Material Imbalances and Game Outcomes

I posted this on reddit yesterday and thought you guys might be interested. I used the Caïssabase database (4.02M games) to look at the effect of common material imbalances on game outcomes... In particular, I looked at the win rate when the game features:

1. A queen vs. two rooks or a rook and minor piece
2. A rook vs two minor pieces in an ending
3. The bishop pair

I was interested in these material imbalances in particular because we hear stuff about them (e.g., two rooks are better than a queen, two minor pieces better than a rook, bishop pair is better than B+N)

Here's what I found: sites.google.com/view/patrick-coulombe-phd/chess-analytics/material-imbalances-and-game-outcomes I found the first one in particular suprising personally, but in any case let me know your thoughts

This is interesting, and I'm quite surprised at the 2R v Q statistics. I can't help but wonder if that is a case of it being easier to capitalize on time-pressure blunders with the Queen, as forks come out of nowhere.

I'm curious if the statistics hold true when both players are good. For instance, under 2300, the so-called Linares variation of the QGA (1.d4 d5 2.c4 dxc4 3.e4 c5?!) scores better for Black than for White, but above 2300 White basically never loses. I've also heard that the surest way to tell how good a player is is to see how well they wield the two Bishops.

So, in short, do these statistics change when both sides are above 2300? 2500? What about in engine matches? Something to ponder. Regardless, thanks for the interesting post!

@SmithyQ ,
Both Stockfish and Leela prefer Queen over Two rooks in both endgame and middle game

This is a matter of data, and strength, not logic. I used @SmithyQ 's answers to make a player -strength map. Players under 1500 prefer queen over the 2 rooks. These players also prefer rook vs 2 minors. The same players prefer the bishop pair. Players 1500-2000 prefer... queen over 2 rooks, 2 minors over a rook, and a bishop pair over a bishop knight duo. Players 2000+ prefer the 2 rooks, and the 2 bishops over a rook, and the two bishops over the knight duo. @drmrboss i am not ignoring your data, it is correct, engines prefer the queen. Although they prefer the rook, and say its a draw! But the bishop vs knight is in the bishops favour. Good research @Patrizsche i read it all and loved it. This is very interesting. I prefer the 2 rooks. The rook over the minors, and the knight duo, so this is also opinion- wise. Thanks for the time, Anshul

@SmithyQ that's an interesting question, and I did look at differences between rating ranges (with 100 increments, as given by Scid), and there was basically no relationship, line graphs showed flat lines, i.e. that pattern was the same across the board... The only exception was that there were more draws for games between players >2700 (there were very few of those, but I did include them in the graphs)

one question, @Patrizsche was there any opinion wise data in your research?

When you investigated Q vs. RR, were there other pieces present or only pawns and the omnipresent kings?
Conventional wisdom is
RR > Q
RRN < QN
A queen coordinates well with a knight and a rook does not coordinate well with a knight.
Conventional reasoning is that RR can attack a pawn twice, while the queen can only defend it once.

About the bishop vs. knight your research concures with that of Kasparov, who derived a bishop is worth 3.25 pawn and a knight is worth 3 pawns, as previously said by Fischer.

@tpr like the resoaning

@MUMAnshul130105 I'm not sure what you mean by opinion wise, but I used chess games from the database Caïssabase, searching by patterns. I didn't inject any other information into my analysis, this is merely descriptive.

@Patrizsche i mean did you take people's opinions in your data. ok