> Ratings are not reality.
i think that we can probably say that a rating system
for, say, 19x19 go with komi relative to handicap and
time controls roughly the same for each contest (or not,
you choose!) is anything that turns a set of:
(p1,p2,h,t,r) [player 1, player 2, handicap, time, result]
5-tuples
into a set of:
(p1,k) [player 1, rank]
2-tuples, where rank might be some function as opposed
to a constant.
which preserves some minimal assumptions about how
the p_i's should be ordered. (a universally accepted set
of such assumptions is hard to state, which is why
disagreement about ranking systems exists at all).
which is a pretty gigantic set of functions.
however, one particularly nice way of looking at ranking
is that it would be nice if two different players' ranks could
be used to predict the probability that one or the other of them
would win a contest between them if it were to take place right now.
minimizing the error in such a model gives a pretty sweet
(in the sense of usefulness for calculating stone difference, for
instance) ranking system.
s.
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