From: hau4@ellis.uchicago.edu (sven  hauptfeld)
Subject: Re: Inflation in ELO's system
Reply-To: hau4@midway.uchicago.edu
Organization: University of Chicago Computing Organizations
Date: Wed, 30 Sep 1992 00:21:58 GMT

In article <1992Sep29.202709.26356@noose.ecn.purdue.edu> watsonb@alcohol.ecn.purdue.edu (Bradley S Watson) writes:
>
>Sven Hauptfeld writes:
>>     [...]                                              Therefore, when a
>>player leaves the pool, 'taking away' points, players still in the pool
>>gain points and make up for the loss. 
>
>How?

Patence, patience! It is explained right below.

>>Let's be more precise (math haters skip this paragraph): There are N(t)
                        ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
I now regret saying this. This paragraph (and the following) is crucial.

>>players in the pool at time t. Their average rating is r(t) and the sum
>>of their ratings is R(t)=N(t)*r(t). In time dt, dN[-] players leave the
>>pool and dN[+] enter. Their average ratings are respectively r[-] and r[+].
>>So the number of players changes by dN = dN[+] - dN[-], the rating sum by
>>dR = r[+]dN[+] - r[-]dN[-] and average rating, to first order, by dr=dR/N.
>
>Correct so far, and since r[+] is < r[-], the system is deflationary.

No. ASSUMING r[+]<r[-], THIS PART of the system is deflationary.

>>However, this is not the whole change. All players in the pool 'improve' in
>>time (for generality, allow improvement to be negative as well - all this
>>is valid whether they improve or deteriorate). If their rate of improvement
>>is I, defined as I(t) := dr[improvement](t)/dt, where r[imp.] is change due
>>only to individual changes of players in the pool (i.e. not due to players
>>only to individual changes of players in the pool (i.e. not due to players
>>leaving and entering the pool), then TOTAL change in rating sum is
>>        dR = r[+]dN[+] - r[-]dN[-] + NI.
>
>No, you're confusing strength with rating.

No, I am not. That is why 'improvement' is in quotes. Improvement, I, is 
defined above using nothing but rating, so it is you who are confusing it
with improvement as usually used in speech.

>  In a pure ELO system with no
>inflationary measures, the only way to create or destroy points is to 
>bring in new players or remove old players from the pool.  Improvement
>doesn't create points.  If everyone in the country magically improved their
>strength by 3 classes tonight, the average rating would be unchanged.

As I said, you are confusing the terms. This is true for improvement in the
sense of quality of play, but that is not what I was referring to.

Voltaire said: "If you want to talk, define your terms." Well, I did, but 
damn it, read my definitions!   ;-)

>Bonus and feed-back points were intended to counter the massive deflation that
>occured in the 70's because of the Fischer boom.

This contains a very interesting point that I haven't considered yet: what 
happens when the system is disturbed (taken out of equilibrium). Namely, my
arguments are strictly valid for a steady state, i.e. when the rates at which
players leave and enter the pool are fairly constant in time and the system
has been working for a long (compared with an average player's career) time.
Something like thermodynamics. What happens shortly after sudden changes (like
the Fischer boom, when unusually many new players entered the pool) has to be
scrutinized more, although I'd intuitively predict that we'll find the LONG
TERM effect still to be zero.

Also, we need a unique definition of inflation and deflation. Is it a change 
in average rating, or a change in rating corresponding to equal value of
playing strength?

If we adopt definition 1, then the Fischer boom SHOULD HAVE caused deflation
if the system is to be practically applicable, because many weak players with
less consistent interest for chess entered the pool.

I suggest that we make sure we agree on the definition before we proceed.

>>                                      However, if there exists any other
>>inflation mechanism, this will amplify it, because the TRUE differences 
>>between players will be smaller than their ratings predict and thus the 
>>scores with positive sum will appear more often than those with negative sum.
>
>Not necessarily.  It depends on who the major beneficiaries of the inflation are.
>If lower rated players' ratings are more inflated more than the high rated players,
>then the true differences will be greater than the ratings predict and the
>opposite effect will occur.

Good point. So instead of aplification, this provides a feedback mechanism and
its sign depends on the actual distribution of the (in/de)flationary mechanism.
(Hey! We made some progress in the discussion! Unbelievable! :-)

>While we're on the subject of ratings, does anybody out there
>know why FIDE ratings are always multiples of 5?

I believe they are just PUBLISHED like that, hiding insignificant digits. Why
is this any stranger than USCF ratings always being integers? (However, I
wouldn't bet that USCF ratings are not actually computed as integers. Actually,
I wouldn't bet on ANYTHING about USCF ratings, considering how sloppily they
are maintained :-)


	Sven