From: adrian@stein.u.washington.edu (Adrian Mariano)
Subject: Re: winning ratio
Organization: University of Washington
Date: Sat, 21 Nov 1992 00:41:03 GMT

In <1992Nov20.082459.6464@uxmail.ust.hk> schmidt@uxmail.ust.hk (DR. ROY SCHMIDT) writes:

>adrian@stein.u.washington.edu (Adrian Mariano) writes:
>>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.

No handicaps would suggest a 5.5 komi to me.  That's the standard komi
for even games (at least, in some places).  There are no draws to
worry about.  

>>>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.

No it did not. 

>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

If you really want a way to get linear graphs out of exponential
functions, take logarithms.

What Jos said (in rON's quote) about this is

>function of x-y. I have done this measurement with a database of about
>2000 tournament games a few years ago. Actually if x weaker than y, the
>function P(x-y) = ((1/3)^(y-x))/2 with x and y in units of half handicap
>stones and beginning gives only half a stone more on the board.
>When this function was used for the probability in a giant maximum likelyhood
>fit for all these results the graph of measured strength versus generally
>accepted strength was linear (with some scatter of course) from 5 dan to
>15 kyu! I had not expected this in advance and it is something I still
>do not understand.

I don't think there's enough information to figure out what's going
on here.  I don't know what the parameter for the maximum liklihood
was, or what the "measured strength" was.  It would be nice to know
what distribution of ranks were present in the data.  (Probably no 15
kyus played 5 dans.)  

>anything in Joe's post that said that all 2000 games were played
>without handicap.

This was obviously true, or the games would not have been suitable for
his analysis.  

>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.

My previous post expressed too much confidence in the result.  It
would be good to see more detailed information about the data and
analysis. 


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