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For quite some time I have been interested in determining whether material or mobility is more influential in determining the outcome of a game in chess, and I recently did a statistical analysis on a large database of expert-level games to try and answer that question.

The results are rather surprising, and I have written a brief technical summary of the methodology as well as the results. The R code used to perform the analysis is included.  

I will be writing up a research article on this and submitting it to a journal for publication, as I believe it represents an original contribution to the understanding of chess.

Read long the article: Chess Material vs. Mobility: a Statistical Analysis in R

Below is the conclusion:

These results, while both interesting and surprising, are certainly not definitive. The tests above were performed drawing samples from only one dataset of expert games. Also, I have my doubts that the same results will hold for non-expert games, and I am hoping to obtain a large database of such game data to do a comparison.

Further, the results presented here should be confirmed by others performing their own independent analyses. For this reason I am making my code freely available on Github, not only so others can perform their own tests, but also so others can discover if I have made errors in either my code or my analysis. If so, I welcome the feedback so these errors can be corrected and the tests rerun. [Note: I have not yet put this code on Github, but will update this document with a link when I do.]

However, if my analysis was done correctly, then the test data in Tables 5-8 leads to a fascinating answer to our question, “Which is a more important factor in determining the winner of a chess game - material or mobility?” The answer seems to be, It depends whether you are black or white!!

-Kurt Godden

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Comment by Kurt Godden on January 27, 2016 at 6:01pm

Thanks for the note, Morten.  There are MANY more questions I plan to study, and I think many of them can be answered with the data. I plan to continue this research for a long, long time.

Comment by Kurt Godden on January 27, 2016 at 6:00pm

Tahsin, you are correct that mean material is dependent on game length, and perhaps my personal expectation was incorrect.  But in the full article (link above) a hypothesis test clearly shows that mean material for black when black wins is smaller than for the population (which includes white wins and draws), and is significant at the 0.95 level of confidence.  There is no statistical evidence that white's material is different in white wins than it is in the population.  I find it interesting that there is that difference between white and black.  Thank you for pointing out about the influence of game length.  I will study that as I continue my research!

Comment by Tahsin Reasat on January 5, 2016 at 9:40am

Hi Kurt, very interesting article. But I think it is not correct to think that mean material value of a particular side (e.g. white) should increase in case of the sample pool where that (white) is side winning.
Mean material value depends on length of the game. As more moves are played out (the game progresses through opening, middle game, end game), there is a high probability of the pieces getting exchanged, therefore decreasing the mean material value.
In case of decisive games, it is seldom the case that one of the players is defeated in few opening moves and most games are decided in a middle game or an endgame (and pieces gets exchanged), thereby reducing mean material value.
But for the drawn games, in case of the games which has little importance in terms of tournament standing of the involved players, it is not uncommon to agree to a draw in opening few moves, which should increase the mean material value.
Besides, in a game if one side has greater material, it does not always mean he has a better/winning position (e.g., positions regarding exchange sacrifices, piece sacrifices, gambits etc.). It should be difficult to associate any sort of relationship with material and good position.
Just my thoughts... I could be wrong though. Anyway, Keep up the good work :) 

Comment by Morten Bunes Gustavsen on January 5, 2016 at 6:32am

Thanks... very interresting ! 
I guess this kind of anaysis could be used to answer all kinds of chess questions... like the relative value of a pair of Knights and Bishops under various circumstances... To overcome the limits of your computer, you could consider renting a powerfull viritual machine for some hours... I have tested the Microsoft Azure platform, and it looks quite promising (and cheap) ..

Keep up the good work !



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