Does engine score correlate with winning chances?

Question

I was wondering if there is a statistical or probabilistic (at least approximate) way of looking at a score of a chess position of a certain fixed engine, say "crafty version 5" for example.

i.e. maybe +2 could be interpreted as "if the engine keeps on playing, 60% wins white, 30% black and 10% draw. I know this isn't the purpose of the score, but maybe it can be translated to approximate probabilities, maybe someone has done a statistical test with hundreds of games to see the correlation. And the amount of draw maybe depends on the "sharpness" of the position.

Answer 1

On the website of Houdini, one of the best chess engines (see for instance CCRL or CEGT), the author writes

Houdini 4 uses calibrated evaluations in which engine scores correlate directly with the win expectancy in the position. A +1.00 pawn advantage gives a 80% chance of winning the game against an equal opponent at blitz time control. At +2.00 the engine will win 95% of the time, and at +3.00 about 99% of the time. If the advantage is +0.50, expect to win nearly 50% of the time.

The Chess Programming Wiki mentions a study where data from more than 400 000 computer games have been used to find a relation between pawn advantage (P) and winning percentage (W).

W = 1 / (1+10^(-P/4))