The NEW College Hockey Computer Ranking
by Keith Instone
1989-90, including all games up to the NCAA tournament (3/12/90)
[Discussion below]
Rank Team Overall Div. I Rating Old Rank
1 Michigan State 34 5 3 33 5 3 100.00 1
2 Maine 31 9 2 28 9 2 95.06 3
3 Lake Superior 31 8 3 31 8 3 92.04 2
4 Wisconsin 32 9 1 32 9 1 91.99 6
5 Boston College 26 11 1 26 11 1 86.20 4
6 North Dakota 27 11 4 27 11 4 84.96 8
7 Colgate 28 5 1 27 5 1 83.83 5
8 Minnesota 25 14 2 25 14 2 83.51 7
9 Michigan 24 12 6 24 12 6 79.65 10
10 Boston University 21 14 2 21 14 2 78.85 9
11 Providence 22 10 3 21 10 3 77.73 12
12 Bowling Green 25 15 2 25 15 2 75.79 11
13 Northern Michigan 22 19 1 22 19 1 70.69 15
14 Clarkson 21 9 3 19 9 3 69.31 13
15 Minnesota-Duluth 20 19 1 19 18 1 69.29 14
16 Northeastern 16 19 2 16 19 2 63.16 18
17 New Hampshire 17 17 5 16 17 5 62.65 22
18 Denver 18 24 0 18 23 0 62.13 17
19 RPI 20 14 0 19 14 0 58.58 16
20 Cornell 16 10 3 15 10 3 57.30 20
21 St Cloud 17 19 2 17 19 2 55.17 21
22 Colorado College 18 20 2 16 20 2 54.70 26
23 Alaska-Anchorage 21 9 2 12 9 2 54.38 23
24 St Lawrence 13 15 4 13 15 4 49.75 19
25 Harvard 13 14 1 13 14 1 49.54 25
26 Lowell 13 20 2 13 19 2 47.91 24
27 Ohio State 11 24 5 11 23 5 47.16 27
28 Western Michigan 14 24 2 12 24 2 46.03 29
29 Miami 12 24 4 11 23 3 43.19 31
30 Princeton 12 14 1 12 14 1 42.68 28
31 Michigan Tech 10 30 0 10 30 0 40.49 35
32 Ferris State 11 23 6 11 23 6 39.86 34
33 Brown 10 16 3 10 15 3 36.76 32
34 Merrimack 10 24 1 9 24 0 35.31 33
35 Illinois-Chicago 10 27 1 10 27 1 34.84 36
36 Vermont 9 20 2 8 19 2 27.74 30
37 Yale 8 20 1 8 20 1 27.38 37
38 Army 10 16 4 8 16 3 24.15 40
39 Alaska-Fairbanks 10 20 0 5 17 0 22.70 38
40 Dartmouth 4 18 4 4 18 4 16.02 41
41 Air Force 15 13 2 7 11 2 15.47 39
42 Alabama-Huntsville 10 21 4 3 18 2 3.36 43
43 Notre Dame 16 15 0 4 14 0 0.07 42
44 Kent State 14 16 3 4 11 1 0.00 44
OTHERS 21 72 7
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Instead of trying to improve my existing ranking system (now called the
"old" ranking), I started over. I found a method for ranking college
football teams, developed by RJ Leake of Notre Dame in 1976. It didn't
take much work to get it to make sense for hockey.
This isn't how I implemented it, but this is probably how I have to
explain the NEW ranking. First, make a schedule graph, a node-branch
diagram of who(m) played who(m). Each team is a node. Every time two
teams play each other, connect those two nodes with a branch. Next,
assign a value to each branch based on the Game Outcome Measure (GOM).
The GOM is specified by me, based on what I think the important
criteria are (see below). Each branch is also assigned a weight, based
on how important I think that game is. After the branches are assigned
numbers, the problem is to assign values to the *nodes*. These node
values will be the ratings for the teams. Finding the ratings means
solving a system of linear equations: for 44 teams, there are 43
unknowns (one arbitrary team is chosen as the refernce team). A least
squares distance measure is used to find the ratings. For you math
buffs out there, I used simple Gaussian elimination to solve the
equations.
I think this is an interesting system because a team's performance is
tied closely to its opponents. With the old way, I tried to separate
how a team performed (Win%) from who they played (SOS%). This way,
however, the concept of schedule strength is automatically and
intimately included.
Here are the changes I made that are particular to hockey.
I weighted all the games equally because that is what the NCAA
selection committee does. Personally, I think the league championship
is more important than a regular season game, but I didn't do that
here.
The heart of the rating is the GOM. Whatever this number turns out to
be for a given game, the winning team gets a value of (positive) +GOM
on the branch and the losing team gets (negative) -GOM. Even if the GOM
is zero, it still affects the ratings because the fact that the two
teams played is recorded.
My hockey GOM:
The winning team gets 20. Add the margin of victory, with a maximum
of 5 (Sagarin might call this a "diminishing returns principle" because it
doesn't help teams who blow out weak opponents).
If the winners were on the road, add 1;if home subtract 1; if neutral, 0.
If the winners won in overtime, subtract one.
If the teams tied, then start with zero, call the visiting team the winner,
and apply the home/road rule from above.
For example, if Team A hosts Team B and loses 5-3, the GOM would be:
20 + 2 (margin of victory) + 1 (road) = 23. B gets +23, A -23.
If A and B had tied, then B would get +1 and A -1.
Team A 4 - 3 Team B, ot = 19.
Team A 10- 2 Team B = 24.
I included the rankings that I got from my old, simple method so you can
compare. I would say the old way wasn't too bad, considering how simple it
was.
Finally, I "normalized" the ratings that you see above to make them all
go from 100 down to zero. Before I normalized, Yale had a rating of
zero because they were the reference team. Everyone else's rating was
relative to Yale. I may not always normalize: I haven't decided yet.
Now, I need to verify my mathematical operations some more. Then I plan on
fiddling with different GOMs and weights.
Boy, this is fun. .............Keith
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