From: sloan@cis.uab.edu (Kenneth Sloan)
Subject: Re: F-S II Ratings
Organization: CIS, University of Alabama at Birmingham
Date: Tue, 6 Oct 1992 14:56:04 GMT

In article <SOO729N@mailgzrz.tu-berlin.de> krause@math.tu-berlin.de writes:
>In article <1992Oct5.143550.14789@bnr.ca> pmarko@bnr.ca (Peter Marko)  
>writes:
>> After 15 games, this is how they measure up...
>>...
>> 
>>           Re   Pe    G  W  L  D   S   Pa    Rp    Rn
>> 
>> Fischer  2700  64%  15  5  3  7  8.5  57%  2647  2675
>> Spassky  2600  36%  15  3  5  7  6.5  43%  2653  2625
>> 
>>...
>
>Oh, please drop this rating stuff. Performance rating is nearly
>meaningless.

"Nearly meaningless" is not quite the same as "meaningless".
PR's are volatile, and difficult to interpret when they are based on
small samples.  That doesn't make them meaningless.

>... Why is Spasski's performance rating higher then
>Fischer's, although Fischer has won more games.

Because Mr. Marko has used the zero-th order method of calculating PR.
As I have already pointed out (while critiquing *my* calculations - I'm
not criticizing Mr. Marko's calculations) - you can do slightly better
by noting that the difference in PR's should be (in this case) 47 points
(let's round that to 50).  Choice of the absolute numbers is a tad
arbitrary, but the usual choice is the mid-point of the pre-event
ratings - which Mr. Marko assumes to be 2650.  This gives Spassky a PR
of 2625 and Fischer a PR of 2675.  Happy now?  

>
>I also doubt your estimated ratings before the match! You got them
>from nowhere.
>

Not quite nowhere.  His arguments where reasonable (if debatable).  I
don't personally see any reason to start anywhere except 2550 and 2760.
There is certainly no reason to use anything other than 2550 (2560?) for
Spassky.  The only issue is the validity of Fischer's 2760.  I can't
think of any principled reason to start anywhere else - Mr. Marko
disagrees (but not by all that much, eh?).   It turns out that both sets
of assumptions lead to the same conclusions.  How nice.

>The calculation above is a good example of the misuse of
>mathematics/statistics. Do something with many numbers and parameters
>and most people believe it, whether it is true or not.

Sorry - it's the "belief" that might be a misuse.  No one actually
posting the calculations has asked you to believe them blindly to the
last insignificant digit.  Instead, use them as a basis for discussion.
Start with your own assumptions (were you brave enough to post your
assumptions *before* the match? Mr. Marko was.) and do your own
calculations.  Report your results.

You give our readers too litle credit, methinks.  Do you really believe
that well-established computations whould not be done, because someone
might mis-interpret them?  Please...attack the mis-interpretation, not
the computation.

I find it amusing that it is the *critics* of these calculations who
appear to believe that the numbers are intended to be carved in stone.
The folks offerring them up don't think so, and haven't claimed so.  
All we've done is make our assumptions *concrete* and examined the
implications of those assumptions.  If you disagree with the
assumptions, then make your own (but be sure to examine the implications
- reality checks are useful).  If you simply think that ratings are
silly, then go and read the (un)solvability thread, instead.


-- 
Kenneth Sloan                   Computer and Information Sciences
sloan@cis.uab.edu               University of Alabama at Birmingham
(205) 934-2213                  115A Campbell Hall, UAB Station 
(205) 934-5473 FAX              Birmingham, AL 35294-1170
Newsgroups: rec.games.chess