From: schmidt@uxmail.ust.hk (DR. ROY SCHMIDT)
Subject: Re: winning ratio
Organization: Hong Kong University of Science and Technology
Date: Fri, 20 Nov 1992 08:24:59 GMT

In article <1992Nov18.060917.27210@u.washington.edu> adrian@stein.u.washington.edu (Adrian Mariano) writes:
>In <1992Nov18.021006.14737@uxmail.ust.hk> schmidt@uxmail.ust.hk (DR. ROY SCHMIDT) writes:
>
>>>>
>>>>P = 1/2 * (2/3)^(2*d)
>>>>
>>>>where d is the absolute rank difference and P is the probability
>>>>that the weaker player will win.
>
>>There are several problems with such a "formula" approach.
>
>>1.  If we assume no difference in ranks, then the formula yields a 
>>    probability of 0.333 of a given player winning.  Since the game is
>>    not three-handed, we would have to assign the remaining 1/3 to draws
>>    Having played not a few games in my life, draws just don't seem to
>>    come up often enough :-).
>
>No.  1/2 * (2/3)^0 = 1/2.  This is the expected result. 
>

Oops!  There seems to be a line missing here!  My post should have read
that the formula yields a .50 probability of a given person winning, but
if we are being even-handed, we should assign a probability of 0.333 of
a given player winning.  After the word "Since" it is correct, and an
attempt to inject some humor into this thing.   p = 1/2 is not the
expected result, because there must be an allowance for draws.  We did
say *no handicaps* right?  I assume this means no komi, as well.

>>2.  Such a formula would have to be strength-dependent.  That is, the
>>    probability that a 16-kyu would beat a 12-kyu is likely much higher
>>    than the probability that a ten-kyu would beat a six-kyu in an even
>>    game, and so forth.
>
>So you would think, but it turns out not to be the case. 

This I've got to see!

>
>[ one problem omitted]
>

Now, why did you omit the most serious problem with this formula? :-)

>>4.  The formula lacks an empirical basis.  First, you have to find a
>
>The formula was obtained from study of over 2000 games played in
>tournaments.  The study was done by Jos Vermaseren.  This doesn't
>conform to the (omitted) guidlines you demand, but it is the best
>emperical basis you can reasonably expect.  It shows (to some degree)
>what happens when real people with real ranks (however they were
>determined) play games.
>

Hmm.  The study by Joe Vermaseren you refer to had a different formula.
That formula also did not allow for draws.  Joe also admitted that the
difference in ranks seemed to be affected by extended play.  I found
his reasoning to be a little hard to follow (because there was not much
presented, and some problems with the English used).  Also, the idea
that a linear relationship (his conclusion) could be represented by an
exponential function does make one wonder.  PLUS, I couldn't see
anything in Joe's post that said that all 2000 games were played
without handicap.

BTW, I did not *demand* anything -- just tried to outline what a large
number of games would be needed to get a fair sample at different rank
levels, differences, etc.  So 2000 games would not be enough to make a
good generalization, once you chopped them up into the various
categories (e.g., 6 kyu vs 5 kyu, 6 kyu vs 4 kyu, etc.).

Perhaps Joe could help by showing us a little more of his data and the
regression(?) analysis he did for each of the differences in ranks.
At least what he has could be a starting point, but I rather doubt it
could be the conclusive result which you seem to think it is.


-- 
Roy Schmidt        schmidt@usthk.ust.hk        schmidt@uxmail.ust.hk
Business Information Systems Dept, School of Business and Management
         The Hong Kong University of Science and Technology
                Clearwater Bay,  Sai Kung,  HONG KONG
Newsgroups: rec.games.go