"Ralph N. Baer" said:
 
> Seeing how important the RPI calculation has become to deciding who
> should make the NC$$ tournament (and in filling my mailbox the last
few
> days), does anyone know if there is any scientific basis for the
way
> that the multipliers for three factors (record, opponents' record,
and
> opponents' opponents' record) were chosen?
 
I can't think of any GOOD, OBJECTIVE way to come up with weights but
studying how the three components (WP OWP OOWP) combine to explain
variability among the teams at the end of the season might be a
MEDIOCRE, OBJECTIVE way.
 
A half hours worth of principal component analysis (based on the
correlation matrix for those that care) shows some possibly
interesting things (anyone can do this and come up with their own
interpretations):
 
1. OWP and OOWP are moderately correlated but poorly correlated (all
+) with WP (that's probably good).
 
2. The first principal component axis explains 70% of the variability
among teams while the first two together explain 92% (okay).
 
3. The "weights" for the first two axes are:
 
          PRIN1         PRIN2
 
WP        0.477198      0.858986
OWP       0.601580      -.473208
OOWP      0.640612      -.195491
 
The first axis __MIGHT__ be considered an averaging of the components
with relative weights ROUGHLY .3 .35 .35 (vs old RPI of .2 .4 .4 and
new RPI of .25 .5 .25). The second axis MIGHT be considered a "how
well I did VS how well my opponents did" comparison. (the old RPI is
closer to what __THIS PARTICULAR__ principal component analysis might
suggest)
 
Taking it a little further than Ralph asked:
 
4. Principal component scores (for each team) can be computed using
the new axes. The weights are applied to the variables (WP OWP OOWP)
after centering and scaling (maybe bad as RPI uses variables as is -
analysis based on covariance matrix would be closer, but I did that
and it "wasn't interesting")
 
5. Plotting scores for first two axes generally groups the "good"
teams together. Harvard and MI are kinda different because of poor
opponents' records. MSU and WMU are virtually on top of one another.
St. Cloud is closer (than MSU/WMU) to the region where most of the
"good" teams are at (virtually on top of WI and MN - does that show
my bias!). RPI (the team) is quite distant, actually right on top of
Clarkson. (interesting maybe)
 
 
This is for discussion among interested parties. I used Erik's final
pre-selection RPICH. I won't defend any interpretations.