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Estimating White's Advantage

Posted: Sat Aug 15, 2015 8:51 pm
by IanCalvert
In practice,White doubtless gets a higher % score than Black.

Does anyone know of reliable analysis of the variation in this facet of ECF (or even FIDE) stats?

Given the approximate linear relationship between rating difference and expected score implicit in the ECF system, I guess such information translated into rating points might well inform club level discussion.

Re: Estimating White's Advantage

Posted: Sat Aug 15, 2015 9:29 pm
by Roger de Coverly
IanCalvert wrote: Does anyone know of reliable analysis of the variation in this facet of ECF (or even FIDE) stats?
The best place to look is in a monstrous database that has a tree constructed.

As a for example I have one that gives

1. e4 (51.4% of all games) scores 53%
1. d4 ( 31.7%) scores 55%
1. Nf3 ( 7.7%) scores 55%
1. c4 ( 6.7%) scores 54%
1. g3 ( 0.7%) scores 54%
1. f4 (0.7%) scores 48%

Assuming the remaining 1.1% is 50%, that gives a weighted average of 53%

I'm not sure that's desperately important for modifying rating formulae. Back in the 1990s, the PCA rating list reflected colours.

What would worry me more would be the effect of treating stalemate as a win, as advocated by some. Apart from overturning much King and pawn endgame theory and with it the theory of many other worse but drawn endings, what would it do to white's winning percentage?

(edit) my rule of thumb is that having white is worth up to 5 ECF points. So if White is 165 and Black 170, they will score their grade if White wins 10 game match by 5.5 to 4.5, 55% in other words. (/edit)

Re: Estimating White's Advantage

Posted: Sat Aug 15, 2015 9:32 pm
by NickFaulks
FIDE has details of all individual rated games, including colour, since 2007. I expect I can get this.

edit: Having read Roger's post above, is his figure of 53%, which looks entirely credible, in fact all that is needed?

Re: Estimating White's Advantage

Posted: Sun Aug 16, 2015 9:58 am
by Brian Towers
Roger de Coverly wrote:What would worry me more would be the effect of treating stalemate as a win, as advocated by some. Apart from overturning much King and pawn endgame theory and with it the theory of many other worse but drawn endings, what would it do to white's winning percentage?
Surely following the example of hexagonal chess and awarding the player delivering stalemate 0.75 and the player on the receiving end 0.25 would be more sensible?

Re: Estimating White's Advantage

Posted: Sun Aug 16, 2015 10:22 am
by IanCalvert
NickFaulks wrote:FIDE has details of all individual rated games, including colour, since 2007. I expect I can get this.

edit: Having read Roger's post above, is his figure of 53%, which looks entirely credible, in fact all that is needed?
Roger and Nick, thanks very much.

As Nick might have guessed this is also part of my Cunning Plan to produce optimal team player strategies, for team discussion before a move is made. The individual Board strategies are essentially about " going for the win " or "playing safe" to maximise the probability that the team will win, given expected scores. in the statistical sense , on each Board. Unfortunately the objective function is non-linear but at least polynomial.

Re: Estimating White's Advantage

Posted: Sun Aug 16, 2015 11:02 am
by MartinCarpenter
Pointless anyway I'd think because the expected score for given players vary a huge amount :)

Firstly in general about how often they'll lose/draw/win (some people draw lots, some are very much more random). Also that white 'advantage' is a population average. Some players have a much larger one than in general, some less, the odd rare player even scores better with black.

Also major variance in terms of who people are playing - some are very good at stonewalling mildly stronger players, some super efficient vs weaker ones etc.

Re: Estimating White's Advantage

Posted: Sun Aug 16, 2015 11:24 am
by E Michael White
Roger de Coverly wrote:The best place to look is in a monstrous database that has a tree constructed.

As a for example I have one that gives

1. e4 (51.4% of all games) scores 53%
1. d4 ( 31.7%) scores 55%
1. Nf3 ( 7.7%) scores 55%
1. c4 ( 6.7%) scores 54%
1. g3 ( 0.7%) scores 54%
1. f4 (0.7%) scores 48%

Assuming the remaining 1.1% is 50%, that gives a weighted average of 53%
Don't arbiter pairing methods and stratification of players into open/major/minor ensure stronger players get slightly more whites than blacks ?

Re: Estimating White's Advantage

Posted: Sun Aug 16, 2015 11:32 am
by Kevin Thurlow
1.b3 happens about 0.4 % of the time and scores about 50 %.

I did a survey of Civil Service League games many years ago. Division 3 had (I think) 8 players and Division 4 had 6, so if you got promoted, you not only got tougher games anyway, you had to find two extra players, so we proposed having a 7-board division. One person at the AGM screamed that this was unfair as if you got fewer whites than the opposition, you were going to lose.

So the next year, I found that in Division 1, white scored 55 %, in Division 3, white scored 50 %, and in Division 5, white scored 45 %, so overall, it's about 50 %. I speculated that in Division 5, white had the disadvantage that he moved first and was very slightly more likely to make a catastrophic blunder first.

This doesn't help predict individual scores of course (as Martin said).

Re: Estimating White's Advantage

Posted: Sun Aug 16, 2015 11:51 am
by E Michael White
Kevin Thurlow wrote:I speculated that in Division 5, white had the disadvantage that he moved first and was very slightly more likely to make a catastrophic blunder first.
Good points Kevin. Similarly white is more likely to lose on time, fall foul of the touch move rule or make an illegal move !

Re: Estimating White's Advantage

Posted: Sun Aug 16, 2015 12:13 pm
by David Shepherd
I think a more meaningful comparison is the wins by white compared to the wins by black - there are a number of circumstances where both players are happy with a draw which I believe distorts the level of advantage when just looking at white overall percentages, as it smooths the statistic pulling it towards 50%.

Re: Estimating White's Advantage

Posted: Sun Aug 16, 2015 1:07 pm
by Ian Thompson
E Michael White wrote:Don't arbiter pairing methods and stratification of players into open/major/minor ensure stronger players get slightly more whites than blacks ?
Why? I can see that pairing methods mean that stronger players are more likely to retain colour sequence than weaker ones, but not why they are more likely to get white than black.

Re: Estimating White's Advantage

Posted: Sun Aug 16, 2015 5:46 pm
by Nick Grey
Marginal at our levels.
As for team play most players play the same way (not really looking at match situation).
Opening 1.b3 against a player that is far to aggressive with any colour may well be best (you know me so well).
Personally I'll play something a bit more aggressive with white.

Re: Estimating White's Advantage

Posted: Mon Aug 17, 2015 9:41 am
by E Michael White
Ian Thompson wrote:
E Michael White wrote:Don't arbiter pairing methods and stratification of players into open/major/minor ensure stronger players get slightly more whites than blacks ?
Why? I can see that pairing methods mean that stronger players are more likely to retain colour sequence than weaker ones, but not why they are more likely to get white than black.
Hello Ian,
My line of thinking was that under CAA pairings where a tournament has an odd number of boards, say 21 then the stronger player out of the two on each board in the first round is more likely to be white. In the case of 21 boards, 11 of the players will be white and likely stronger than their opps whereas only 10 black players could be stronger. Maintaining colour sequences over an odd number of rounds will likely but not necessarily give an overall rating advantage to white. This effect will reduce the apparent advantage that a straight % score shows to favour white.

Having 3 separate sections Open/Major and Minor is likely to increase the effect compared to having one large section. Also in the Open and Minor sections the distribution of ratings is likely to be skewed to the right and left respectively which may increase the effect. In League matches including 4NCL the effect may be reduced to around 0.

Re: Estimating White's Advantage

Posted: Mon Aug 17, 2015 9:55 am
by Roger de Coverly
E Michael White wrote: In the case of 21 boards, 11 of the players will be white and likely stronger than their opps whereas only 10 black players could be stronger.
Isn't that assuming you always give White to the top seed? I thought CAA rules required this either to be pre-determined by the calendar year as in the British Championships, or randomly assigned?

In any event, checking the percentages of results of five million recorded games from the whole of chess history isn't going to be affected by CAA rules.

Re: Estimating White's Advantage

Posted: Mon Aug 17, 2015 9:56 am
by IM Jack Rudd
E Michael White wrote:My line of thinking was that under CAA pairings where a tournament has an odd number of boards, say 21 then the stronger player out of the two on each board in the first round is more likely to be white. In the case of 21 boards, 11 of the players will be white and likely stronger than their opps whereas only 10 black players could be stronger.
The official rules for CAA pairings state that the top seed's round 1 colour is chosen randomly, which rather demolishes that argument.