From: watsonb@alcohol.ecn.purdue.edu (Bradley S Watson)
Newsgroups: rec.games.chess
Subject: Re: Inflation in ELO's system
Date: 29 Sep 92 20:27:09 GMT
Organization: Purdue University Engineering Computer Network

[Explanation of deflationary nature of ELO system deleted]

Sven Hauptfeld writes:
>This sounds very fishy. First of all, there is no obvious correlation 
>between average rating of all players and the points for which players
>compete. Secondly, people leave the pool higher rated than they enter
>because they, on the average, gain points as they play. Therefore, when a
>player leaves the pool, 'taking away' points, players still in the pool
>gain points and make up for the loss. 

How?

>Let's be more precise (math haters skip this paragraph): There are N(t)
>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.

>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.  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.


[ Stuff deleted for brevity]

>Could you give an example of an intentional inflation (or anti-deflation)
>mechanism being in use? I haven't heard of any.
>
>Bonus points (of yesteryear) and rating floors (of today), which indeed cause
>inflation, were established for quite different purposes, so inflation is their
>side-effect rather than desired effect. Floors actually cause large inflation
>of USCF (where they exist) ratings. The way they work is obvious: if the 
>player at his floor would lose points by rating formula, the sum change of the
>two players' ratings is positive instead of zero, which is not ballanced by
>any 'opposite' situation (which doesn't exist).

Bonus and feed-back points were intended to counter the massive deflation that
occured in the 70's because of the Fischer boom.  During 1980 they carried
it even further by simply giving points to all active players under 2100 each
supplement.

>But there is also a more subtle inflation mechanism, which plagues FIDE as well
>as USCF ratings. It is caused by the K factor (maximum up or down change in one
>game) being dependent on the player's rating. For example, USCF K factor is 32
>for players under 2100, 24 for players between 2100 and 2400 and 16 for players
>above 2400. (Maybe the proper definition actually gives only half of these
>numbers, but this is true: if I beat Kamsky, my rating would go up 32 points,
>but his would fall only 16.)

>Actually, in most cases everything works fine: even though the sum change in
>individual games is not zero, the stronger player will win just as many more
>games as necessary to pull the sum back to zero. (This is because ratings are
>based on probability of the outcome.) 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.

[other stuff deleted]

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

Bradley