John Whelan wrote earlier:
 
>The MAAC teams do anomolously well in pairwise comparisons due to
>three criteria: record in last 16 games, record vs Teams Under
>Consideration and RPI, and that effect is amplified by the fact that
>they have almost no head-to-head games with other teams under
>consideration and very few common opponents.  I would say that RPI
>falls into a different category than the other two: it is more robust,
>and only fails because the example is so extreme, and is thus fair
>under normal circumstances.
 
  I would disagree with you regarding RPI's relative robustness and
fairness, especially due to its' overbearing influence on PWR.
 
  If you look at the following chart you will see that how closely PWR
tracks RPI.  It would seem very difficult for a team to have a PWR > 2
positions different from their RPI.  In fact, only Niagara has a difference
>2 and theirs is largely explained by the fact that MANY teams ahead of
them in RPI do not have >.500 records and are thus not eligible for PWR.
 
I will take a stab at explaining why PWR is so tightly bound to RPI below
the table.
 
  It can also be seen that there are plenty of other ranking formulas that
do a much better job with the MAAC teams.  Why not replace RPI with the
KRACH algorithm that seems to track RPI very well excepting the MAAC teams?
 It is not perfect either but it is obviously much better than RPI when
stressed by insular scheduling.
 
Note that the CHODR rankings here are from 3/1/99, all others are 3/8/99
RANK   TEAM NAME     PREV CCHP CHODR KRACH MASSEY  AVG  RPI PWR
-------------------------------------------------------------------------
  1  New Hampshire      1    1    1    2     1    1.25   2   2
  2  North Dakota       3    2    4    1     2    2.25   1   1
  3  Maine              2    3    2    3     3    2.75   3   3
  4  Michigan State     4    5    3    4     4    4.00   4   4
  5  Boston College     6    4    5    6     6    5.25   7   9
  6  Colorado College   5    6    6    5     7    6.00   5   6
  7  Clarkson           7    7    7    7     5    6.50   6   5
  8t St Lawrence       10    9    9   10    14   10.50  10  10
  9t Michigan           9   12   13    9     8   10.50  11  11
 10t Denver            13   13   14    8     9   11.00   8   7
 11t Providence         8    8    8   16    12   11.00  20  20
 12  Notre Dame        11   10   10   11    15   11.50  12  12
 13  Northern Michigan 11   11   11   12    13   11.75  13  13
 14t Ohio State        13   16   12   15    11   13.50  16  15
 15t Rensselaer        15   14   17   13    10   13.50  14  14
 16  Mass Lowell       16   15   15   18    16   16.00  22  22
 17t Princeton         18   20   19   14    18   17.75  15  16
 18t Boston University 17   17   16   21    17   17.75  23   0
 19  Colgate           20   18   18   17    25   19.50  17  17
 20  Ferris State      19   19   20   19    22   20.00  21  23
 21  Bowling Green     26   24   29   20    19   23.00  25  25
 22  Yale              21   22   27   22    24   23.75  24  24
 23  Cornell           24   23   22   26    31   25.50  29   0
 24t Wisconsin         27   30   30   24    20   26.00  28   0
 25t Northeastern      27   21   24   30    29   26.00  37   0
 26  Minnesota         22   29   23   23    30   26.25  26   0
 27  St Cloud          25   25   26   28    27   26.50  33   0
 28  Vermont           22   26   25   27    34   28.00  30   0
 29  Harvard           32   34   34   25    21   28.50  31   0
 30  Mass Amherst      30   32   31   29    23   28.75  34   0
 31  Merrimack         27   27   21   37    33   29.50  41   0
 32  MSU-Mankato       31   28   28   33    32   30.25  19  19
 33  Miami             33   35   37   31    28   32.75  38   0
 34  Lake Superior     37   36   38   34    26   33.50  39   0
 35  Brown             34   31   32   36    37   34.00  36   0
 36  Niagara           36   33   33   35    36   34.25  32  21
 37  Alaska-Anchorage  34   37   35   32    35   34.75  35   0
 38  Dartmouth         38   38   36   39    39   38.00  40   0
 39  Alaska-Fairbanks  39   40   40   38    38   39.00  44   0
 40  Western Michigan  40   41   41   40    40   40.50  43   0
 41  Minnesota-Duluth  41   39   39   43    42   40.75  48   0
 42  Michigan Tech     42   42   42   42    41   41.75  46   0
 43  Nebraska-Omaha    43   43   43   44    43   43.25   0   0
 44  Quinnipiac        44   46   44   41    44   43.75   9   8
 45  Union             45   44   45   48    45   45.50  49   0
 46t Air Force         46   47   47   47    47   47.00  45   0
 47t Army              47   45   46   49    48   47.00  50   0
 48t Connecticut       48   48   48   45    49   47.50  18  18
 49t Holy Cross        49   49   49   46    46   47.50  27  26
 50  Canisius          50   50   50   50    50   50.00  42   0
 51  Iona              51   51   51   51    51   51.00  47   0
 52  Fairfield         52   52   52   52    52   52.00  51   0
 
RPI drives PWR because:
 
1: All teams have an RPI (unlike other PWR criteria) and there is rarely if
ever a tie so it counts in all pairwise comparisons.
2: RPI is used to break PWR ties.
 
Using the final 97-97 RPI/PWR as an example to show why RPI is much more
important than H2H games in influencing the PWR:
 
Among the 171 Pairwise comparisons between the 19 teams under consideration
(TUC) there were 113 cases in which there were no H2H games, 7 cases in
which the H2H was even and only 9 cases in which the H2H difference was
greater than 1. So in only 9 of 171 comparisons was the H2H more important
than RPI, 42 cases of equal importance,
and 120 cases where the RPI carried more weight.
 
Also, there were 19 ties amongst those 171 PWR comparisons
of TUC in the 97-98 PWR, all of which were broken by RPI.
 
Mitch Hawker
 
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