Greg Berge writes:
>Say BU and Maine have identical records against identical opponents, except
>that Maine sweeps BU in their season series.
>
>Doesn't this guarantee that BU will have a better RPICH?
>
>The reasoning: opponents' pct is valued higher than your own winning
>percentage.  Therefore, as BU's percentage drops and Maine's increases, at the
>same time BU's opponents' is creeping up, while Maine's is creeping down.
 
I'm glad you brought this up, because it will give me a chance to
clear up two common misconceptions about the RPI.  Let me first say
that I know I am only one of a bunch of people on HOCKEY-L who (we
hope) understand how RPI works to some degree; or at least, I would say,
more than many people do.  I don't consider myself an expert, but I do
think I have looked at it enough to understand several key aspects of
it.  It also helps that I have discussed it with other people who
understand it too. :-)
 
I hope everyone will pay attention to this, maybe even file it away,
because understanding the following two points goes a long way towards
understanding how the RPI works.
 
First: In the above scenario, BU would not be guaranteed of a better
RPI than Maine.  In calculating OWP (opp win%), you do *not* include
the results of head to head games between the teams.  So for example,
if BU is 25-5-2 and Maine is 27-3-2, and Maine went 2-0-2 against BU,
then in calculating BU's OWP, Maine's record is 25-3-0.  And in
calculating Maine's OWP, BU is 25-3-0.
 
Note that since BU and Maine played each other 4x, the OWP of 0.8929
(25-3-0) would factor in 4x for each team.
 
Second: Contrary to what the weights (25-50-25) may indicate, WP
(win%) actually has a much greater effect on the RPI than OWP and OOWP
(opp opp win%) *combined*!
 
Read the preceding one more time so it sinks in before you go on. :-)
 
Even though WP has a weight of only 25% in the total RPI, the reason
it has a greater effect on the RPI is that the standard deviation of
WP among the 44 teams is much greater than the std dev of OWP and of
OOWP.  An examination of any of the RPICHs posted by Erik will show
this to be true.
 
In fact, in discussing this further with Keith, who originally posted
this piece of information about a month ago, he explained to me that
in the RPI, the "real" weight of WP works out to be about 4.57, while
that of OWP & OOWP combined is about 2.42.
 
This can be determined by the following (again, as told to me by Keith):
 
4.57 = (0.25 * standard deviation of WP)
2.42 = ((0.50 * std dev of OWP) + (0.25 * std dev of OOWP))
 
where 0.25 = RPI weight of WP, 0.50 = RPI weight of OWP, 0.25 = RPI
weight of OOWP.
 
RPI is certainly not perfect, but in many of the ways in which people
consider it to be imperfect, it actually does a better job than would
appear at first glance.
---                                                                   ---
Mike Machnik                                            [log in to unmask]
Cabletron Systems, Inc.                                    *HMM* 11/13/93