Statistically Sharp Openings

@savagechess2k

I got your definition, my question was if there's more to it. Any relation to "conventional" chess metrics or any insights you want derive from it. It's possible to define a lot of different things.

"A game is Blong if the first bishop move was at move 7 or later"
"A position is Ggreat if the g8-knight was moved from its initial square"
" A game is c-lose if the c-file is empty at least once during the game"

As @Chillkroete77, @Linsolv pointed out, your definition fails to predict the "common sense sharpness" of the position in several cases. Apparently it's not what you wanted to predict. But how about explaining beyond the definition instead.

P.S. I'd suggest
"Given a position p in a database /database A" instead of "Given a position p"

EDIT: Ok, I missed the last sentence in the OP. So you want this metric to help you decide if a position is ("sharp" = worth studying)? I have my doubts about this approach for humans.

Magnus Carlsen frequently plays rare or new moves. He is the best player in the world. The definition by #1 poster is for the most popular and most common moves. These are also the most obvious and the least creative moves. These moves are the least likely to surprise the opponnent.

I should come up with another name. Sharpness creates confusion.

Also, of course there are Lssharp (and even Mssharp) positions in which the best move is not good.

#13 Yes, i am also a little bit confused.
I would say a sharp position is a difficult position (complex position) where it is easy to make a mistake or blunder, even for good players.
Your sharpness definition implies that this is a 'sharp' position after white moves
d4? (Master Database used)

lichess.org/analysis#6

I would say this is a blunt position (a lot of good obvious moves can be played without to make a mistake)
Interesting topic anyway, this is my definition of 'sharpness':

A complex position is a position where the probability that someone will make a error is high
The basic formula for this approach is:

e = sum(P * D)
**************

e : predicted error, same as predicted centipawn lost (cpl)
and similar to a relative complexity value of a chess position
P : Probability vector (that is a tough nut)
The probabilities p_i for each possible move to be played by someone.
P = (p_1, ..., p_m)
where:
m = count of legal moves in a given position
and sum(P) = 1.0
D : Difference vector (errors for all possible moves)
the centipawn (cp) differences of the best move to all possible moves
D = ( (cp_1-cp_1), (cp_1-cp_2), ..., (cp_1-cp_i), ...(cp_1-cp_m) )
where:
cp_1 is the bestmove, cp_2 second best and ... cp_m the worst one.

edit: that was my example:
lichess.org/analysis/standard/rnb1kbnr/ppp1pppp/8/q7/8/2N5/PPPP1PPP/R1BQKBNR_w_KQkq_-

@kettwiesel
Edit: Yes, that position is sharp according to my definition. My point is that I should name it something else.

The rest of this was posted before seeing your edit.

No. The position after 1. d4 is not sharp. Black has two equally-played options ...d5 and ...Nf6.

I should name this thing ( where the top move is much more played than the second top move) something other than sharpness.

But noone is suggesting a name for this. They are saying "Sharpness is not that" instead.

Yes, that is my point. Sharpness is not this. I am talking about this kind of opening positions where the most played move is 3x more played than the second most played move. And I know that is not sharpness. But I can not rename it if noone suggests a new name.

You can say "MainLinish" positions , even though it is not The best Word probably .

How about most common positions and moves.

No. A position in which an overwhelming majority of games played one specific move.

Why not just call it f() though

That's anti chess.