On Mon, 11 Mar 1996, MR ADAM C WODON wrote:
 
> However, now I am told that the NCAA doesn't strictly go by this.  Why
> then are we wasting our time figuring it out?
 
Well, yes and no.
 
There was an interview with a member of the selection committee, NMU
Coach Rick Comley, on MSC during one of the intermission breaks in the
WCHA Final Five.
 
Comley said that the selections are made strictly by the numbers, and
that the committee has gone to great lengths to remove all human
prejudice. He made quite a point of that.
 
However, he never said exactly what numbers that they use. We (I'm using
the royal 'we' here) have heard that the selection committee is using
five factors for consideration:
 
Record in last 20
Record against teams at or above .500
Record in head to head meetings
Record against common opponents
Ratings Percentage Index
 
These are used to compare two teams. These are exactly the factors that
Tim uses in his PWR comparisons, and that Erik emulates in his rankings.
 
However, there has been *no* confirmation that the way Erik and Tim are
using these numbers is correct. We know the five factors, but not the
exact way these factors will be weighted. What Tim has done for our
hockey page (C'mon, I have to give it a plug!) is only a guess as to the
actual process.
 
> This seems like an unfair "double-dip" of the RPI.
 
It is even worse than that. In doing the calculations, Tim and I have
noticed that the RPI is used not once, not twice, but *three* times.
 
That is, it is used as:
 
1) one of the comparison factors
2) tie break between two teams tied in rating the five comparisons
3) tie break between two teams tied in number of comparisons won
 
This gives an unfair advantage (as Adam has pointed out) to any team with
a high RPI rating. To point out one example (forgive me for including
Minnesota), Lake State, Michigan, and Minnesota are all in a virtual dead
heat for third, fourth, and fifth place in the comparisons.
 
If we look at the individual comparisons, we see that MN beats LSSU in
two comparisons: record against teams >=.500 and record against common
opponents. LSSU beats MN in two comparisons: record in last 20, and RPI.
Thus the teams tie. Tie breaker? RPI, goes to LSSU.
 
MN beats UM in two comparisons: record against teams >=.500, and one head
to head meeting. UM beats MN in two comparisons: record in last 20, and
RPI. Tie breaker? RPI, goes to UM.
 
The difference in RPI between these three teams is:
 
LSSU  .6050
UM    .6052
MN    .6029
 
For a maximum difference of .0023, which, it could be argued, is too
small to be statistically significant.
 
Note: LSSU beats UM *despite* losing RPI (and just barely!) on the
strength of 2 head to head wins (to one loss), record in last 20, and
record against teams >=.500. UM wins RPI, one head to head win, and
record against common opponents.
 
All information taken from our PWR information sheet, located at
http://www.math.umn.edu/~urton/chockey/articles/PWH2H
 
One can imagine a situation where one team ties the number of comparisons
due to RPI, then wins it because of RPI (like the examples above) and then
beats the same team with the same number of team comparisons won due to
having RPI.
 
Ignoring the RPI for a moment, the *other team* wins the comparisons
outright (without having to go to tie breakers), and then wins the other
battle of team comparisons from winning that *one* comparison with that
*one* team.
 
Is that as clear as mud or what?
 
The point is that the RPI is invoked THREE times, which seems like too
many. It is hardly surprising that the PWR comparisons approximate RPI as
closely as they do (the top 12 have NEVER been different, only permuted
slightly, from RPI since Tim began computing them).
 
After throwing around ideas for a while, Tim and I have come to the
conclusion that RPI should be used as a tie-breaker (there will always be
ties, after all, and *something* has to break them) but NOT as one of the
criteria that the RPI is used as the tie-breaker for.
 
Also, there is some question in our minds if the common opponent criteria
has much statistical meaning when there is just a game or two that a
two given teams have in common (this happens especially often in the
comparisons with WCHA vs teams from other conferences, due to the small
number of non-conference games played, although it does happen
elsewhere, as well).
 
 
One last comment: the committee has mentioned using the five criteria
that we are using to choose which twelve teams are going to be included
in the 12 team NCAA Tournament. There has been nothing said, or even
hinted at, about using these to choose seedings for deciding who gets the
four byes.
 
I have heard a rumor (printed in the Minneapolis Star-Tribune a few weeks
ago) stating that any team winning their regular season and their
conference tournament will get a bye. If this is true, Boston University,
Vermont, and Lake State/Michigan may be in line for receiving a bye if
they win their respective tournaments. This is not too surprising in the
case of BU and LSSU/Mich, but it may give some credence to the people
from the ECAC suggesting Vermont deserves a bye from the East. Of course,
they still have two games to win. :-)
 
                                -Lee-nerd
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"It is not written in the stars that I will always understand what is
going on - a truism that I often find damnably annoying."
                                -Robert Heinlein
 
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