Looking at Piece Heatmaps in Different Openings
I thought that one might also get some insights into an opening by looking at heatmaps of the pieces. Since they show the average position of each piece, one might see where a piece belongs in a certain opening. So I generated heatmaps from grandmaster games to look at a few different openings. Note that the images are a bit blurry here (I don't know why), so if this bothers you, you can read the post on Substack.
To generate the heatmaps, I downloaded between 500 and 1000 grandmaster games for each opening I looked at and counted the number of moves a piece was standing on each square. I then divided these move numbers by the total number of moves to get the percentage of moves the piece spent on that square. Note that I counted the squares for each piece type. So I always looked at the position of both knights at once, instead of having one heatmap for the kingside knight and one for the queenside knight. As a first example, I looked at heatmaps in the exchange variation of the Queen's Gambit Declined. So I only looked at games that reached the following position: https://lichess.org/study/z6Yz25Hp/xVzWSHFB Here are the heatmaps for both colors from 800+ GM games: It’s really interesting to see where the pieces spent most of their time. Some pieces, like the white’s king bishop on d3, find a clear home, whereas other pieces, like black’s queenside knight, move around a lot throughout the games. Looking at the heatmap of the white bishops, one also sees that the light squared bishop seems to be much longer on the board than its counterpart on the dark squares. This indicated that the dark squared bishop gets traded off earlier and more often than the light squared bishop. The pawn structure in the center looks very rigid, but one can see that both sides move the pawns on the flanks to many different squares without any clear pawn push being favored.
One thing that stands out in the heatmaps above is that many pieces spend a lot of time on their starting squares. This comes from the fact that every piece spends the first couple of moves in every game on that square, so they will light up in a heatmap. One could avoid this by only counting a piece after it has moved once. But I didn't like that approach because it doesn't show which pieces stay on their starting squares longer. Instead, I only looked at the pieces after move 7 (an arbitrary cutoff) and generated the heatmaps again. The biggest change is probably in the king positions, since e1 and e8 aren’t very common squares for the kings anymore. Now it’s also quite clear that the white queen doesn’t stay on d1 that long, and most of the time moves to c2. Another thing to note is that as the game progresses, the structure and the placement of the pieces changes a lot, depending on the specific game. So when looking at openings, it might make sense to also introduce an upper limit for the move number one looks at. Below are again the heatmaps for the same games, but now only showing the average piece positions between moves 7 and 30. The visual differences are very subtle, but when one looks at the colorbar besides the heatmaps, it’s clear that the heatmaps are much more concentrated. For example, the black king spent around 30% of the moves on g8 when looking at all moves after move 7 but when introducing the cutoff at move 30, it spends around 40% of the time on g8. Also white’s kingside pawn pushes become less pronounced, which might indicate that many of them only happen in the endgame.
