There's something wrong about the equation. Since you take the lowest S as the sharpest, as white's win percentage increases, sharpness decreases. You want any win to increase sharpness, while all draws decrease it.
So, simply adding Ww+Bw is better. But this is still not accurate enough, as I think any equation based only on win/draw percentages would be. One has to take into account a lot of things, such as number of possible checks, captures, threats, pins, the pieces on the board, if the position is open or not, king safety etc.
The subject is very interesting if you look at it from a computer chess point of view, especially "personalities" of chess engines which are adjustable in various ways.
Doing my reading about the Ruy Lopez, I read that some lines are considered sharp, while others are considered quiet. So, I asked myself: if I don't have a GM next door, how can I determine if an opening is sharp or quiet? And eureka! I might have come up with a measure for sharpness (although a primitive one), but I think it can, at least, give a hint about the sharpness of an opening. All it requires is that we look at the stats in an opening database (I use the Game Explorer at the moment), and perform a simple calculation. The calculation will yield a number. If this number is low, the lines springer from the given position are likely to be sharp, if it's high, it's most likely a more positional opening.
The formula is like this:
S = ( Ww% / Bw% ) x D%,
where S is sharpness, Ww% is White's winning %, Bw% is Black's winning %, and D% is the drawing percentage. Here's an example:
After 1.e4 e5 2.Nf3 Nc6 3.Bb5, for 3...a6, these are the numbers:
So, doing the calculation with these numbers we see that,
Doing the same calculation with some other common replies, we get these results:
This shows (if my hypothesis is correct), that 3...f5 is the sharpest of these replies, which is in accordance with what I've read. It also shows that 3...a6 is a positional reply, leading to a more quiet game.
Any thoughts?
Please note: I'm not claiming this to be perfect, it's just a hypothesis. If anyone can find counter examples rejecting my hypothesis, that's fine.