From: sloan@cis.uab.edu (Kenneth Sloan)
Subject: Re: FS performances - second half
Organization: CIS, University of Alabama at Birmingham
Date: Tue, 6 Oct 1992 14:11:57 GMT

In article <1992Oct5.195117.24591@midway.uchicago.edu> hau4@midway.uchicago.edu writes:
>In article <1992Oct5.145906.24234@cis.uab.edu> sloan@willis.cis.uab.edu (Kenneth Sloan) writes:
>>
>>"Better" Performance Ratings can be calculated by noting that the
>>*difference* in PR should be approximately 110 points,
>
>By whose fiat?

Elo's.  In particular, the table he gives, based on the logistic function.

Really - this is too elementary for words.  If you question this
calculation, then we have nothing to discuss.  You *have* read Elo's
book, haven't you?  Or, at least the 2 page blurb from USCF?  Or, are
you just making this up as you go along?

>
>> and using your
>>favorite method of choosing a mid-point.  For example, it is reasonble
>>to choose (2760+2550)/2 = 2655 as the midpoint 
>
>Why is that reasonable? Because it is Timman's rating (if it is)?

I think it's reasonable for two reasons:

    0) it's the midpoint of the players' pre-event ratings
    1) it's the method recommended by Elo for calculating PR's
       in a match.

You were invited to make your own choice - go ahead.  Report your
results.  Try and convince us that your choice is better.  Good luck.

>
>>
>>[hmmm - no matter how you slice it, the conclusion that the match is
>>being played at a "solid 2600 level" continues to hold up.
>>Interesting.... But then, it's hard for it not to, as long as we pick
>>2655 as the midpoint.  Skeptics should do a sensitivity analysis.]
>
>Well, it is obvious that due to that pick the match is at a solid 2655 level.
>

"Skeptics should do a sensitivity analysis".  Which word don't you understand?

>>
>>[And...congratulations to the person who - *before* the match -
>>estimated the players' strengths as 2600 and 2700.  The first half
>>performances, and the current established rating calculations agree
>>perfectly with that prediction.
>
>Sure - they are based on that prediction (with 10 points added to Fischer's
>rating).

No.  They were not.  The above calculations are based on the previously
published established ratings of 2550 and 2760.  The calculations *lead
to* the conclusion that the new established ratings have converged (so
far) to 2600 and 2710.

The *prediction* was based on an extra-chess analysis of the motivations
of the two players, and defensible theories on why the predicted ratings
might be expected to be different than the actual published ratings.
[Briefly - *Bobby's been gone for 20 years, but he's been studying, but
he's getting old...subtract 60 points, and *Boris has been fat, lazy,
and bored, but now he's motivated...add 50 points]
While the published ratings have not been exactly invalidated - the
prediction of 2600/2700 is slightly better.  But, the prediction was
most certainly *not* based on the result - and the results are not based
on the prediction.

Exercises for the skeptic:
    * assume pre-event ratings of 2600 and 2700, 
      and calculate post-event ratings.  
    *assume pre-event ratings of 400 and 500,
      and calculate post-event ratings.  
    *assume whatever pre-event ratings you find reasonable,
      and calculate post-event ratings.  

In each case, justify your assumption and explain what you have learned
from the calculation.  


-- 
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