Statistically correct moves and openings

Here we continue our little work on statistical evaluations of openings.  Please look here

https://www.chess.com/forum/view/chess-openings/statistical-sharpness-and-evaluation

for definitions. I use the data of the chesstempo database considering only positions with 100+ master games. The statistical evaluation of the initial position (defined as the mean value) is equal to +0.39. It suggests the following definition.

Definition 1. A move in the initial position is called statistically correct if its statistical evaluation is no less than +0.39.

It implies that statistically incorrect moves decrease the statistical evaluation of the position. Our calculations in the previous thread give us 5 statistically correct moves in the initial position:

• 1. d4, 595170 games, sh1=1.1, sh2=0.8, ev=+0.46
• 1. Nf3, 170046 games, sh1=1.0, sh2=0.7, ev=+0.47
• 1. c4, 119941 games, sh1= 1.1, sh2=0.7, ev=+0.48
• 1. g3, 14379 games, sh1=1.1, sh2=0.8, ev=+0.42

General definition. Let a position Y be a legal successor of a position X by a move m: X->Y. We say that m is statistically correct if ev(Y)>=ev(X) when white moves and vice versa when black moves.

We'll give examples starting from the post #4.

• #4 King's Pawn opening
• #37 Queen's Pawn opening (Differentiation2)

 N.B. My special thanks to Differentiation2 who contributed a lot to this thread. 

SylentSwords: Thanks for this meaningful comment shedding some light on statistical evaluations.

Let's denote KP the position after the move 1. e4. According to our general definition, a move m: KP -> Y is statistically correct if ev(Y)=< ev(KP)+0.1=0.4. Here's the list of statistically correct black replies to the King's Pawn opening:

• 1...c5 Sicilian defense, ev=+0.1
• 1...e5 King's Pawn game, ev=+0.4
• 1...e6 French defense, ev=+0.4
• 1...c6 Caro-Kann defense, ev=+0.3
• 1...d6 Pirc defense, ev=+0.4
• 1...g6 Modern defense, ev=+0.1
• 1...Nf6 Alekhine defense, ev=+0.4
• 1...Nc6 Nimzovich defense, ev=+0.3

Here we have our first surprise. The Modern defense is, statistically, as strong as Sicilian.

Statistically incorrect defenses:

• 1...d5 Scandinavian defense, ev=+0.6
• 1...b6 Owen defense, ev=+0.5
• 1...a6 St. George defense, ev=+0.7

Differentiation2: I consider positions with 100+ master games.

There are three types of lies in this world. lies. dammed lies and statistics. 

Mark Twain

I don't think that statistics of 16000+ master games could be anomalous, the probability is close to zero. I guess that Kramnik uses sublines outside of mainstream Petrov where black statistics become correct.

Also, when a position is really drawish with low sharpness, the statistical evaluation becomes less important.

LoL

It's okay cuz white moves and the evaluation of 1. e4 e5 is +0.4. So, the evaluation of a statistically correct white move should be higher or equal to +0.3.

Yeah, it's a big surprise for me too that Petrov has so poor statistic results for black.

0.04 is not so important difference imho in this context. We can consider that the Modern defense is as good as Sicilian.

What is more surprising for me is that 1...g6 is much better than 1...d6. I thought that these moves are almost fully interchangeable.

Sorry brah but chess is an art, no place for objective evaluations, just feelings.

Indeed, black has only 16% of wins !?!

Yeah, but for mathematicians statistics are also an art.

stop refuting my comments 

Thanks for another insightful thread, Yigor (and thank you to those of you who collaborate). I'm afraid I've got no insight to add, but I love reading things like this.

Traxler countrattack is indeed very double-edged and tricky. We discussed it a lot here. It turns out, for example, that 5. Nxf7 with great engine evaluations is not good for white with correct black's play. Engines miss it even at high depth.

Hey, U are welcome! Actually, these calculations are really easy, U can do it yourself.

Thanks for these interesting insights and I'm glad that U have a hypothetical explanation.

One more big surprise: 1...d5 is statistically incorrect reply to the Queen's Pawn opening 1. d4, ev(1...d5)=+0.7.