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This question is an offshoot of Ramon Snir's earlier one 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. 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.

  • 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. – Michael Jul 2 '12 at 13:37
  • @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. – ETD Jul 3 '12 at 15:24
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    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. – Evan Harper Jul 10 '12 at 7:30
  • @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". – Daniel B Jul 25 '12 at 13:16
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    Just to follow up, Wikipedia has a nice page on chess game collections. 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. – Daniel B Jul 25 '12 at 13:28
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+50

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, 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

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

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 double-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
  • 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. – ETD Jul 27 '12 at 18:13
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    @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. – Daniel B Jul 31 '12 at 6:14
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    Wow. That was quite an answer. Fantastic. – James Tomasino Aug 17 '12 at 13:00
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    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. – dfan May 29 '13 at 12:48
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    @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. – Daniel B May 30 '13 at 6:44

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