4 statistical subcategories of moves and openings

This is our little joint work with Differentiation2, cf.

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

https://www.chess.com/forum/view/chess-openings/statistically-correct-moves-and-openings

https://www.chess.com/forum/view/chess-openings/statistically-excellent-openings

In our evaluations, we use the chesstempo database (2200+ vs. 2200+)

https://chesstempo.com/game-database.html

considering positions with 100+ master games. The statistical evaluation of the initial position IP (calculated as the mean value) is equal to +0.39.

Statistically excellent moves:

• IP (ev=+0.39) --> 1. c4 English (ev=+0.48), sh = 0.92 | 0.71 = 1.63
• IP (ev=+0.39) --> 1. Nf3 Réti (ev=+0.47), sh = 0.80 | 0.54 = 1.34
• IP (ev=+0.39) --> 1. d4 QP (ev=+0.46), sh = 0.88 | 0.60 = 1.48
• 1. e4 KP (ev=+0.30) --> 1...c5 Sicilian (ev=+0.19), sh = 0.94 | 0.79 = 1.73
• 1. e4 KP (ev=+0.30) --> 1...g6 KP: Modern (ev=+0.24), sh = 1.14 | 0.92 = 2.06
• 1. d4 QP (ev=+0.46) --> 1...d6 Löwe (ev=+0.32), sh = 0.98 | 0.74 = 1.72
• 1. Nf3 Réti (ev=+0.47) --> 1...g6 Réti: KF (ev=+0.17), sh = 0.87 | 0.75 = 1.62
• 1. c4 English (ev=+0.48) --> 1...b6 English: QF (ev=+0.05), sh = 0.97 | 0.92 = 1.89
• 1. g3 Benko (ev=+0.42) --> 1...e5 Benko: KP (ev=+0.16), sh = 0.92 | 0.79 = 1.71

Statistically good (correct) moves:

• IP (ev=+0.39) --> 1.g3 Benko (ev=+0.42), sh = 0.92 | 0.65 = 1.57
• 1. d4 QP (ev=+0.46) --> 1...g6 QP: Modern (ev=+0.38), sh = 1.15 | 0.83 = 1.98
• 1. d4 QP (ev=+0.46) --> 1...Nf6 Indian (ev=+0.39), sh = 0.87 | 0.63 = 1.50
• 1. d4 QP (ev=+0.46) --> 1...e6 Horwitz (ev=+0.46), sh = 0.89 | 0.61 = 1.50
• 1. Nf3 Réti (ev=+0.47) --> 1...c5 Réti: Sicilian  (ev=+0.28), sh = 0.75 | 0.59 = 1.34
• 1. Nf3 Réti (ev=+0.47) --> 1...d6 Réti: Pirc (ev=+0.28), sh = 0.95 | 0.74 = 1.69
• 1. Nf3 Réti (ev=+0.47) --> 1...b6 Réti: QF (ev=+0.30), sh = 0.89 | 0.68 = 1.57
• 1. Nf3 Réti (ev=+0.47) --> 1...d5 Réti: QP (ev=+0.42), sh = 0.77 | 0.54 = 1.31
• 1. Nf3 Réti (ev=+0.47) --> 1...b5 Réti: Polish (ev=+0.46), sh = 1.03 | 0.70 = 1.73
• 1. c4 English (ev=+0.48) --> 1...g6 Great Snake (ev=+0.17), sh = 0.87 | 0.74 = 1.61
• 1. c4 English (ev=+0.48) --> 1...e5 King's English (ev=+0.29), sh = 0.93 | 0.72 = 1.65
• 1. c4 English (ev=+0.48) --> 1...d6 Paulsen (ev=+0.45), sh = 1.34 | 0.92 = 2.26
• 1. g3 Benko (ev=+0.42) --> 1...d5 Benko: QP (ev=+0.30), sh =0.86 | 0.66 = 1.52
• 1. g3 Benko (ev=+0.42) --> 1...c5 Benko: Sicilian (ev=+0.32), sh = 0.85 | 0.64 = 1.49
• 1. b3 NLA (ev=+0.10)--> 1...e5 NLA: Classical (ev=+0.02), sh = 0.87 | 0.86 = 1.73
• 1. b3 NLA (ev=+0.10)--> 1...e5 NLA: Modern (ev=+0.06), sh = 1.03 | 0.98 = 2.01
• 1. f4 Bird (ev=-0.25) --> 1...d5 Bird: Dutch (ev=-0.31), sh = 0.88 | 1.16 = 2.04
• 1. f4 Bird (ev=-0.25) --> 1...Nf6 Bird: Indian (ev=-0.30), sh = 0.85 | 1.10 = 1.95

Statistically suboptimal moves:

• IP (ev=+0.39) --> 1.e4 KP (ev=+0.30), sh = 0.92 | 0.71 = 1.63
• 1. e4 KP (ev=+0.30) --> 1...c6 Caro-Kann (ev=+0.37), sh = 0.82 | 0.60 = 1.42
• 1. e4 KP (ev=+0.30) --> 1...Nc6 Nimzo (ev=+0.39), sh = 1.25 | 0.90 = 2.15
• 1. e4 KP (ev=+0.30) --> 1...e5 KPG (ev=+0.40), sh = 0.82 | 0.58 = 1.30
• 1. e4 KP (ev=+0.30) --> 1...e6 French (ev=+0.41), sh = 0.94 | 0.66 = 1.60
• 1. e4 KP (ev=+0.30) --> 1...Nf6 Alekhine (ev=+0.41), sh = 1.05 | 0.75 =1.80
• 1. e4 KP (ev=+0.30) --> 1...d6 Pirc (ev=+0.46), sh = 1.07 | 0.73 = 1.80
• 1. d4 QP (ev=+0.46) --> 1...f5 Dutch (ev=+0.57), sh = 1.14 | 0.72 = 1.86
• 1. d4 QP (ev=+0.46) --> 1...c5 Old Benoni (ev=+0.59), sh = 1.36 | 0.86 = 2.22
• 1. d4 QP (ev=+0.46) --> 1...b6 English Defense (ev=+0.62), sh = 1.29 | 0.80 = 2.09
• 1. Nf3 Réti (ev=+0.47) --> 1...c6 Réti: Slav (ev=+0.53), sh = 0.88 | 0.57 = 1.45
• 1. Nf3 Réti (ev=+0.47) --> 1...Nf6 Réti: Symmetrical (ev=+0.57), sh = 0.78 | 0.50 = 1.28
• 1. c4 English (ev=+0.48) --> 1...f5 English: Dutch (ev=+0.49), sh = 1.14 | 0.76 = 1.90
• 1. c4 English (ev=+0.48) --> 1...Nc6 Anglo-Lithuanian (ev=+0.51), sh = 1.17 |  0.78 = 1.95
• 1. c4 English (ev=+0.48) --> 1...e6 Agincourt (ev=+0.60), sh = 0.81 | 0.50 = 1.31
• 1. c4 English (ev=+0.48) --> 1...Nf6 Anglo-Indian (ev=+0.61), sh = 0.93 | 0.58 = 1.51
• 1. c4 English (ev=+0.48) --> 1...c5 English: Symmetrical (ev=+0.65), sh = 0.75 | 0.45 = 1.20
• 1. g3 Benko (ev=+0.42) --> 1...g6 Benko: Symmetrical (ev=+0.55), sh = 0.91 | 0.59 = 1.50
• 1. g3 Benko (ev=+0.42) --> 1...f5 Benko: Dutch (ev=+0.59), sh= 1.25 | 0.79 = 2.04

Statistically bad (incorrect) moves:

• IP (ev=+0.39) --> 1.b3 NLA (ev=+0.10), sh = 0.95 | 0.87 =1.82
• IP (ev=+0.39) --> 1.b4 Sokolsky (ev=-0.03), sh = 1.19 | 1.23 = 2.42
• IP (ev=+0.39) --> 1.c3 Saragossa (ev=-0.05), sh = 1.13 | 1.19 = 2.32
• IP (ev=+0.39) --> 1.a3 Anderssen (ev=-0.08), sh = 1.15 | 1.23 = 2.38
• IP (ev=+0.39) --> 1.d3 Mieses (ev=-0.09), sh = 0.87 | 0.95 = 1.82
• IP (ev=+0.39) --> 1.Nc3 van Geet (ev=-0.12), sh = 0.94 | 1.05 =1.99
• IP (ev=+0.39) --> 1.e3 van't Kruijs (ev=-0.13), sh =1.14 | 1.29 = 2.43
• IP (ev=+0.39) --> 1.g4 Grob (ev=-0.21), sh = 1.34 | 1.63 = 2.97
• IP (ev=+0.39) --> 1.f4 Bird (ev=-0.25), sh = 0.94 | 1.17 = 2.11
• 1. e4 KP (ev=+0.30) --> 1...d5 Scandinavian (ev=+0.57), sh = 1.04 | 0.66 = 1.70
• 1. e4 KP (ev=+0.30) --> 1...b6 Owen (ev=+0.65), sh = 1.49 | 0.90 = 2.39
• 1. e4 KP (ev=+0.30) --> 1...a6 St. George (ev=+0.74), sh = 2.46 | 1.41 = 3.87
• 1. d4 QP (ev=+0.46) --> 1...d5 QPG (ev=+0.67), sh = 0.81 | 0.49 = 1.30
• 1. d4 QP (ev=+0.46) --> 1...Nc6 Mikenas (ev=+0.71), sh = 1.48 | 0.87 = 2.35
• 1. d4 QP (ev=+0.46) --> 1...c6 QP: Slav Invitation (ev=+0.74), sh = 1.04 | 0.60 = 1.64
• 1. d4 QP (ev=+0.46) --> 1...b5 QP: Polish (ev=+0.98), sh = 1.70 | 0.86 = 2.56
• 1. Nf3 Réti (ev=+0.47) --> 1...Nc6 Réti: Black Mustang (ev=+0.71), sh =1.10 | 0.65 = 1.75
• 1. Nf3 Réti (ev=+0.47) --> 1...f5 Réti: Dutch (ev=+0.74), sh =1.15 | 0.66 = 1.81
• 1. Nf3 Réti (ev=+0.47) --> 1...e6 Réti: QG Invitation (ev=+0.86), sh = 1.12 | 0.60 = 1.72
• 1. c4 English (ev=+0.48) --> 1...c6 English: Caro-Kann (ev=+0.76), sh = 0.82 | 0.46 = 1.28
• 1. g3 Benko (ev=+0.42) --> 1...Nf6 Benko: Indian (ev=+0.88), sh = 1.04 | 0.55 =1.59
• 1. b3 NLA (ev=+0.10)--> 1...Nf6 NLA: Indian (ev=+0.41), sh = 0.93 | 0.66 = 1.58

Here I'll post biggest surprises of our statistical evaluations.

• 1. e4 is suboptimal
• 1. e4 g6 is statistically excellent and almost as good as Sicilian
• 1...g6 is strong vs almost everything
• 1. d4 d5 is statistically bad
• 1...d6 is statistically the best reply to 1. d4
• 1...b6 is the best reply to 1. c4
• 1. Nf3 b5 is statistically good
• French 1. e4 e6 and Caro-Kann 1. e4 c6 are suboptimal
• Anglo-Indian 1. c4 Nf6 and Réti: Symmetrical 1. Nf3 Nf6 are suboptimal
• Bird's opening 1. f4 is statistically very bad.

Statistical evaluations of Sokolsky opening.

Initial Position (ev=+0.39) --> 1. b4 Sokolsky (ev=-0.03), statistically bad

1. b4 Sokolsky (ev=-0.03) --> 1. b4 e5 Sokolsky: KP (ev=-0.26), statistically excellent

1. b4 Sokolsky (ev=-0.03) --> 1. b4 d5 Sokolsky: QP (ev=-0.10), statistically good

1. b4 Sokolsky (ev=-0.03) --> 1. b4 Nf6 Sokolsky: Indian (ev=-0.06), statistically good

There are no enough master games to evaluate other replies properly.

I started to add the sharpness statistics. Statistically excellent moves require sh >= 1.25  while statistically good ones will require sh >= 1.

KP: Modern [1. e4] g6 is the sharpest statistically excellent move so far with sh=2.06.

N.B. 1. e4 itself is statistically suboptimal.

NMinSixMonths: It was also noticed by Differentiation2. I guess that U've made a good explanation. Also, let's look at 2 sequences leading to the same position:

• IP (+0.39) --> 1.e4 (+0.30↓) --> 1...d6 (+0.46↑) --> 2. d4 (+0.49↑)
• IP (+0.39) --> 1.d4 (+0.46↑) --> 1...d6 (+0.32↓) --> 2. e4 (+0.49↑)

The whole story happens in the narrow band ev(IP)±0.1  around the evaluation of the initial position ev(IP)=+0.39.

Notations:

--> excellent

--> good

--> suboptimal

N.B. Please recall that, if white moves, a good/excellent move increases the evaluation and a bad/suboptimal move decreases it (inversely, if black moves). Consequently, 2 juxtaposed good moves compensate each other (the same for 2 juxtaposed suboptimal moves).

It's defined in the previous threads mentioned in the first post, I didn't want to rewrite it. Briefly, a white's move is statistically good (correct) if it increases the statistical evaluation of the position and statistically bad (incorrect) otherwise (inversely for black's moves). The best statistically good moves are called statistically excellent while statistically incorrect moves, which are close to be correct, are called statistically suboptimal.

I indicate the sharpness in the following format:

sh = sh1 | sh2 = sh1+sh2.

So far, the statistically good Paulsen defense 1. c4 d6 is the sharpest one with sh= 1.34 | 0.92 = 2.26.

While this may not be in official books or advertised as "official" theory, I like this. Looks very useful. In 2017 engines basically, give us the "Truth" and allow regular players to find perfection previously only reserved for teams of grandmasters working together. However, the only problem is a small issue with the fallacy of division. That was is true for the whole must also be true of all or some of its parts. For example, the sample of thousands of master, i.e. high-level games, diffusing to a statistical average doesn't tell you that the position is that particular evaluation for EACH particular game played, especially for a pool of players less advanced than the sampling pool. For example, many times, playing a very well known opening against an 1800 level tournament player, they usually rely (overly most of the time) on being booked up on opening theory, and will play better against "optimum" moves, especially if they know the variations and you do not. Sometimes, playing suboptimal moves, especially if you've trained in the variations can be very jarring to players booked up on traditional openings, and by playing "weaker" openings a developing player might win far more games through traps, surprises, or better, esoteric preparation. I know a guy who got to 2260, National Master, for years...by only playing one opening system as white. 1.e4, 2.Qh5. An "inferior" opening by engine and database standards, but while everyone else was spending their time preparing for everyone to play like Fischer, he went through thousands of possible variations of this, and spent more time on this opening, probably than anyone in the United States. No one ever expected it, and everyone was out of the book immediately over the board with it, against a person who had studied it their entire life. By being "worse" it evaded the study of just about everyone and offered a unique opportunity to surprise everyone he played. It's one of those unintuitive, Freakonomics things where worse is better and less is more kinda things. Finally, +0.75 through -0.75 is meaningless between players below probably 2200, who will not be able to see, much less convert, such fine advantages. I struggled against a chess engine (set just above my level) for years playing regular openings. I played bullshit 1.a3, 2.h3, 3,b4, 4.g4 the other night, and crushed it for the first time. I wasn't even happy with beating for the first time. I simply don't know why that worked when my "real" openings didn't. Psychologically, we play looser, braver, and easier with stuff we aren't serious about, and that makes a huge difference against someone really trying with a lot on the line. Psychology matters a lot. There was a guy here who played in the state championship, and won games left and right with the bullshit Grob attack...because no one took it seriously or ever studied it. Humans are weird, strange things, and surprise is often far more effective than logic.

However...With all thing being said, It is Friday night, and a cocktail of various substances has impelled me to write that long ramble..and despite the fact that all of it is absolutely correct...it is still best to study proper openings, and your work here is utterly awesome and I'm going to study it for hours.

Yiger, can you do the stats for the Nimzo Larsen Attack and the Parham Attack?  

Another round of drinks for FaceCrusher!  I enjoyed your post very much.

In Magnus's last classical tournament he didn't do very well, and Kramnik said that Magnus needs to work on his openings.

So then Magnus plays the "statistically very bad" 1. f4 against Kramnik in a rapid game and wins!  Magnus practically flips the Bird in Kramnik's face and wins contra Yigor's statistics, and in total accord with FaceCrusher's thesis about surprise and psychological value of theoretically and statistically weaker openings.

Thanks for your detailed comment above. All right, I'll make it later today for NLA (there are not enough master games with Praham attack to make accurate statistical measurements) and I'll post it here. Differentiation2 started to do it (post #119):

https://www.chess.com/forum/view/chess-openings/statistically-correct-moves-and-openings?page=6

but we have refined our definitions and changed the source database to more accurate chesstempo (2200+ vs. 2200+). U can also look at my thread about general trends of NLA during 19th century :

https://www.chess.com/forum/view/chess-openings/nimzo-larsen-attack-during-19th-century-general-trends

SeniorPatzer: Yeah, U are right about the surprise value of Bird. It's statistically very bad but, at least, it has a quite good sharpness sh = 0.94 | 1.17 = 2.11. That's why I started to add the sharpness statistics that turns out to be an important criterion too.

Now, for the fun of it, I often make here the first 2 moves using the generator of random integers, starting sometimes with the total crap. But, when I wanna play seriously from the very beginning, I use my statistical results.

Nobody spoke about the perfection. Btw many players here of various rankings consider that it's useful.

What's optimal or suboptimal depends on the strengths and weaknesses of the player.

It is suboptimal to have a low "granny gear" on a multi-gear bicycle because the bike has a lighter weight with two front gears instead of adding a third one.  But if you have my so-so level of skill and strength, there are times shifting down to the granny gear on long, steep hills can mean the difference between riding the bike up the hill or walking up the hill with the bike.

I'm currently working on completing the sharpness results in the list (post #1). Old Benoni is one more relatively sharp opening: sh= 1.36 | 0.86 = 2.22.

2 additional sharp openings, Symmetrical English is the most drawish so far: D= 45.4 %, sh = 0.75 | 0.45 = 1.20.

All right, I've finished to calculate evaluation and sharpness results for IP, KP, QP, Réti, English and Benko. Now I'm planning to check and to add Differentiation2's results for the Nimzo-Larsen attack (NLA) 1. b3 as well as for less popular first moves and black replies.

LoL Take it easy, bro.

What have you come up with for Colle System for white and The Modern Pirc for black. I know I could look, but I want to make sure I'm reading it right and not getting it wrong. I figure you'd be able to answer far better than I could interpret from the original post. 

Edit: Never mind, I believe I have it. Both 1.d5 and 1...g6 against e4 appear to be Excellent, in the highest catagory. I am pleased to see this. I am not surprised to see Nf3 and d4 as two of the highest rated opening moves. If pressed to play a two games as white for the finals of the world championship, these are the two I would choose. I am not surprised to see 1.e4 as suboptimal, since it has an inherent flay by comparison to 1.d4, that you leave an intrinsically hanging pawn with your opening move. With 1.d4, you have a built in a defender from the beginning, and two pawns left to advance to the third rank to cut off the diagonals leading to f2, as opposed to only one with 1.e4. In my view, 1.d4 is inherently, just simply better.