This post delves into building the "perfect" computer rating system.  So you
can stop here if you're just not interested.  (But then don't _whine_
later!)
 
I'm told (correct me if I'm wrong) that RPI, when figuring "opp win %"
throws out the games you play with that opponent.  I assume that is because
those games would then count twice; once in your "win %", then again in the
"opp win %".  Logically (at least to me) then the "opp opp win %" would also
discount games already counted by either "win %" or "opp win %".  But I
don't think RPI works that way (sinde nobody told me it did; again, correct
me if I'm wrong).  My guess is that "opp opp win%" doesn't discount 'already
counted' games because it gets tough to do.
 
[notation:  opp-opp-opp-win-% => opp^3]
 
But if you could discount 'already counted' games, it wouldn't take too many
"opp opp opp"s before you've exhausted all the games.  A problem with that,
however, is that when you get to the far end of the "opp opp opp"s, the
games that go into calculating it would be very few (hence high statistical
spreads) and some teams may have non-zero opp^5 values (indicating that
opp^4 didn't exhaust all the games) while other teams' last non-zero value
is opp^4 or lower.  Whew!
 
Plus, there is the issue of what to do with the six "uninvited" D-1 schools
(UConn, Canisius, Holy Cross, Fairfield, Villanova, and Iona).  I know RPI
doesn't count games versus them.  Army is the only D-1 tournament-eligible
team that plays them, but that can send ripples through the opp^n
calculations.  If you just disallow games vs the "uninvited", then you trash
6 or 7 of Army's games.
 
Any thoughts?  What would you consider a tennet of the perfect system?
 
Steve G
 
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