From: Pieter Stouten <stoutepf <at> CARBON <dot> DMPC <dot> COM>
Date: 13 jul 1996
Subject: "Theoretical" Elo ratings

At 21:22 -0400 96/07/12, Sean Chasworth wrote:

>>How can you have an absolute rating scale?
>
>Perhaps a better term, would be 'ordinal' scale.  Elo ratings are converted
>to wins a certain percentage of the time, while the Dan/Kyu rankings merely
>say that one player is better, with only an intuitive degree of how much
>better.
>
Not quite. Dan and kyu grades relate to handicaps (although not linearly at
large grade differences) and are more than an intuitive measure of
strength. Although somewhat crude, the European "points" promotion system
that I cooked up many years ago (and that was based on the system of the
British Go Assocation (Federation?)) does relate winning percentages to
dan/kyu grade differences.

The basic difference between dan/kyu grades and Elo ratings is that dan/kyu
grades reflect historic peak performances while Elo ratings reflect actual
current playing strengths. Since one never lose one's grade, in order to
reduce inflation the promotion system has to be somewhat conservative.

In this respect, it is interesting that Albrecht Heeffer wrote:

>I believe these theoretical grades are used for acquiring a higher grade.
>If they are overrated this would imply that one has to perform
>significantly above the average rating of a grade during 6 months to get
>one, which seems to be unfair to me.
>
Without a definite answer from Eric Cheymol, it is speculation that these
grades are used for promotion. As far as I know the "points" system is
still being used. Its inherently inflationary character plus the tendency
of Elo ratings to decrease may explain why the observed average Elo rating
for each grade is lower than the expected (i.e., theoretical) number. I may
well be wrong here and really Eric Cheymol is the only one who can let us
know what the theoretical Elo ratings mean, how they were derived and what
they are being used for. Eric, would you mind letting us in on the secret?
Also, bear in mind that assuming a non-uniform (e.g. a Gaussian or
half-Gaussian) distribution of ratings the average rating for a grade will
be lower than the median (i.e., the "theoretical value"). But even if Elo
ratings were used for dan/kyu promotion it should be born in mind that
dan/kyu grades are titles awarded after peak performance. Since players'
Elo ratings fluctuate, it is not unreasonable to assume that they would
tend to be lower than the threshold set for promotion.

Having said all this, it would still be good investigate whether the Elo of
the entire population has decreased and, if so, shift the entire
population. Unfortunately, as Jeroen Tiggelman pointed out, the population
may be too small to draw any statistically meaningful conclusions. It's a
longstanding wish of mine to integrate the European, DC Shogi Club's and
amateur Renmei's Elo lists, but not much progress has been made yet.

Cheers, Pieter.

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