Answers.Body: <p>I am not aware of a study of this kind, but why not make our own? Let us parse some WCC PGNs!</p>
  
  <p><a href="https://i.sstatic.net/VK5k6.png" rel="noreferrer"><img src="https://i.sstatic.net/VK5k6.png" alt="WCC games results"></a></p>
  
  <p><a href="https://i.sstatic.net/HHXdt.png" rel="noreferrer"><img src="https://i.sstatic.net/HHXdt.png" alt="Fraction of draws by round"></a></p>
  
  <p>To me, this does not seem to have any definite regularities for when a draw is more likely (also note, that at the very high number of rounds, only a few games are available - there have been only a few very long WCC matches).</p>
  
  <p><strong>EDIT</strong></p>
  
  <p>Recent events only. Looks like more draws overall and slight tendency for more draws towards the end of a match.</p>
  
  <p><a href="https://i.sstatic.net/paoHC.png" rel="noreferrer"><img src="https://i.sstatic.net/paoHC.png" alt="WCC games results - post 1985"></a></p>
  
  <p><a href="https://i.sstatic.net/mGYI1.png" rel="noreferrer"><img src="https://i.sstatic.net/mGYI1.png" alt="Fraction of draws by round - post 1985"></a></p>
  
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2016-11-14T21:42:09.120Z
Answers.Text: That's for all the world championship matches? Does it change if you look only at recent ones?
Answers.UserDisplayName: user1583209
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Answers.Text: @user1583209 All except the events where champions were decided in a tournament format (i.e. not a 1v1 match). Also, see my edit.
Answers.UserDisplayName: GloriaVictis
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Answers.CreationDate: 2016-11-14T21:57:21.577Z
Answers.Text: If you want to answer the original question, you should not calculate the fraction of draws per round number, because say in a match of 50 rounds, round number 10 would be the still in the "start" phase, while in a match of 12 rounds it would already be at the end. I believe what you basically should do is to normalize the x-axis (divide by number of total rounds).
Answers.UserDisplayName: user1583209
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Answers.Text: The >25 games matches are outliers, vast majority of matches are much shorter.
Answers.UserDisplayName: GloriaVictis
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Answers.Text: I understand that, however you still have matches with between say 12 and 24 games or so.  In one case round 12 would be in the end phase and in the other case it would just be in the intermediate phase. When you calculate the "fraction of draws" diagram you basically throw them together which you should not, if you want to answer the question whether there are more draws at the start of a match or at the end, etc.
Answers.UserDisplayName: user1583209
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Answers.Text: I can think of two ways to analyze this. First option: Consider each match to consist of three parts (start/middle/end). So for a match of 12 rounds you have the first 4 rounds in "start", the next 4 rounds (round 5 to 8) in "middle" and rounds 9 to 12 in "end". Similarly for a match of 24 rounds you'd have rounds 1-8 in "start", 9-16 in "middle" and 17-24 in "end". Collect all the games of all matches from and see what the draw percentage is in each of the three slots ("start"/"mid"/"end").
Answers.UserDisplayName: user1583209
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Answers.Text: What was the WC match that only had 4 games?
Answers.UserDisplayName: RemcoGerlich
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Answers.Text: @RemcoGerlich Seems that's how the playoff in Kramnik - Topalov match was labelled in the PGN I have... So not a real match as such.
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Body: <p>Some commentators have expressed surprise at the two relatively bland draws to open out the most recent (Carlsen-Karjakin) World Championships.  I'm wondering whether there's been any study as to whether 'feeling-out' is a real phenomenon: are draws more likely to happen at the start of a championship match, in the middle, or towards the end?  Has any objective research (whether specifically WCC or any high-level chess match play) been done on this?</p>
  
Tags: <draw><statistics><world-championship>
Title: Draws by game number in championship matches
ThreadText: # Draws by game number in championship matches
  
  (Asked by: username_0 on 2016-11-14)
  
  Some commentators have expressed surprise at the two relatively bland draws to open out the most recent (Carlsen-Karjakin) World Championships. I'm wondering whether there's been any study as to whether 'feeling-out' is a real phenomenon: are draws more likely to happen at the start of a championship match, in the middle, or towards the end? Has any objective research (whether specifically WCC or any high-level chess match play) been done on this?
  
  **Tags:** draw, statistics, world-championship
  
  
  ---
  
  ## 1 answers
  
  ### Answer by username_1 on 2016-11-14. Score: 11 | Accepted answer
  
  I am not aware of a study of this kind, but why not make our own? Let us parse some WCC PGNs!
  
  [![WCC games results](https://i.sstatic.net/VK5k6.png)](https://i.sstatic.net/VK5k6.png)
  
  [![Fraction of draws by round](https://i.sstatic.net/HHXdt.png)](https://i.sstatic.net/HHXdt.png)
  
  To me, this does not seem to have any definite regularities for when a draw is more likely (also note, that at the very high number of rounds, only a few games are available - there have been only a few very long WCC matches).
  
  **EDIT**
  
  Recent events only. Looks like more draws overall and slight tendency for more draws towards the end of a match.
  
  [![WCC games results - post 1985](https://i.sstatic.net/paoHC.png)](https://i.sstatic.net/paoHC.png)
  
  [![Fraction of draws by round - post 1985](https://i.sstatic.net/mGYI1.png)](https://i.sstatic.net/mGYI1.png)
  
  > **Comments:**
  > **username_2**: That's for all the world championship matches? Does it change if you look only at recent ones?  
  > **username_1**: @username_2 All except the events where champions were decided in a tournament format (i.e. not a 1v1 match). Also, see my edit.  
  > **username_2**: If you want to answer the original question, you should not calculate the fraction of draws per round number, because say in a match of 50 rounds, round number 10 would be the still in the "start" phase, while in a match of 12 rounds it would already be at the end. I believe what you basically should do is to normalize the x-axis (divide by number of total rounds).  
  > **username_1**: The >25 games matches are outliers, vast majority of matches are much shorter.  
  > **username_2**: I understand that, however you still have matches with between say 12 and 24 games or so.  In one case round 12 would be in the end phase and in the other case it would just be in the intermediate phase. When you calculate the "fraction of draws" diagram you basically throw them together which you should not, if you want to answer the question whether there are more draws at the start of a match or at the end, etc.  
  > **username_2**: I can think of two ways to analyze this. First option: Consider each match to consist of three parts (start/middle/end). So for a match of 12 rounds you have the first 4 rounds in "start", the next 4 rounds (round 5 to 8) in "middle" and rounds 9 to 12 in "end". Similarly for a match of 24 rounds you'd have rounds 1-8 in "start", 9-16 in "middle" and 17-24 in "end". Collect all the games of all matches from and see what the draw percentage is in each of the three slots ("start"/"mid"/"end").  
  > **username_3**: What was the WC match that only had 4 games?  
  > **username_1**: @username_3 Seems that's how the playoff in Kramnik - Topalov match was labelled in the PGN I have... So not a real match as such.  
  
  ---
  
  