From: watsonb@alcohol.ecn.purdue.edu (Bradley S Watson)
Newsgroups: rec.games.chess
Subject: Re: Inflation in ELO's system
Date: 30 Sep 92 20:50:45 GMT
Organization: Purdue University Engineering Computer Network


>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.

This part IS the entire system.  Do a balance on the rating pool:

         Accumulation = Input - Output + Generation

dR is the accumulation, r[+]dN[+] is the input, r[-]dN[-] is the output, and
the generation term is zero in a pure system with no bonus points, rating
floors, different K values, etc.

>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.

The generation term, NI (which should be NIdt to make the units
consistant) is zero.  In a pure system, there is no way to generate points
except from players entering or leaving the system.  If you gain 300 points,
your opponents lose 300 points.  r[imp] is zero no matter what.
If I=0, then why would r[-] be > r[+]?  Simple.  Beginners improve faster
than veterans, so I for beginners is positive and I for the veterans is
negative, with the overall I being 0.  After a couple of years, the beginner's
ability levels off and his rating starts to decrease like the veterans.
This discourages him, and he quits.  Rarely will he have the tenacity to 
stick around long enough for his rating to drop all the way back to his
initial rating, so r[-] is > r[+].


>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?

I vote for definition #1, since #2 would be too hard to judge without
time machines to compare today's players with yesteryear's.  

>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.

By 1979, things had settled down.  Most of the beginners who joined during
the Fischer boom had quit, and those who didn't quit had developed into pretty
decent players during the intervening seven years.  I don't think there
were THAT many more weak players than today, but the ratings at the low
end of the scale were ridiculous.  I remember open adult tournaments that
had class prizes for under 400, 400-599, etc.  It was not unusual for 
scholastic players to have ratings below 100.  Four people in Tennessee
actually got ratings of one!  I don't think things were quite that
bad in other parts of the country (we had lots of big scholastic programs),
but deflation was still clearly out of hand.


>>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 :-)

I wasn't sure whether they were just rounding to the nearest 5 or doing
something strange and mysterious.  Thanks for the info!

Bradley
Newsgroups: rec.games.chess