Answers.Body: <p>I wanted to remove effects of the early opening and the endgame from the analysis. So, I did a similar analysis as Daniel B, but I only used moves 10 to 29 (inclusively). Here are the results.
  <a href="https://i.sstatic.net/m4cOk.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/m4cOk.png" alt="Move frequencies in the middle game by Elo rating" /></a></p>
  <p>Many trends are visible in this chart.</p>
  <ul>
  <li>King moves get less frequent the better the player.</li>
  <li>Queen moves get less frequent the better the player.</li>
  <li>Rook moves are more frequent for bad players, but plateau around Elo 2000 and the trend upwards again.</li>
  <li>Bishop moves are less frequent for bad players, but plateau from 1500 to 2000 and then tend to trend downwards again.</li>
  <li>Knight moves get more frequent for better players.</li>
  <li>Pawn moves get more frequent for better players.</li>
  <li>As for castling, there seems to be a trend for good players to castle more, plateauing at Elo 2700, and then a sharp downwards trend for the elite players with Elo bigger than 2700.</li>
  </ul>
  <p>Some technical notes:</p>
  <p>I did my analysis on the <a href="http://rebel13.nl/dl/mb-3.45.7z" rel="nofollow noreferrer">Rebel 13 Dataset</a> which contains 3456762 games. Some data cleanup was needed for me to parse everything (in particular, I had to remove non-ASCII characters). I only analyzed games where the Elo of both players was given. This resulted in 2375013 games with a total of 84909433 plies used.</p>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2022-03-23T08:13:35.590Z
Answers.LastActivityDate: 2022-03-23T08:13:35.590Z
Answers.UserDisplayName: Eigentime
Answers.Body: <p>Here is a quick an dirty analysis based on the "Million Base" PGN database.  I did this in a bit of a rush, so there may well be errors in my programming or logic.  Please don't use it for anything too serious.  <strong>Update - Note:</strong> Actually, I've just noticed I made a mistake with the data set, and limited it to the first 1 million records.  I'll post an update when I get some free time to run it again on the full thing.  In the meantime, these numbers should be interesting, nevertheless. </p>
  
  <h1>Obtaining the data:</h1>
  
  <p>I obtained the Million Base 1.74 file from <a href="http://rapidlibrary.com/files/old-million-base-1-74-rar_ulztvvxqf8i89on.html" rel="noreferrer">this URL</a>, since the top-5000.nl site seems to 404 when you actually try to download it.  The file contains just over 1 million games in PGN export format (that is to say, easy to parse).</p>
  
  <p>Unfortunately, more than 60% of the games lacked any rating information (I was looking for "WhiteELO" and "BlackELO" tags), and even fewer had ratings for both players.  In the end, I decided to get as large a sample size as I could, and counted a player's moves if his or her rating was known, regardless of the other player's rating.</p>
  
  <h1>Process:</h1>
  
  <p>The games were parsed one by one, and if a player's rating was known, all of <em>their</em> moves for that game would be added to the aggregate for the player's rating group.  I chose to divide the ratings into groups of 100, so e.g. 1600 to 1699 was a single group.</p>
  
  <p>Since the actual movetext in PGN is SAN, I used the following shortcut to count the moves:  Knight (N), Bishop (B), Rook (R), Queen (Q) and King (K) moves all begin with their piece's letter.  Castling (O-O and O-O-O) was counted separately, as a special case.  All remaining moves were counted as pawn moves without further examination.</p>
  
  <p>No data cleanup was done.  There was no attempt to identify outliers and remove them (e.g. exceedingly short and long games, etc).  I kept, but did not include in the following analysis, the results from ratings below 1600 - the sample size for these games was well below 100, leading to large variations in results.  The raw data is provided at the end of this post.</p>
  
  <p>Some shortcomings of the information:  at the moment, I've only collected very basic totals, and provided averages.  I am pretty sure that in general, the data is NOT normally distributed, but won't be able to say more without actually outputting the raw counts and running them through a statistical program.  I may do so, if there's interest.  For the moment, this means no confidence intervals, or other information about the distribution of the numbers that those averages represent.  I also haven't checked how many years the data set spans - if it represents many years, it may be beneficial to attempt to correct for the overall strength of the field.</p>
  
  <h1>Some Trends:</h1>
  
  <p>A word on player ratings - the most frequent rating groups encountered were, in order:  2400 to 2500, 2500 to 2600, and 2300 to 2400.  These rating groups provided 72% of the games counted.   </p>
  
  <p>Looking at the actual results, average game length was a bit of a surprise:</p>
  
  <p><img src="https://i.sstatic.net/AbtqU.jpg" alt="Average number of moves by rating group"></p>
  
  <p>The sub-2000 rating groups all had significantly shorter games than the higher groups.  This may well be explained by the possibility that they were playing stronger opponents (see the average rating, above), and that they were defeated in fewer moves.  This seems to go against the slightly shorter games played by the top rating group, although that may be contributed to a smaller sample size.   </p>
  
  <p>The relatively large differences in average game length meant that providing the frequency of moving a certain piece, rather than the total number of times a piece is moved, is perhaps the more fair comparison.  Calculating the frequencies results in the following graph:</p>
  
  <p><img src="https://i.sstatic.net/z0Yz9.jpg" alt="Move frequencies by piece"></p>
  
  <p>The following trends seem to be present:</p>
  
  <ul>
  <li>The frequency of knight moves seems to trend slightly downwards with rating.</li>
  <li>Bishop moves trend downwards until about 2000, then slowly trend upwards.</li>
  <li>Rook moves trend sharply upward at roughly the same point, and stay more frequent than Bishop moves in high-level play.</li>
  <li>Pawn moves seem to trend slightly downwards with increased rating.  A large exception is the top category, 2800 to 2900.  This brings us to the next point:</li>
  <li>The top rating category provides outliers or counter-trends in quite a number of measurements.  This may be explained in a variety of ways - 1) the sample size is fairly low at 363, not tiny, but 10% of the next smallest sample size included.  2) Since they are at the top of the ratings groups, they never play "stronger" opponents than themselves.  3) Or simply at this level, their play style has transcended the levels below them.  My guess would be a combination of 1) and 2).</li>
  <li>The differences in queen moves and castling moves is very small without any real trends, other than a tiny trend downwards in both cases.</li>
  <li>The frequency of king moves has some of the largest differences.  No clear trend is visible, and it seems to change direction 3 or 4 times.</li>
  </ul>
  
  <h1>Further Analysis</h1>
  
  <p>Some ideas for future analysis:</p>
  
  <ul>
  <li>Basic statistical fixes:  I feel that extremely short and long games should probably be excluded.  Also, the distribution of the actual counts might be very telling.</li>
  <li>Splitting the analysis further up may also yield interesting results.  For example, I would be interested to know how the frequencies for black and white match up (Are they the same, or different?  Why?).  </li>
  <li>Categorisation by difference in rating might also be interesting, do players playing a much stronger opponent (say, 200 ratings above them) play with different move frequencies?  Unfortunately this requires both players' ELO to be known, which is rare in this data set.</li>
  <li>Tendency to short vs. long-castle might also vary by rating.</li>
  <li>Piece promotion statistics, some light structural analysis (e.g. incidence of doubled pawns, en passant, pins, forks, shown by rating) might be insightful.</li>
  <li>"Heat-maps" of piece placement on the actual board, shown by rating might also be quite intersting.</li>
  </ul>
  
  <h1>Aggregate data in CSV format</h1>
  
  <p>For those who want to play with the data, feel free.</p>
  
  <p>Rating Range,Sample Size,Average Game Length,Average Pawn Moves,Average Knight Moves,Average Bishop Moves,Average Rook Moves,Average Queen Moves,Average King Moves,Average Castling</p>
  
  <pre><code>1100 to 1200,4,28.500,7.000,4.000,4.000,6.500,3.750,2.750,0.500
  1300 to 1400,16,34.125,9.250,6.813,5.000,4.438,4.563,3.188,0.875
  1400 to 1500,35,33.800,9.400,6.114,5.514,4.514,4.057,3.400,0.800
  1500 to 1600,61,33.607,8.705,7.459,4.984,4.443,4.033,3.148,0.836
  1600 to 1700,163,33.153,9.227,6.485,5.110,4.699,3.969,2.816,0.847
  1700 to 1800,301,31.811,8.894,6.223,5.402,4.468,3.734,2.296,0.794
  1800 to 1900,307,34.251,9.537,6.642,5.577,4.889,4.039,2.759,0.808
  1900 to 2000,450,35.551,9.731,6.778,5.451,5.444,4.442,2.871,0.833
  2000 to 2100,3958,38.731,10.302,7.095,6.072,6.242,4.668,3.481,0.871
  2100 to 2200,11217,38.905,10.501,7.116,6.086,6.245,4.629,3.445,0.884
  2200 to 2300,50848,39.446,10.595,7.167,6.174,6.420,4.717,3.484,0.889
  2300 to 2400,79322,39.248,10.551,7.141,6.141,6.469,4.653,3.402,0.891
  2400 to 2500,111867,38.394,10.398,7.013,6.086,6.294,4.542,3.168,0.893
  2500 to 2600,92225,38.308,10.396,6.972,6.082,6.344,4.515,3.104,0.896
  2600 to 2700,33193,39.340,10.565,7.061,6.295,6.579,4.630,3.318,0.891
  2700 to 2800,4805,40.938,10.945,7.221,6.725,6.930,4.726,3.494,0.895
  2800 to 2900,363,38.865,11.311,6.879,6.284,6.160,4.391,2.983,0.857
  </code></pre>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2020-11-10T14:47:57.697Z
Answers.Text: Did you exclude resigned games? Those at the very top are more likely to resign much earlier in a lost game, which would greatly skew *everything*.
Answers.UserDisplayName: user21820
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2012-07-27T18:13:31.747Z
Answers.Text: Nice! Thanks for running the numbers here. By the way, if you think any of the ideas in your "further analysis" section are ripe to be asked about, please don't hesitate to do so.
Answers.UserDisplayName: ETD
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2012-07-31T06:14:44.200Z
Answers.Text: @EdDean thanks, and I will probably do some further analysis when time permits.  I've also noticed some further improvements that can be made (e.g. filtering out blitz and simultan games, and possibly others), so it's probably going to be a bit of work.  I'll create an update when I have something.
Answers.UserDisplayName: Daniel B
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2012-08-17T13:00:23.557Z
Answers.Text: Wow. That was quite an answer. Fantastic.
Answers.UserDisplayName: James Tomasino
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2013-05-29T12:48:26.923Z
Answers.Text: I wouldn't be surprised if, say, the increased number of rook moves among strong players just means that they are more likely to end up in long rook endings, rather than that they move rooks more often in similar positions.
Answers.UserDisplayName: dfan
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2013-05-30T06:44:10.480Z
Answers.Text: @dfan I agree, these numbers might have more to do with various 2nd-order effects, e.g. lower rated players blundering early on and not getting into a long endgame, etc.  I have various ideas on how it could be made more accurate, but unfortunately no time to implement them.
Answers.UserDisplayName: Daniel B
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2012-07-26T19:53:18.543Z
Answers.LastActivityDate: 2019-09-21T13:37:10.417Z
Answers.LastEditDate: 2019-09-21T13:37:10.417Z
Answers.UserDisplayName: Daniel B
Body: <p>This question is an offshoot of Ramon Snir's <a href="https://chess.stackexchange.com/q/979/167">earlier one</a> about how often different types of pieces get moved, on average, in a game of chess. My question:</p>
  
  <blockquote>
    <p>Do the relative numbers of moves for the given types of pieces differ when one looks at the games of stronger players as opposed to the games of weaker players? (For example, maybe the weaker players tend to make more pawn moves at the expense of piece moves, or they make too many queen moves. I don't know.)</p>
  </blockquote>
  
  <p>I was able to give an answer to the earlier question using raw data that had been extracted from a large database <a href="http://www.vanheusden.com/cchess/datamining_on_chess.html" rel="noreferrer">by someone else</a>. That data came from a sample of 4M+ games, ranging from grandmaster play down to weak amateur play, and the aggregate numbers for move totals that are given there don't discriminate on the basis of player strength. Answering my question will require getting separate data for games between strong players and games between weak players, and <em>I am looking for answers backed up by data rather than anecdotes</em>.</p>
  
  <p>Here's a more specific form of my question:</p>
  
  <blockquote>
    <p>Is there some Elo rating threshold N such that, when one looks at the average numbers of moves in a game broken down by type of piece, there's a significant difference between what one finds in games featuring players above N, and what one finds in games featuring players below N.</p>
  </blockquote>
  
  <p>It would be interesting if more of this sort of thing could be found too, i.e. concrete differences between stronger and weaker players that can be detected by data mining. Such findings could point to specific behaviors that hold players back, or conversely ones that propel them forward. Now, maybe there aren't any such differences to be found just by looking at this kind of data, but I'd be interested to know that too.</p>
  
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2012-07-02T13:37:51.280Z
Comments.Text: I'm a bit suspicious about such aggregated data, because it might miss the point. Some games are decided by play with pieces others by pushing pawns. The frequency of a piece moved says nothing about the quality of the moves. There is a rule of thumb that says you shouldn't move a single piece frequently in the opening. However, strong players adopt this tactics sometimes, if it is justified by the position.
Comments.UserDisplayName: Michael
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2012-07-03T15:24:55.920Z
Comments.Text: @Michael, I agree entirely that a factor such as the one I'm asking about wouldn't in itself be indicative of good play; if I move my piece types at the same relative frequency as Aronian, say, it of course doesn't mean that I'm playing as well as he is. But that's exactly why it could be that above, say, Elo 1800, there is no detectable difference in these relative frequencies (though there is a huge range of abilities above 1800), while below 1800 it's significantly skewed. That finding in the data could indicate *one factor* behind a player being below that strength threshold.
Comments.UserDisplayName: ETD
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2012-07-10T07:30:45.517Z
Comments.Text: Keep in mind that the data are going to show you what grandmasters do _when they are facing other grandmasters_, and likewise with lesser players. Ideally you'd want to compare what better and worse players do _in identical positions_, but that would probably not be possible through datamining, except for in the opening.
Comments.UserDisplayName: Evan Harper
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2012-07-25T13:16:06.063Z
Comments.Text: @EdDean - this is quite an interesting topic.  Any idea where exactly he got the 4M+ games?  Is there a place where we could get something of significant size (say, 100K+ games), from a reputable but free source?  I'm specifically thinking of an easily downloadable source, as opposed to "online searchable".
Comments.UserDisplayName: Daniel B
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2012-07-25T13:28:07.943Z
Comments.Text: Just to follow up, Wikipedia has a nice page on [chess game collections](http://en.wikipedia.org/wiki/Chess_game_collection).  Out of these, the first link seemed by far the most promising (relatively small number of zipped PGNs to download), but large sections are missing (ECO codes B to E), which would make the analysis very one sided and quite useless.
Comments.UserDisplayName: Daniel B
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2012-07-26T07:43:22.740Z
Comments.Text: @DanielB, there are free sources of games like the Million Base 1.74 PGN database that's available here: http://www.top-5000.nl/pgn.htm
Comments.UserDisplayName: ETD
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2012-07-26T07:54:11.047Z
Comments.Text: @EdDean that looks quite good.  The main website's download link seems to be broken, but I think it's possible to find copies of it on the net.  I should have a bit of free time in the next few weeks, I'll see if I can extract some data from it.
Comments.UserDisplayName: Daniel B
Tags: <learning><statistics><pieces>
Title: Do strong players move their pieces with different relative frequencies than weak players?
ThreadText: # Do strong players move their pieces with different relative frequencies than weak players?
  
  (Asked by: username_0 on 2012-06-30)
  
  This question is an offshoot of Ramon Snir's [earlier one](https://chess.stackexchange.com/q/979/167) about how often different types of pieces get moved, on average, in a game of chess. My question:
  
  > Do the relative numbers of moves for the given types of pieces differ when one looks at the games of stronger players as opposed to the games of weaker players? (For example, maybe the weaker players tend to make more pawn moves at the expense of piece moves, or they make too many queen moves. I don't know.)
  
  I was able to give an answer to the earlier question using raw data that had been extracted from a large database [by someone else](http://www.vanheusden.com/cchess/datamining_on_chess.html). That data came from a sample of 4M+ games, ranging from grandmaster play down to weak amateur play, and the aggregate numbers for move totals that are given there don't discriminate on the basis of player strength. Answering my question will require getting separate data for games between strong players and games between weak players, and *I am looking for answers backed up by data rather than anecdotes*.
  
  Here's a more specific form of my question:
  
  > Is there some Elo rating threshold N such that, when one looks at the average numbers of moves in a game broken down by type of piece, there's a significant difference between what one finds in games featuring players above N, and what one finds in games featuring players below N.
  
  It would be interesting if more of this sort of thing could be found too, i.e. concrete differences between stronger and weaker players that can be detected by data mining. Such findings could point to specific behaviors that hold players back, or conversely ones that propel them forward. Now, maybe there aren't any such differences to be found just by looking at this kind of data, but I'd be interested to know that too.
  
  **Tags:** learning, statistics, pieces
  
  > **Comments:**
  > **username_1**: I'm a bit suspicious about such aggregated data, because it might miss the point. Some games are decided by play with pieces others by pushing pawns. The frequency of a piece moved says nothing about the quality of the moves. There is a rule of thumb that says you shouldn't move a single piece frequently in the opening. However, strong players adopt this tactics sometimes, if it is justified by the position.  
  > **username_0**: @username_1, I agree entirely that a factor such as the one I'm asking about wouldn't in itself be indicative of good play; if I move my piece types at the same relative frequency as Aronian, say, it of course doesn't mean that I'm playing as well as he is. But that's exactly why it could be that above, say, Elo 1800, there is no detectable difference in these relative frequencies (though there is a huge range of abilities above 1800), while below 1800 it's significantly skewed. That finding in the data could indicate *one factor* behind a player being below that strength threshold.  
  > **username_2**: Keep in mind that the data are going to show you what grandmasters do _when they are facing other grandmasters_, and likewise with lesser players. Ideally you'd want to compare what better and worse players do _in identical positions_, but that would probably not be possible through datamining, except for in the opening.  
  > **username_3**: @EdDean - this is quite an interesting topic.  Any idea where exactly he got the 4M+ games?  Is there a place where we could get something of significant size (say, 100K+ games), from a reputable but free source?  I'm specifically thinking of an easily downloadable source, as opposed to "online searchable".  
  > **username_3**: Just to follow up, Wikipedia has a nice page on [chess game collections](http://en.wikipedia.org/wiki/Chess_game_collection).  Out of these, the first link seemed by far the most promising (relatively small number of zipped PGNs to download), but large sections are missing (ECO codes B to E), which would make the analysis very one sided and quite useless.  
  > **username_0**: @username_3, there are free sources of games like the Million Base 1.74 PGN database that's available here: http://www.top-5000.nl/pgn.htm  
  > **username_3**: @EdDean that looks quite good.  The main website's download link seems to be broken, but I think it's possible to find copies of it on the net.  I should have a bit of free time in the next few weeks, I'll see if I can extract some data from it.  
  
  ---
  
  ## 2 answers
  
  ### Answer by username_3 on 2012-07-26. Score: 41 | Accepted answer
  
  Here is a quick an dirty analysis based on the "Million Base" PGN database. I did this in a bit of a rush, so there may well be errors in my programming or logic. Please don't use it for anything too serious. **Update - Note:** Actually, I've just noticed I made a mistake with the data set, and limited it to the first 1 million records. I'll post an update when I get some free time to run it again on the full thing. In the meantime, these numbers should be interesting, nevertheless.
  
  # Obtaining the data:
  
  I obtained the Million Base 1.74 file from [this URL](http://rapidlibrary.com/files/old-million-base-1-74-rar_ulztvvxqf8i89on.html), since the top-5000.nl site seems to 404 when you actually try to download it. The file contains just over 1 million games in PGN export format (that is to say, easy to parse).
  
  Unfortunately, more than 60% of the games lacked any rating information (I was looking for "WhiteELO" and "BlackELO" tags), and even fewer had ratings for both players. In the end, I decided to get as large a sample size as I could, and counted a player's moves if his or her rating was known, regardless of the other player's rating.
  
  # Process:
  
  The games were parsed one by one, and if a player's rating was known, all of *their* moves for that game would be added to the aggregate for the player's rating group. I chose to divide the ratings into groups of 100, so e.g. 1600 to 1699 was a single group.
  
  Since the actual movetext in PGN is SAN, I used the following shortcut to count the moves: Knight (N), Bishop (B), Rook (R), Queen (Q) and King (K) moves all begin with their piece's letter. Castling (O-O and O-O-O) was counted separately, as a special case. All remaining moves were counted as pawn moves without further examination.
  
  No data cleanup was done. There was no attempt to identify outliers and remove them (e.g. exceedingly short and long games, etc). I kept, but did not include in the following analysis, the results from ratings below 1600 - the sample size for these games was well below 100, leading to large variations in results. The raw data is provided at the end of this post.
  
  Some shortcomings of the information: at the moment, I've only collected very basic totals, and provided averages. I am pretty sure that in general, the data is NOT normally distributed, but won't be able to say more without actually outputting the raw counts and running them through a statistical program. I may do so, if there's interest. For the moment, this means no confidence intervals, or other information about the distribution of the numbers that those averages represent. I also haven't checked how many years the data set spans - if it represents many years, it may be beneficial to attempt to correct for the overall strength of the field.
  
  # Some Trends:
  
  A word on player ratings - the most frequent rating groups encountered were, in order: 2400 to 2500, 2500 to 2600, and 2300 to 2400. These rating groups provided 72% of the games counted.
  
  Looking at the actual results, average game length was a bit of a surprise:
  
  ![Average number of moves by rating group](https://i.sstatic.net/AbtqU.jpg)
  
  The sub-2000 rating groups all had significantly shorter games than the higher groups. This may well be explained by the possibility that they were playing stronger opponents (see the average rating, above), and that they were defeated in fewer moves. This seems to go against the slightly shorter games played by the top rating group, although that may be contributed to a smaller sample size.
  
  The relatively large differences in average game length meant that providing the frequency of moving a certain piece, rather than the total number of times a piece is moved, is perhaps the more fair comparison. Calculating the frequencies results in the following graph:
  
  ![Move frequencies by piece](https://i.sstatic.net/z0Yz9.jpg)
  
  The following trends seem to be present:
  
  * The frequency of knight moves seems to trend slightly downwards with rating.
  * Bishop moves trend downwards until about 2000, then slowly trend upwards.
  * Rook moves trend sharply upward at roughly the same point, and stay more frequent than Bishop moves in high-level play.
  * Pawn moves seem to trend slightly downwards with increased rating. A large exception is the top category, 2800 to 2900. This brings us to the next point:
  * The top rating category provides outliers or counter-trends in quite a number of measurements. This may be explained in a variety of ways - 1) the sample size is fairly low at 363, not tiny, but 10% of the next smallest sample size included. 2) Since they are at the top of the ratings groups, they never play "stronger" opponents than themselves. 3) Or simply at this level, their play style has transcended the levels below them. My guess would be a combination of 1) and 2).
  * The differences in queen moves and castling moves is very small without any real trends, other than a tiny trend downwards in both cases.
  * The frequency of king moves has some of the largest differences. No clear trend is visible, and it seems to change direction 3 or 4 times.
  
  # Further Analysis
  
  Some ideas for future analysis:
  
  * Basic statistical fixes: I feel that extremely short and long games should probably be excluded. Also, the distribution of the actual counts might be very telling.
  * Splitting the analysis further up may also yield interesting results. For example, I would be interested to know how the frequencies for black and white match up (Are they the same, or different? Why?).
  * Categorisation by difference in rating might also be interesting, do players playing a much stronger opponent (say, 200 ratings above them) play with different move frequencies? Unfortunately this requires both players' ELO to be known, which is rare in this data set.
  * Tendency to short vs. long-castle might also vary by rating.
  * Piece promotion statistics, some light structural analysis (e.g. incidence of doubled pawns, en passant, pins, forks, shown by rating) might be insightful.
  * "Heat-maps" of piece placement on the actual board, shown by rating might also be quite intersting.
  
  # Aggregate data in CSV format
  
  For those who want to play with the data, feel free.
  
  Rating Range,Sample Size,Average Game Length,Average Pawn Moves,Average Knight Moves,Average Bishop Moves,Average Rook Moves,Average Queen Moves,Average King Moves,Average Castling
  
  ```
  1100 to 1200,4,28.500,7.000,4.000,4.000,6.500,3.750,2.750,0.500
  1300 to 1400,16,34.125,9.250,6.813,5.000,4.438,4.563,3.188,0.875
  1400 to 1500,35,33.800,9.400,6.114,5.514,4.514,4.057,3.400,0.800
  1500 to 1600,61,33.607,8.705,7.459,4.984,4.443,4.033,3.148,0.836
  1600 to 1700,163,33.153,9.227,6.485,5.110,4.699,3.969,2.816,0.847
  1700 to 1800,301,31.811,8.894,6.223,5.402,4.468,3.734,2.296,0.794
  1800 to 1900,307,34.251,9.537,6.642,5.577,4.889,4.039,2.759,0.808
  1900 to 2000,450,35.551,9.731,6.778,5.451,5.444,4.442,2.871,0.833
  2000 to 2100,3958,38.731,10.302,7.095,6.072,6.242,4.668,3.481,0.871
  2100 to 2200,11217,38.905,10.501,7.116,6.086,6.245,4.629,3.445,0.884
  2200 to 2300,50848,39.446,10.595,7.167,6.174,6.420,4.717,3.484,0.889
  2300 to 2400,79322,39.248,10.551,7.141,6.141,6.469,4.653,3.402,0.891
  2400 to 2500,111867,38.394,10.398,7.013,6.086,6.294,4.542,3.168,0.893
  2500 to 2600,92225,38.308,10.396,6.972,6.082,6.344,4.515,3.104,0.896
  2600 to 2700,33193,39.340,10.565,7.061,6.295,6.579,4.630,3.318,0.891
  2700 to 2800,4805,40.938,10.945,7.221,6.725,6.930,4.726,3.494,0.895
  2800 to 2900,363,38.865,11.311,6.879,6.284,6.160,4.391,2.983,0.857
  
  ```
  
  > **Comments:**
  > **username_0**: Nice! Thanks for running the numbers here. By the way, if you think any of the ideas in your "further analysis" section are ripe to be asked about, please don't hesitate to do so.  
  > **username_3**: @EdDean thanks, and I will probably do some further analysis when time permits.  I've also noticed some further improvements that can be made (e.g. filtering out blitz and simultan games, and possibly others), so it's probably going to be a bit of work.  I'll create an update when I have something.  
  > **username_6**: Wow. That was quite an answer. Fantastic.  
  > **username_7**: I wouldn't be surprised if, say, the increased number of rook moves among strong players just means that they are more likely to end up in long rook endings, rather than that they move rooks more often in similar positions.  
  > **username_3**: @username_7 I agree, these numbers might have more to do with various 2nd-order effects, e.g. lower rated players blundering early on and not getting into a long endgame, etc.  I have various ideas on how it could be made more accurate, but unfortunately no time to implement them.  
  > **username_5**: Did you exclude resigned games? Those at the very top are more likely to resign much earlier in a lost game, which would greatly skew *everything*.  
  
  ---
  
  ### Answer by username_4 on 2022-03-23. Score: 1
  
  I wanted to remove effects of the early opening and the endgame from the analysis. So, I did a similar analysis as username_3 B, but I only used moves 10 to 29 (inclusively). Here are the results.
  [![Move frequencies in the middle game by Elo rating](https://i.sstatic.net/m4cOk.png)](https://i.sstatic.net/m4cOk.png)
  
  Many trends are visible in this chart.
  
  * King moves get less frequent the better the player.
  * Queen moves get less frequent the better the player.
  * Rook moves are more frequent for bad players, but plateau around Elo 2000 and the trend upwards again.
  * Bishop moves are less frequent for bad players, but plateau from 1500 to 2000 and then tend to trend downwards again.
  * Knight moves get more frequent for better players.
  * Pawn moves get more frequent for better players.
  * As for castling, there seems to be a trend for good players to castle more, plateauing at Elo 2700, and then a sharp downwards trend for the elite players with Elo bigger than 2700.
  
  Some technical notes:
  
  I did my analysis on the [Rebel 13 Dataset](http://rebel13.nl/dl/mb-3.45.7z) which contains 3456762 games. Some data cleanup was needed for me to parse everything (in particular, I had to remove non-ASCII characters). I only analyzed games where the Elo of both players was given. This resulted in 2375013 games with a total of 84909433 plies used.
  
  
  ---
  
  