Chess Endgame Statistics

Statistical work on chess endgames has been done by Müller and Lamprecht back in 2001 (See the book "Fundamental Chess Endings", or the frequency table summarized in Wikipedia). In this article we will present a similar frequency calculation with "refreshed" data (7,040,139 games as of December 2012 that reached 549,314 endgame positions with five or less chess pieces) plus few additional interesting metrics related to the topic. We also narrow down the measurements and come up with relative evaluation criteria helpful to assess the strength of individual players in endgame positions. We have calculated those metrics for few hundred thousands of players.

The table in the Appendix below summarizes the frequency of appearance of each endgame configurations with five or less chess pieces (Two Kings plus at most 3 other pieces). Frequency is defined as the percentage of the time in which the type of endgame appeared at least once. For example: We reach an endgame with Rook and a pawn vs Rook. After 10 moves the pawn is taken and we have a rook vs rook endgame (where players agree for a draw). This example with a single game will result in 50% Rook+Pawn vs Rook and 50% Rook vs Rook. Then, for each end game type we present the percentage of times in which one of the players blundered in this configuration (Blunder means that one of the players could have achieved a draw with optimal play, but after his move he would be losing against optimal play, or, that he had a win but after his move his position was draw or losing. Note that we are not excluding positions in which a blunder was not possible, e.g. when every move is winning or losing, if one does that the blunder rate percentages would increase).

Optimal Endgame Play

As part of ChessDB player database we have calculated how each chess player performs in such endgames and for each player can show you some sample endgame blunders that he/she did. Just search for a player from our home page, or see some examples: The Endgame Optimal Play metric is the rate of how often a player did maintain his winning or drawing position in an endgame (with up to 5 pieces. Analysis with 6, 7 and more pieces is currently ongoing). In other words if a player, before he made a move, had a winning (or drawing) position (as determined by endgame tablebases), and he still had it after he had made the move, then this is considered an "optimal move" for this metric. The optimal play is the percentage of total number of optimal moves from the total number of played moves in the selected endgame positions.

Optimal Endgame Checkmating

While the optimal endgame play metric only measures if the player "maintained" his winning or drawing position this metric (which we call optimal checkmate) considers if the player had made the theoretically best move to reach a checkmate. For example, if theoretically a player had "Mate in 8 moves" but he went for a "Mate in 12" then this is not considered an optimal checkmating move. An optimal checkmating move in this example would be a move (if more than one exists) that actually leads to the mate in 8 moves. The optimal checkmating percentage is usually much lower than the optimal endgame play rate, as people in real environment are not so much bothered to find the best checkmate but most often they see the safest or just any checkmate enough.

Strength in the Most Common Endgames

This Chess-DB feature is coming soon: We would benchmark the relative strength and blunder rate of a play in the three most typical endgames:
  • Pawn endgames (probability of entering such endgame being 22%)
  • Rook endgames (probability of entering such endgame being 19%)
  • Bischop/Knight vs Pawn endgames (probability of entering such endgame being 15%)

Appendix: Frequency and Average Blunder Rate

The tables below summarize the frequency of appearance of each endgame configurations with four to seven chess pieces (the two Kings plus at most 5 other pieces).

Appendix: Average Blunder Rate

The tables below summarize the frequency of appearance of each endgame configurations with five pieces (The two Kings and 3 other pieces) as well as the percentage of times a player facing such configuration blundered on the board.

 White pieces  Black pieces  Frequency  Blunder
15.07% 10.79%
10.99% 3.50%
6.11% 2.16%
6.04% 2.52%
3.92% 4.51%
2.88% 1.84%
2.75% 8.83%
2.72% 2.93%
2.34% 0.26%
2.33% 0.73%
1.82% 0.00%
1.77% 0.11%
1.76% 27.85%
1.53% 2.07%
1.45% 8.26%
1.39% 0.55%
1.37% 7.49%
1.34% 6.12%
1.28% 1.24%
2.38% 2.56%
1.15% 1.44%
1.15% 1.88%
1.15% 1.32%
1.09% 0.77%
1.07% 3.74%
1.06% 7.50%
1.02% 5.33%
0.95% 7.82%
0.95% 0.35%
0.94% 48.35%
0.93% 6.19%
0.79% 2.30%
0.73% 4.46%
0.72% 11.12%
0.71% 3.78%
0.65% 0.08%
0.62% 16.97%
0.55% 0.13%
0.55% 0.00%
Others 11.95% 2.73%
Total 100.00% 5.18%