Well,  here goes nuthin'.   We've all complained about the weighting
factors in RPI or RPICH.   Yesterday,  I noted that the mathematical
expression has the wrong form too.   I think that Ken Butler, the KRACH
author has said the same sort of thing about the form of the RPI model.
(Of course Ken uses a much more sophisticated argument than I will here.)
 
        Basically the idea is that the won-loss percentage should be
multiplied by a "degree of difficulty" to obtain a corrected won-loss
percentage.   How is the degree of difficulty to be calculated?   Well,
the most obvious way would be the opponents won-loss record.
 
        But of course not all opponents were created equal.   So we need
information about the opponents' opponents.   This will of course involve
the opponents won-loss multiplied by the opponents' degree of difficulty
-- which of course will use the opp-opp won-loss percentage.   But lets
be REALLY scientific and renormalize the factors at each step so that
we don't get any built in biases.
 
        Here's how it works.   Find the maximum won-loss percentage of all
the opp-opp's.   From the latest RPICH table by Biever,  that would be
0.5475 of Northeastern.   Normalize all the opp-opp won-loss percentages
to that value ==> for Northeastern the normalized value will be 1.0!!!
For Maine it would be 0.9843.
 
        Now multiply the opponent won-loss percentages by the normalized
opp-opp values to get the corrected opponent won-loss.   For Maine,  that
would be 0.5396,  which incidentally,  will turn out to be the maximum
corrected opponent won-loss percentage.   Therfore,  we use that value
to normalize the corrected won-loss percentages and Maine gets a normalized
1.0 for degree of difficulty (or strength of schedule if you will).
 
        Finally,  the normalized opponents' corrected won-loss percentage
is multiplied by the teams' actual won-loss percentage to obtain the relative
rankings.   I've done this by hand for the top 21 RPICH teams,  and the
resulting table for the top 15 is given below:
 
 1.  Maine      0.8529
 2.  CC         0.7705
 3.  BU         0.6969
 4.  Denver     0.6697
 5.  Brown      0.6558
 6.  Minn.      0.6507
 7.  Mich.      0.6349
 8.  MSU        0.6287
 9.  NH         0.6218
10.  NU         0.5452
11.  Clarkson   0.5262
12.  BGSU       0.5220
13.  RPI        0.5060
14.  Harvard    0.4947
15.  Wisc.      0.4582
 
        Disclaimer:  I did this by hand and may have made a couple of minor
mistakes.   But I don't think that there is anything major wrong with the
calculations.
 
        This method has produced some results which are kind of interesting.
The top 4 are the same as RPICH,  MN and Brown swap places,  and Harvard
drops from 10th to 14th.   The latter effect is probably valid  --  in KRACH
Harvard was all the way down to 20th.
 
        I'd be interested in private comments.
 
        -- Dick Tuthill