username_1 on 2019-12-31. Score: 6
  
  Yes, there are such studies. You can check [this recent paper](https://content.iospress.com/articles/icga-journal/icg0012) and references therein for the older ones. Various ideas have indeed been tried in order to quantify the "complexity" of position (e. g., in terms of complexity of search tree or dynamics of the evaluation function as the depth grows), but I think you better read the papers if you are interested in details.
  
  
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  ### Answer by username_2 on 2019-12-31. Score: 4
  
  Not that I know of. You could do this yourself for each world champion, taking a sample size of something like 20-30 games for each. That may give you fairly good statistics, since as the sample size goes above that there won't be any dramatic changes.
  
  It's a good point to mention the bias, but in who's favour this works isn't clear. If world champions get in tougher positions, there tend to be fewer acceptable moves (meaning the number of choices to match with the engine's best choice is smaller). But in a solid position, there are often many acceptable moves (and you need to find the one the engine likes best).
  
  > **Comments:**
  > **username_0**: It is true that in solid positions there are a variety of moves which are available while in very sharp positions the best move needs to be found however solid positions are also very intuitive and in sharp positions a lot of calculation is needed.  
  > **username_2**: @username_0 Yes, that's why I don't know which way the bias goes (although there is definitely some bias).  
  
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