Upset Prizes

[wintdoan]

@wilecoyote

@wintdoan

There’s no mathematical basis for that. The assumption underlying the Elo calculations is that the probability of a draw is 2p(1-p) where p is the “winning expectancy” value given the rating calculations. It’s very well-known that that’s a bit low for IM/GM level players, and way high for players in the 800-1400 range where draws are rather rare, even for evenly matched players. However, if you use that as the basis, then the probability of a win with a rating difference dR is close to the probability of a draw with rating difference 3(dR) (rather than 2(dR)) across much of the range from dR=100 to dR=300.

Thank you for this. I’ve never seen the formula for the probability of a draw.

It’s not the empirical probability of a draw (as I mention). It’s the mathematically convenient probability of a draw—with that, you just have to know opponents’ ratings and the overall score and not the breakdown into wins, losses and draws.

[GKarRacer]

@wilecoyote

@wintdoan

There’s no mathematical basis for that. The assumption underlying the Elo calculations is that the probability of a draw is 2p(1-p) where p is the “winning expectancy” value given the rating calculations. It’s very well-known that that’s a bit low for IM/GM level players, and way high for players in the 800-1400 range where draws are rather rare, even for evenly matched players. However, if you use that as the basis, then the probability of a win with a rating difference dR is close to the probability of a draw with rating difference 3(dR) (rather than 2(dR)) across much of the range from dR=100 to dR=300.

Thank you for this. I’ve never seen the formula for the probability of a draw.

For those interested, I believe this is the current rating formula used by US Chess in all its gory detail: http://glicko.net/ratings/rating.system.pdf.

[wintdoan]

However, that does not show the math underlying the R=R0+K(S-E) update, which is where the 2p(1-p) draw probability comes into play.

[kevin_bachler]

McMahon!

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