### Advantage for White; Bayeselo (to Rémi Coulom)

Posted:

**Sat Mar 03, 2012 11:22 pm**Inspired by Daniels topic "why chess has small chance of being a black win ?" I conducted some tests on the correlation between White Advantage and Elo-Average of both players.

As testdata I used the current CCRL 40/40 Database. Removing all games with incomplete Elo Information I was left with 394860 games.

Using the formulas from Bayeselo

According to the webpage the default-values for Bayeselo are

I am getting the best fit with:

EloDraw = avg * 0.096 -135

EloAdvantage = avg * 0.0108 -2.4

In other words with increasing level of play the Draw Rate increases (no new information really; see http://kirill-kryukov.com/chess/kcec/draw_rate.html), but also the advantage of moving first increases.

Another interesting finding was that with increasing level of play the Probability for White Scoring (=P(white win) + P(draw) * 0.5) increases. Regarding Daniels topic I see this as an indication that chess is not won by black. Extrapolating the trends suggest that at an Elo of 8000 94.5% of the games will end in a draw, 4% are won for white and the remaining 1.5% are won for black.

Rémi Coulom, is Bayeselo still under development? If so, I would suggest to improve its output by considering the level of play of the opponents. Especially for Ratinglists like CCRL the effects would be significant. On the low end the average elo of the two engines is 1945 (with an EloDraw of 51.72) and at the high end it is 3280.5 (with EloDraw of 179.928)

As testdata I used the current CCRL 40/40 Database. Removing all games with incomplete Elo Information I was left with 394860 games.

Using the formulas from Bayeselo

I searched for the maximum-likelihood values for eloAdvantage and eloDraw.f(Delta) = 1 / (1 + 10^(Delta/400))

P(WhiteWins) = f(eloBlack - eloWhite - eloAdvantage + eloDraw)

P(BlackWins) = f(eloWhite - eloBlack + eloAdvantage + eloDraw)

P(Draw) = 1 - P(WhiteWins) - P(BlackWins)

According to the webpage the default-values for Bayeselo are

In my tests I found a significant correlation with the average Elo of the two players.eloAdvantage = 32.8

eloDraw = 97.3

I am getting the best fit with:

EloDraw = avg * 0.096 -135

EloAdvantage = avg * 0.0108 -2.4

In other words with increasing level of play the Draw Rate increases (no new information really; see http://kirill-kryukov.com/chess/kcec/draw_rate.html), but also the advantage of moving first increases.

Another interesting finding was that with increasing level of play the Probability for White Scoring (=P(white win) + P(draw) * 0.5) increases. Regarding Daniels topic I see this as an indication that chess is not won by black. Extrapolating the trends suggest that at an Elo of 8000 94.5% of the games will end in a draw, 4% are won for white and the remaining 1.5% are won for black.

Rémi Coulom, is Bayeselo still under development? If so, I would suggest to improve its output by considering the level of play of the opponents. Especially for Ratinglists like CCRL the effects would be significant. On the low end the average elo of the two engines is 1945 (with an EloDraw of 51.72) and at the high end it is 3280.5 (with EloDraw of 179.928)