I get the HOCKEY-D version of this list,  so my responses are
somewhat delayed.   However,  when I sent out the original post on this,
I was sure that it would fly out into the great diaspora never to return.
I must say that I am a little amused by all the reaction.
 
        First of all,  why is the subject important??   Because the RPI
is used by the NC$$ in the tournament selection process.   And,   ...
last year CC got royally screwed by it  --  to put it politely.
 
        Second,  for those who thought otherwise,  I wasn't trying to
describe the RPI,  I was trying to explain another method which I feel *may*
be better.
 
         Third,  an expression which is in the form of nested products
can never be equivalent to a summation (except for perhaps a range of
values of the arguments),  so we are not arguing about the weighting
factors at all.   We are arguing about the *form* of the expression used.
And,  I would submit that the form which I propose weights win% equally
with strength of schedule.   That is an inherent feature of a mathematical
product is it not?   (Viewing the final product as un-nested,  that is)
 
        Fourth,  normalization is important isn't it?   Otherwise doesn't
one of the nests of the product gain more weight and the results start
to exhibit skew?   (That is the engineer in me asking the question.   My
math degree was a *long* time ago.:-)
 
        Fifth,  it should be pointed out that the RPI,  while resembling
a truncated series,  simply is not  --  and it certainly isn't a
truncated Taylor series which,  if it were,  would make it very
attractive.   For one thing,  the arguments for each term are different!!
"Yet Another",  on the other hand is a nested product that could be
carried out ad infinitum if desired,  and is truncated at the third term.
 
        Finally,  the fatal flaw in RPI is that a team can play a tough
schedule,  win *NO* games,  and yet get a pretty good rating simply because
strength of schedule is 75% weight and *additive* to win%.   A good example
of this sort of thing (although less dramatic) is Harvard's ranking in
the latest RPI.   I'm sorry,  but I have a REAL problem with a 0.500 team
in the national top ten.   I think 14th place (just out of the tournament)
is a much more appropriate ranking for Harvard at this point in time.
 
        -- Dick Tuthill