Curious about the effect of certain individual games, I decided to
change Maine's 4-2 loss to Mass Amherst to a win and see how it
affected the RPI rating (Rating Percentage Index).
 
(note: I have also written a program to calculate the RPI...I only
plan to use it for analysis here and there.  I added in the rankings
of teams in the various factors.  Also, I decided to multiply the
floats by 100 because I could not get rid of the leading '0' in C++,
as in '0.5992', and so my numbers are in a slightly different format
from Erik's RPICH although they are actually the same.)
 
Here are the top 5 before and after the change.
 
WITH UMA BEATING MAINE (no change)
RPI                                             Opp         OppOpp
RK                     G  W  L  T   Win% RK     Win% RK     Win% RK      RPI
1  Boston University  25 17- 5- 3  74.00 4     57.45 1     50.26 13    59.79
2  Michigan           23 18- 4- 1  80.43 2     52.92 8     50.04 17    59.08
3  Maine              29 21- 2- 6  82.76 1     49.67 22    51.59 6     58.42
4  Colorado College   28 21- 7- 0  75.00 3     50.15 16    52.17 2     56.87
5  New Hampshire      25 16- 6- 3  70.00 6     52.75 9     49.70 23    56.30
 
WITH MAINE BEATING UMA (only change Sat Maine-UMA score)
RPI                                             Opp         OppOpp
RK                     G  W  L  T   Win% RK     Win% RK     Win% RK      RPI
1  Boston University  25 17- 5- 3  74.00 4     57.70 1     50.27 14    59.92
2  Maine              29 22- 1- 6  86.21 1     49.67 22    51.73 5     59.32
3  Michigan           23 18- 4- 1  80.43 2     52.92 8     50.03 17    59.08
4  Colorado College   28 21- 7- 0  75.00 3     50.15 16    52.21 2     56.88
5  New Hampshire      25 16- 6- 3  70.00 6     52.66 9     49.66 25    56.25
 
WHAT HAPPENS
Maine effectively lost a spot in the RPI simply by losing the game to
UMA, as they fell from 2 to 3 and Michigan moved up.  Maine's rating
fell from 59.32 to 58.42, a difference of -0.90.
 
Where this is important is in Maine's race with BU for the #1 seed in
the East.  The loss makes the difference between BU and Maine 1.37 as
opposed to 0.60.  Since the threshold below which more detailed
comparisons can occur (including head to head record) is 1.00 (0.01 in
RPICH), a difference of 1.37 means that Maine's +2 head to head
advantage (2-0-2) over BU would not come into play if the season ended
today.  BU would be the top seed in the East.
 
BTW, note that by switching the Maine loss to a win, BU gained in the
RPI because of OppWin% (they played Maine 4x and UMA 2x, and Maine
would have been a little bit better with a win while UMA would have
been a little worse with a loss).  On the other hand, UNH lost ground
in the RPI with the change because UNH has played UMA 3x and Maine
only 2x thus far - but there will still be 2 more regular season
meetings between UNH and Maine.
 
It might be interesting after the season is over and all games have
been played, to then switch the results of individual games to see how
much effect a switch would have had in the end.  I am inclined to
think that as more games are played, we would see a devaluation in the
importance of UMA's win over Maine.  The difference of -0.90 in
Maine's RPI would likely become smaller, but right now, I don't know
by how much.
---                                                                   ---
Mike Machnik                                            [log in to unmask]
Cabletron Systems, Inc.                                    *HMM* 11/13/93