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Old June 14th 06, 10:11 PM posted to rec.games.chess.politics
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Default 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(??)
psychologically--less so, when there
are class ratings.

***

Wlod

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Old June 14th 06, 10:17 PM posted to rec.games.chess.politics,rec.games.chess.misc
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Default 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.

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Old June 15th 06, 06:02 AM posted to rec.games.chess.politics
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Posts: 170
Default 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) 934-2213
University of Alabama at Birmingham FAX (205) 934-5473
Birmingham, AL 35294-1170
http://www.cis.uab.edu/sloan/
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Old June 15th 06, 07:19 AM posted to rec.games.chess.politics
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Default 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.

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Old June 15th 06, 08:19 AM posted to rec.games.chess.politics
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Default 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



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Old June 15th 06, 07:10 PM posted to rec.games.chess.politics
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First recorded activity by ChessBanter: Jul 2004
Posts: 170
Default 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 "time-of-day"? or, "day-of-the-week", or, for women
only...oh, nevermind.


--
Kenneth Sloan
Computer and Information Sciences (205) 934-2213
University of Alabama at Birmingham FAX (205) 934-5473
Birmingham, AL 35294-1170
http://www.cis.uab.edu/sloan/
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