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Mon, 8 Mar 1999 12:33:31 -0600 |
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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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