The thread about the RPI index used by the NC$$ to help decide who will
make the tournament has come up for the first time since tournament
selection time last spring.
 
Mike posted an interesting thought namely that the NC$$ regards the
winning percentage as something that should be considered in
determining bids (no argument from me here :-) ) and also the strength of
schedule should be considered..  Clearly opponents' winning percentage
is a reflection of strength of schedule and I can see how opponents'
opponents' winning percentage can also be important.  The question
which has not received any answer is why .25R0 + .5R1 + .25R2 where R0
is winning percentage, etc.
 
Let us forget the R2 term as it will needlessly complicate this
discussion.  One can combine R0 and R1 in the following manner: aR0 +
(1-a)R1 where a is a constant that has to be chosen.  Note that calling
the first multiplier "a" and the second "1-a" just makes the sum 1 --
it is only for normalization.
 
In order for the constants both to be nonnegative "a" must be between 0
and 1.  (I think that everyone will agree that if either constant were
negative, it would not make sense.)  Let us look at the two extremes.
If a = 1 then we are ignoring R1 and teams will be rewarded for playing
poorer teams where they are almost guaranteed to win.  If a = 0, then
only R1 appears and teams will be rewarded for whom they play, not for
how they do.  Some choice of "a" between these extremes is the optimum
choice.  (Of course one can easily argue that the whole idea of the RPI
system makes no sense, but that's not what I am discussing here.)
 
The NC$$ is now choosing a = 1/3, that is .333 R0 + .667 R1.  (Note
again that I am ignoring R2, the crucial thing is that the NC$$ is
counting R1 twice as heavily in its current formula .25R0+.5R1+.25R2,
thus my use of a=.333.)  Two years ago, "a" was chosen somewhat lower (I
forget what).
 
What should be the effect of increasing "a"?  The effect would be that
teams would not be penalized nearly as much for losing to good teams as
in the past.  Thus teams are encouraged to play better teams because
the loses in R0 due to scheduling and losing to good teams is offset by
an increase in R1.
 
I am under the impression that this same RPI formula is used in b-ball.
The effect there seems to me that good teams have been scheduling other
good teams more frequently in their out-of-conference schedule than in
the past.  (At least that is the way it seems to me here in Washington
where Georgetown didn't play St. Leo's for the first time in years.)
From the fans' point of view it is good to see quality teams playing
each other more freqently.
 
The problem in Hockey is that most of the leagues play so many games in
conference that there is little room for scheduling outside of
confernce.  After a couple of games against traditional rivals, there
is not much room left for attempting to increase R1.
 
 
 
Ralph Baer
Stephen van Rensselaer University '68, '70, '74   :-)