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#1




Whit/black rating. A solution.
We know that "white" in chess
is slightly (or not so slightly?) stonger than "black". Any single rating which would introduce a rectifying bias is wrong though, there is always someone unhappy for a good reason. The perfect solution is simple conceptually but not quite logistically. Each player X should have two ratings: white rating wr(X) and black rating br(X). These ratings would be computed just the way they are now, except that instead of player X imagine that there are two ficticious players wX and bX, where player wX plays games which are played by X with white color, and player bX plays games played by X with the black color. What next? That depends on the rating function. If the rating function is additive then wr(X)+br(X) is the ultimate rating of X. If the rating function is multiplicative than the ultimate rating of X should be wr(X)*br(X). If the rating function is neither additive nor multiplpicative then the situation is unclear. A good rating function perhaps should be one or the other (additive or multipplicative)it is certainly a strong virtue. If one wants to introduce this idea in real life then starting with wr(X) := br(X) := rat(X) where rat(X) is the present rating of X (say FIDE or USCF) is not a bad idea. Then one would continue in the way described above. *** Observe that logarithm log(ar(X)) of a multiplicative rating function mr(X) gives an additive rating function, and exponential exp(ar(X)) of an additive function gives a multiplpicative rating function. Multiplicative notion is more natural. It means that if players play forever and their score is stably in the same proportion a:b than their ratings are also in proportion a:b. Multiplicative rating is always a positive number. In the case of additive rating one needs to know the respective constant f of the system. Then f^(ar(X)  ar(Y)) tells you what to expect in a match of X against Y in terms of proportion. Or you may like to talk about a constant F 0 such that the proportion of the expected scores is: exp(F * (ar(X)  ar(Y))) Of course F = log(f). A normal additive rating function would have F = 1, i.e. f=e. An additive rating function has all real numbers, from minus to plus infinity, as its range. One may shift it so that nobody real falls into the negative range and everybody feels good :) Multiplicative fuunctions are simpler conceptually but less acceptable(??) psychologicallyless so, when there are class ratings. *** Wlod 
#2




Whit/black rating. A solution.
Wlodzimierz Holsztynski (wlod) wrote: Each player X should have two ratings: white rating wr(X) and black rating br(X). These ratings would be computed just the way they are now, except that instead of player X imagine that there are two ficticious players wX and bX, where player wX plays games which are played by X with white color, and player bX plays games played by X with the black color. What next? That depends on the rating function. If the rating function is additive then wr(X)+br(X) is the ultimate rating of X. If the rating function is multiplicative than the ultimate rating of X should be wr(X)*br(X). Sorry, in the additive case the total rating of X should be the arithmetical mean: tr(X) := (wr(X)+br(X)) / 2 and in the multiplicative case it should be the geometrical mean: tr(X) := sqrt( wr(X)*br(X) ) If the rating function is neither additive nor multiplpicative then the situation is unclear. A good rating function perhaps should be one or the other (additive or multipplicative)it is certainly a strong virtue. ==== Wlod PS. The initial post of this thread went to rgcp only. 
#3




Whit/black rating. A solution.
"Wlodzimierz Holsztynski (wlod)" writes:
We know that "white" in chess is slightly (or not so slightly?) stonger than "black". Any single rating which would introduce a rectifying bias is wrong though, there is always someone unhappy for a good reason. The perfect solution is simple conceptually but not quite logistically. Each player X should have two ratings: white rating wr(X) and black rating br(X). These ratings would be computed just the way they are now, except that instead of player X imagine that there are two ficticious players wX and bX, where player wX plays games which are played by X with white color, and player bX plays games played by X with the black color. Will the increased precision gained by noting color offset the loss of precision caused by cutting the number of games rated in half? Some people have noted that some players display greater strength in earlier rounds of tournaments, and weaker strength in the last round. Should we have 4 rating systems: Wearly, Bearly, WlastRound, BlastRound? Surely, this would increase predictive power.  Kenneth Sloan Computer and Information Sciences (205) 9342213 University of Alabama at Birmingham FAX (205) 9345473 Birmingham, AL 352941170 http://www.cis.uab.edu/sloan/ 
#4




Whit/black rating. A solution.
My results are excellent in the TMB variation of the QGD; I have
trouble against the Exchange Variation. So...500 ECO codes x early/late x White/Black = 2000 different ratings. For each time control, of course. 
#5




Whit/black rating. A solution.
Kenneth Sloan wrote: Will the increased precision gained by noting color offset the loss of precision caused by cutting the number of games rated in half? The mean of the two color ratings recovers the number of the games. Also, in the case of someone who played 300 rated games with white and only 100 with the black, the mean value is more fair. Wlod 
#6




Whit/black rating. A solution.
" writes:
My results are excellent in the TMB variation of the QGD; I have trouble against the Exchange Variation. So...500 ECO codes x early/late x White/Black = 2000 different ratings. For each time control, of course. What!? No "timeofday"? or, "dayoftheweek", or, for women only...oh, nevermind.  Kenneth Sloan Computer and Information Sciences (205) 9342213 University of Alabama at Birmingham FAX (205) 9345473 Birmingham, AL 352941170 http://www.cis.uab.edu/sloan/ 
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