we are looking at horse racing. we have a database of 180,000 records,
representing results of probably 15,000 races. we keep only a few
attributes of each runner, and make no attempt to track any particular
horse from one race to the next.
now, over the entire result set, we can drive some simple stats: for a
given field size, top ranked horse wins x% of starts, 2nd ranked horse wins
y% of starts etc. we can also look at it through another independent
dimension, such as starting price, or weight, etc.
so, I have a horse which is ranked #1, had odds of n to 1, weight of
whatever, etc. if I want to calculate its win probability I could search
the database for the intersection of these attributes, but my result set,
hence sample size, could be very small - too small to be reliable.
what I want is a way of combining these independently derived figures from
the entire sample into a figure for that horse that bears some relation to
reality. it may be as simple as a weighted mean - I don't know.
from what I remember of Kosko's book, this seems similar to his examples of
how fuzzy logic works. I realise that fuzzy logic is not probability, but
I'm happy to think in terms of the degree of membership of the set of
winners for a given horse.
my mathematical abilities don't go past high-school algebra, so please keep
it simple.
ta muchly in advance,
-- Andrew - Wizzardabarnett@paws.aus.net