From: hau4@ellis.uchicago.edu (sven  hauptfeld)
Subject: Re: How can we assess Fischer's strength?
Reply-To: hau4@midway.uchicago.edu
Organization: University of Chicago Computing Organizations
Date: Sat, 26 Sep 1992 07:17:13 GMT

In article <1992Sep24.213802.12849@cis.uab.edu> sloan@cis.uab.edu (Kenneth Sloan) writes:
>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"

I provided an implicit definition at the end. Clearly if it contains no more
info than 'Fischer is somewhere between 1st and 100th in the world', it is not
good for any of the purposes for which ratings exist.

>>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?

You are cheating. "They are rated" here means that a player's (established)
rating changes according to the match result, not that one can obtain a rating
based on a match against one opponent. Therefore, your question cannot be
addressed to me. I didn't say this match was (in this aspect) 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".   

You are right.

>>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".

Not quite true, for rating purposes that is. For example, when Huebner was
ill he resigned the match against Korchnoi. Only the games actually played
counted for rating. But due to unusually high purse in this match (and 
perhaps some clause we don't know of, that no money would be given to a
player who leaves before the end - this is likely to exist, mainly because
of Fischer), Spassky is probably willing to play even in a condition in which
he would resign a 'normal' match.

>>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 gave all the reasoning. Being much more quantitative is not possible without
an extensive (and pointless) research, but assuming my recollection of +/-40
standard error already present in the ELO system, this is a good estimate.

If you disagree, the burden of proof is on you, because scientific honesty
requires that, if there is lack of quantitative evidence, a wider margin of
error should be claimed.

>  I
>estimate a 50 point "margin of error" - whatever that is.

As I said, the burden of proof lies on you.

>  Do you mean
>"standard error", "standard deviation", or something else?  And, why 100
>instead of 55?

Good question. I mean whatever Elo means. I guess it is standard error, meaning
in this case that ~68% of one's performances on tournament-by-tournament basis
should fall in this interval. Standard deviation would mean the same on game-
by-game basis, but that obviously must vary more.

>>.. 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...

It does not. He is certainly stronger than me, but I don't need this match to
know that. But there are some IM's posting here, and by 'certainly' I would
understand *three* standard errors, as is usually understood (that is ~99.7%
probability), and to become an IM you must get over 2400...

>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*?

I would have considered Fischer's chances slightly greater, provided I knew 
he was not demented by his possible psychosis - information for which I don't
need to see his games, the news that he arranged the match sufficed. I haven't
changed the assesment during this match.

(BTW, Fischer will *never* play a match against a woman unless she is *at 
least* World Champion, which Judith probably won't ever be and certainly won't
be while Fischer is in reasonable physical health.)

>  If you can honestly say that the games played
>have provided you with "no information at all" -

No information with respect to predicting results of Fischer's games, which is
relevant here. The *games* have certainly given me some info: for example, that
it is a good idea to play eXd4 in the Breyer...

> then I suggest that you
>straighten up and shake the sand out of your ears.

While the first part is good advice after several hours of sitting at the 
computer, the second is unlikely to yield palpable results.  ;-)

>All of your arguments were much stronger *before the fact*.

No. They would have been nonsense *before*.

>  They were
>valid reasons for guessing that Fischer might perform at a wildly
>different level than indicated by his established rating.

I wasn't even considering his established rating. I assumed it was 'unknown',
because there is no other example of a top player returning after 20 years 
so applying FIDE rating reestablishment rules blindly is empirically 
unjustified. (Actually, with Mecking and Fischer we might be beginning to
collect a sample of such events - in 50 years we might be able to form an
opinion!)

>  But the games
>played so far are reasonably consistent with both Spassky's and
>Fischer's pre-event established ratings.

Depends at what point in the match you observe. The match is still in progress,
so you can't tell. And I think that even after Fischer's 5th win, the result is
still closer than the difference of 220 rating points (Fischer's 2780 from '72
and Spassky's current 2560) predicts. And what about inflation? If Fischer had
been *playing* for the last 20 years at his level from '72, his rating would
have gone up. (If you wish to discuss the issue of rating inflation, please
start another thread.)

>  Where there is no surprise,
>there is no need for an "explanation".

I wasn't explaining, I was warning that statistics was abused.

>  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 the same reason why the fact that cutting off a flea's legs and observing
that it doesn't leap when we tell it to, while it did so while it had legs,
doesn't discriminate between theories {Fleas need legs for jumping} and {Fleas
hear with their legs}.

Seriously, you are jumping into your mouth. If your question is to have any
point, Fischer's old rating must be assumed correct. If that is so, and the
results 'fit nicely', then they indeed provide no new information. If, on the
other hand, you do not rely on the old rating (which is the assumption from
which this thread had started), then the comparison is invalid.

But if the results don't fit *perfectly* but are rather ~50 points off (which
I believe is a more accurate statement), then this doesn't provide ground for
accepting or dismissing either the {this performance rating is as good an 
estimate as any other performance rating} or my {the uncertainty of this 
rating is >100 points} hypothesis. So I need not explain any further.

>               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.

Incidentally, that is what common sense told us before the match. But while
Ivanchuk and Fedorowicz are both very strong players, you must agree that the
difference between them is quite large. And at this point, I'd bet on Fischer 
against Ivanchuk if given 6:1 odds and on Fedorowicz against Fischer if given
15:1 odds (and these 'minimum' odds are biased by my conservative approach to
gambling). Fischer's strength is still far less known than those of even the
notoriously unpredictable players, like Speelman or Ljubojevic.

>                         It's an *estimate* and comes complete with
>error bars.  Neither carved in stone, nore written on the wind.

Of course. But the narrower the error bars, the more information is contained
in the estimate.


	Sven