From: Kenneth.Sloan@mailbox.bison.mb.ca (Kenneth Sloan)
Newsgroups: rec.games.chess
Subject: Re: How can we assess Fischer's strength?
Date: 24 Sep 92 21:38:02 CST

Organization: CIS, University of Alabama at Birmingham

In article <1992Sep24.192821.593@midway.uchicago.edu> hau4@midway.uchicago.edu writes:
>Even though Spassky's rating is as accurate and well established as any other
>player's, there are several reasons why it still can NOT serve as a good
>estimator of Fischer's strength:

Depending on your definition of "good"

>
>1) Fischer is playing ONLY Spassky. Players have different styles and perform
>differently against opponents with different styles. For example, Fischer 
>performed against Tal (and, I think, Geller and Korchnoi) worse than expected
>by their respective ratings; Kasparov lost rating points in, as I remember,
>every match with Karpov. A player's rating is meaningful only if obtained
>against a sufficiently large number of opponents.

Perfectly true.  It is also true of all matches.  They are rated,
nonetheless.  Why should this match be any different?

>
>2) A player's rating has finite accuracy. I think the standard error for ELO
>ratings is about 40 points. That means that there is ~68% chance that Spassky
>will perform within 40 points of his chart rating. If you try to approximate
>Fischer's rating based on this, its standard error will be roughly square root
>of 2 times bigger - something like 55 points.

Also true.  Although, I would speak of "finite precision" rather than
"accuracy".   

>
>3) The match setting, rules, background, outside factors,... are rather 
>unusual and it is not clear how the players are affected by that.
>

Probably true, but debatable.  *Every* tournament/match has unique
factors.  Some more than others.  

>4) In some games, the quality of Spassky's play was probably adversely
>affected by his health problems.
>

Quoting Fischer circa 1972 "I have never beaten a healthy GM".  Health
problems, and reaction to stress, are all part of the game, and part of
a player's chess "strength".

>Everything taken together, it seems that Fischer's rating can only be 
>estimated with a >100 points margin of error.

An interesting opinion, unsupported by quantitative evidence.  I
estimate a 50 point "margin of error" - whatever that is.  Do you mean
"standard error", "standard deviation", or something else?  And, why 100
instead of 55?

>.. If the estimator is at ~2700 ELO,
>this means his actual strength might be higher than Kasparov's or close to
>Judith Polgar's (i.e. not enough for top 50). That is just like no information
>at all.

Not at all.  It tell us, for example, that he's certainly stronger than
anyone posting here...

Consider - before the games played so far, how much would you have
seriously wagered on Judit Polgar vs. Fischer?  How much would you
seriously wager *now*?  If you can honestly say that the games played
have provided you with "no information at all" - then I suggest that you
straighten up and shake the sand out of your ears.

All of your arguments were much stronger *before the fact*.  They were
valid reasons for guessing that Fischer might perform at a wildly
different level than indicated by his established rating.  But the games
played so far are reasonably consistent with both Spassky's and
Fischer's pre-event established ratings.  Where there is no surprise,
there is no need for an "explanation".  If you believe that the results
provide "no information at all", then it is up to you to explain why
they fit so neatly. 

For example, if the score were now 5-2 in Spassky's favor, then we would
all be nodding wisely and pontificating on what a shame it was that
Bobby's skill had eroded so badly over the years.  If the score were now
5-0 with no draws, in Fischer's favor, we might be seriously agitated at
the strong case Fischer had made for an immediate match with Kasparov.
But it's not.  The score is consistent with the interpretation that
Fischer would be a strong Candidate - but that he has no better claim to
a match with Kasparov than any of several other very strong players.  I
submit that that's quite a bit of information.

It is not necessary for an estimate to be precise in order for it to be
useful.  Some people seem to think that ratings ought to be calculated
to 5 decimal places, and revere the numbers as if carved in marble.
Others revel in inventing reasons why the calculations ought to be
adjusted one way, or one way, or one way (but never, it seems, both one
way, and the other...).  It's an *estimate* and comes complete with
error bars.  Neither carved in stone, nore written on the wind.

"The purpose of computing is insight"  -Hamming
"The purpose of computing is in sight" -Hamming



-- 
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

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