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I have wondered about piece movement statistics, for example:

  • How many times is a piece moved in average (in general, but also per-piece, as I'm guessing the Queen moves more than any specific pawn)?
  • What is the average maximum number of moves for a specific piece?
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    It would also be interesting to know which pieces need an insurance policy. I bet the center pawns have a poor life expectancy... – Tony Ennis Jun 30 '12 at 13:12
  • @TonyEnnis, +1. That sounds like a good question to ask ;-) – ETD Jun 30 '12 at 15:05
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    @TonyEnnis (& ETD) You'll find life expectancy addressed (by me) at chess.stackexchange.com/questions/6081/… – Charles Rockafellor Jun 24 '16 at 12:56
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I found an interesting page featuring the results of some data mining on a sample of 4,226,520 games, and from which answers to your questions can be extracted, at least for that large sample of games, which is probably reasonably reflective of what happens in general.

According to the numbers there, the average game has a ply count of 57.63 (i.e. total number of moves by both White and Black). So the number of times a single piece is moved is, on average,

57.63 / 32 = 1.8009

The page also lists the total number of moves played in these games by each type of piece of each color, from which we can derive the following per-game figures:

White piece moves
-----------------
P: 7.7708 total moves, .9714 per pawn
N: 5.1677 total moves, 2.5838 per knight
B: 4.6259 total moves, 2.3130 per bishop
R: 4.6985 total moves, 2.3493 per rook
Q: 3.5775
K: 3.1718

Black piece moves
-----------------
P: 7.7998 total moves, .9750 per pawn
N: 5.1576 total moves, 2.5788 per knight
B: 4.3511 total moves, 2.1756 per bishop
R: 4.5364 total moves, 2.2682 per rook
Q: 3.4869
K: 3.2875

These figures ignore the fact that some piece moves will have been made my promoted pieces, but on the whole such moves will be a very small piece of the pie, so these numbers shouldn't be too far off the mark.

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    Extremely cool results :) I overestimated the numbers, so glad I asked. My favourite fun-fact from this is that black tends to move his king and pawns, in the expense of the other pieces. Thanks! – Ramon Snir Jun 30 '12 at 15:20
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    @RamonSnir, That average ply count of 57.63 actually does sound a little low; it puts the average game ending at move 29, which sounds a bit early to me (though I could easily be wrong about that). Perhaps there are a lot of "grandmaster draws" in the database that was used. – ETD Jun 30 '12 at 18:10
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    I find it surprising that the rook moves are not higher than the knight moves. Could it be that these games are ending "prematurely" before the rooks start to come actively into play? – Diedrsch Oct 18 '18 at 18:15
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    @Diedrsch, it's quite possible. I don't know how the games were selected. And that possibility does seem to be suggested by (what strikes me as) the low average ply count per game. – ETD Oct 18 '18 at 18:18
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As a minor modification to EDT's material, above:

According to the numbers there, the average game has a ply count of 57.63 (i.e. total number of moves by both White and Black). So the number of times a single piece is moved is, on average,

57.63 / 32 = 1.8009

A given ply will see only one player's piece moved (castling aside). This means that the simplest average to be obtained should approach:

57.63 / 16 = 3.601875

Note: this necessarily doesn't address any variables such as lost pieces, nor does it seek to address per-piece moves. This is intended only to address the special case of a "lossless" [in terms of pieces captured] game.

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