Statistical sharpness and evaluation

Starting with W/D/B Explorer's statistics I'll define the (white and black) statistical sharpness as the ratios sh1=W/D and sh2=B/D. Statistically, the best moves for white are those when sh1 is big and sh2 is small. When both values are big, it's double-edged. The sharpness of a totally drawish position is 0. The statistical evaluation of a move can be defined as

ev = (sh1/sh2) - 1 = W/B - 1 if sh1 > sh2

ev = 1- (sh2/sh1) = 1 - B/W if sh2 > sh1

Here's the derived sharpness and evaluation data in the initial position:

• 1. e4, 879507 games, sh1=1.2, sh2=0.9, ev=+0.3
• 1. d4, 693538 games, sh1=1.1, sh2=0.8, ev=+0.4
• 1. Nf3, 194186 games, sh1=1.0, sh2=0.7, ev=+0.5
• 1. c4, 142423 games, sh1= 1.1, sh2=0.7, ev=+0.5
• 1. g3, 16927 games, sh1=1.1, sh2=0.8, ev=+0.4
• 1. b3, 7727 games, sh1=1.3, sh2=1.2, ev=+0.1
• 1. f4, 6453 games, sh1=1.3, sh2=1.7, ev=-0.3
• 1. Nc3, 2607 games, sh1=1.4, sh2=1.6, ev=-0.3
• 1. b4, 2036 games, sh1=1.6, sh2=1.9, ev=-0.2

P.S. My thanks go to Sqod who gave me this simple idea of statistical sharpness in an other thread.

Okay, let's now extend our little work to 2 plies. PSCC (pawn structure classification) codes are also indicated. Openings are ordered by the number of master games.

1. I 1. Nf3 Nf6, 94226 games, sh1=1.0, sh2=0.6, ev=+0.6 Réti opening: Symmetrical variation
2. 2d 1. Nf3 d5, 50222 games, sh1=1.0, sh2=0.7, ev=+0.5 Réti opening: Reversed Indian game
3. 2c 1. Nf3 c5, 23201 games, sh1=0.9, sh2=0.8, ev=+0.25 Réti opening: Sicilian invitation
4. 1g 1. Nf3 g6, 11069 games, sh1=1.0, sh2=0.9, ev=+0.1 Réti opening: Kingside Fianchetto variation
5. 2f 1. Nf3 f5, 5791 games, sh1=1.5, sh2=0.9, ev=+0.7 Réti opening: Dutch variation
6. 2d1G 1. g3 d5, 5763 games, sh1=1.1, sh2=0.8, ev=+0.4
7. 1d 1. Nf3 d6, 5317 games, sh1=1.3, sh2=0.9, ev=+0.4 Réti opening: Pirc invitation
8. 1e 1. Nf3 e6, 3403 games, sh1=1.5, sh2=0.7, ev=+1.0 Réti opening: QG invitation
9. 2e1B 1. b3 e5, 3329 games, sh1=1.4, sh2=1.3, ev=+0.0 NLA: Modern variation
10. 1Gg 1. g3 g6, 3109 games, sh1=1.1, sh2=0.7, ev=+0.5 Benko's opening: Symmetrical variation
11. 1G 1. g3 Nf6, 3098 games, sh1=1.4, sh2=0.7, ev=+1.0 Benko's opening: Indian defense
12. 2Fd 1. f4 d5, 2896 games, sh1=1.2, sh2=1.5, ev=-0.3 Bird's opening: Dutch variation
13. 2e1G 1. g3 e5, 2518 games, sh1=1.2, sh2=1.0, ev=+0.2
14. 2d1B 1. b3 d5, 2013 games, sh1=1.2, sh2=1.1, ev=+0.1 NLA: Classical variation
15. 2c1G 1. g3 c5, 1740 games, sh1=1.0, sh2=0.8, ev=+0.3 Benko's opening: Sicilian invitation
16. I 1. Nf3 Nc6, 1433 games, sh1=1.5, sh2=0.8, ev=+0.9 Réti opening: Black Mustang defense
17. 1B 1. b3 Nf6, 1230 games, sh1=1.3, sh2=0.9, ev=+0.4 NLA: Indian variation
18. 1G 1. g3 Nf6, 1109 games, sh1=1.3, sh2=1.7, ev=-0.3 Benko's opening: Indian defense
    

I'll finish later  adding openings starting with e4, d4 and c4 with 1000+ master games.

This might run into problems at higher levels where mega-theory is often used to get easy draws.

Sure. It's just a kind of evaluations, derived from the pure statistics without engines, that might be sometimes useful.

Ok. I find this very interesting and I'll try to fine-tune it along side you and @Sqod.

Nice!

Once again, this required some time on my part to analyze and understand because the presentation is not motivated. Why a ratio, and why those particular ratios? I had to go through some numerical examples to see what you were trying to do, using the above charts from 365chess. One is a notoriously drawish opening--the Exchange French--and another is a notoriously sharp opening--the King's Gambit.

(1) King's Gambit, move 9 (100% draws)

sh1 = W/D = 0/100 = 0 (no sharpness whatsoever)

sh2 = B/D = 0/100 = 0 (no sharpness whatsoever)

This makes sense.

(2) King's Gambit, move 11 (0% draws, 50% wins for each color)

sh1 = W/D =50/0 = infinite (infinite sharpness) 

sh2 = B/D = 50/0 = infinite (infinite sharpness)

This makes sense, at least if you don't mind infinite values.

(3) King's Gambit, move 11 (50% draws, 50% white wins)

sh1 = W/D = 50/50 = 1

sh2 = B/D = 0/50 = 0

OK, so it's "sharp" for White even though Black can't win because White's "enemy" is the threatening draw.

(4) King's Gambit, move 2

sh1 = W/D = 47.4 / 19.0 = 2.49

sh2 = B/D = 33.7 / 19.0 = 1.77

All ratios are above 1 so it's relatively sharp for both sides, as we'd expect.

(5) Exchange French, move 3

sh1 = W/D = 27.2 / 38.5 = 0.706

sh2 = B/D = 34.3 / 38.5 = 0.891

All ratios are below 1, so it's relatively drawish, which we'd expect.

OK, that all makes sense, but it took more time than I wanted to spend, and I haven't even studied the rest of it yet.

Sqod, thanks a lot for these detailed examples! U are not hasty to understand things but when U understand it starts to be perfect.

I've been thinking about this. One of my main criteria for creating formulas or definitions is that it fits very well with a person's intuitive sense. In other words, I regard math as a tool that can fill in the gaps of what humans understand in only a general way, not as a way for humans to try to catch up with what one inventor is trying to do, and then hopefully see how it applies to what they already know.

In my opinion your formula for sharpness fails the intuitive test in case (3). First, when we humans refer to a "sharp" opening we aren't thinking about whether it's sharp for White or Black: we're thinking of a general character of the position as a whole, wherein both players must play very accurate moves to avoid losing. Therefore splitting the definition as you have done doesn't fit the existing concept that people already understand. Second, even if they do understand your altered concept of "sharpness," to say in case 3 that a position that draws 50% of the time has either no sharpness at all (=0), or medium sharpness (=1) doesn't fit intuition, at least not my intuition. My intuition says that perfect sharpness (without consideration of who wins most often) is when there are no draws at all.

I did later come up with an elaborate measurement of sharpness measured over the course of a game that I never posted, but first I'll want to figure out the rest of your reasoning, then spend a long time describing my formula. Maybe I'll have time to do that in the next few days, in between looking for a new job, which is my highest priority right now.

Sqod:

• Don't forget the notion of total sharpness sh=sh1+sh2 which fits better in case 3. I don't write its statistics since it's just the sum of 2 values.
• There are different meanings of sharpness. For example, when U have a long sequence of positions with only 1-2 correct moves (difficult to find) between them. So far, I didn't try to quantify such a positional sharpness. I'll do it later.

Anyway, waiting for your new ideas. Personally, at the moment, I'm fully satisfied with the current definitions.

Does anybody know which club has grown the fastest in the last month?