What follows is a description of the changes I made to my computer
rating from last year, plus a sample ranking from so far this year.
Since there are many newcomers to HOCKEY-L, let me give you a Fruit-
of-the-Loom recap first (I'll keep it brief).
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BRIEF DESCRIPTION OF TCHCR
Here is how The College Hockey Computer Rating works. After a weekend
of games, I type in the data for each game. The important factors are
the two teams involved (duh), the score (so I can see who won and by
how much), where the game was played, and if the game went into OT.
For each game, a GAME OUTCOME MEASURE is computed. It measures how much
one team beat up on the other. If the winner trounced the loser on the
road, then the winner gets a large (positive) GOM. The loser gets the
same GOM, but negative. In the case of a tie on neutral ice, both teams
get a zero, which is factored into the rating "properly". In simple
terms, the larger your margin of victory, the larger your GOM.
All of these GOMs are put into a matrix in a special way to represent a
schedule graph of who has played whom. If each team is a node in the
graph, then a line is drawn to connect two teams that have played each
other. It does not take long before all of the nodes are connected;
once that happens, the teams can be compared. If team A is 5 points
better than B and B is 4 points better than C, then A is 9 points
better than C.
OK so far? Now it gets a little trickier. What happends if A beats B and
B beats C *but* C upsets A. We get a loop in our graph and it is
not clear who the best team is. We take care of that by doing a least
squares optimization; we no longer have "perfect" numbers, but we pick
the optimal numbers to keep everyone happy. (In math terms, I am solving
the system of linear equations.) This intransitivity problem, as I've
heard it called, happens all the time, by the way.
After all the math is done, a rating is left for each team (see table
below, way below). The concept of "strength of schedule" is built into
this model because of the connected schedule graph. If you want to get
your calculator out, you would find that a team's schedule strength is
the average rating of its opponents. That is not an accident; that is a
definition.
Whew, I said I would keep it brief!! If you want to read the paper
where the original algorithm was written up, I'll gladly give you the
reference.
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CHANGES FOR 91-92
Important differences from last year: I added another game outcome
measure (for defense) and changed how the rating is presented.
Noticing that a 4-1 and a 10-7 win both got the same rating last
year, I added a defensive bonus for teams that allow fewer than 25% of
the total goals in the game. I figure a 3-goal win is better when there
are 5 goals scored compared to a "firewagon" affair with 17. Now, a 4-1
win rates 10 (for winning) + 3 (margin of win) + 1 (def. bonus) = 14,
while a 10-7 win is only 10+3=13.
The table of scores which yield the defensive bonus is:
1+ - 0
4+ - 1
7+ - 2
10+ - 3 etc.
If you give up 1 goal, you need to score 4 or more to get the bonus.
Also, all shutout wins get the bonus.
This "defensive" bonus is in response to some coaches who thought
TCHCR was biased toward offensive-minded teams because it looked
at margin of victory. I guess their logic is: Offensive-minded teams
are more likely to stretch their leads, perhaps by scoring 3 late goals
and giving up 1, while defensive-minded teams would try to merely keep
the opponent from scoring again and wouldn't pad their lead. Even
though this bonus is small (roughly equal to 1 additional goal), it
does reward a team that can hold its opponent to very few goals.
Also, the rating is different. Last year I "normalized" the ratings
to make them go from 0 (last team) to 100 (first team). Now, the
ratings are open-ended at the top, plus they are based on a "basis
team" that remains constant throughout the year. The basis team,
with its zero rating, should allow the other 45 teams to always
have positive ratings.
The rating change is in response to list members who wanted to follow
their favorite team's rating from week to week. A team's rating is less
dependent on the teams at #1 and #45 now.
The use of a basis team also allows me to rate teams which are 0-0-0.
I could not do this last year (the math would not let me). Still, I
want to wait a month or more before the first *OFFICIAL* TCHCR comes
out.
With some work, I managed to keep the strength of schedule the same
(average rating of your opponents).
As always, I will gladly argue/answer questions/whatever. Last year,
I asked you to email your questions and I mailed a single summary to
the list. That worked well, so let's do it again.
Keith
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PS Don't forget: doing a REPLY to this message will probably result
in your response being sent to the list. Do you want to do that?
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The College Hockey Computer Rating
Includes games on 11/10/91. Last week's ranking includes games on 11/4/91.
Last Division I Schedule Schedule
Rank Week Team Record Rating Strength Rank
1 1 New Hampshire 5 0 0 90.43 52.98 21
2 2 Boston University 4 0 0 86.71 55.17 16
3 10 Michigan 4 1 1 76.19 59.29 9
4 8 Michigan State 3 0 2 74.49 53.44 20
5 6 Vermont 3 1 0 73.90 55.76 14
6 12 RPI 2 1 0 70.28 63.49 7
7 29 Maine 3 0 0 69.79 36.92 35
8 13 Wisconsin 6 2 0 69.76 55.56 15
9 41 St Lawrence 2 1 0 65.56 50.98 23
10 7 Lake Superior 5 1 0 65.16 37.84 33
11 3 Clarkson 2 1 0 64.70 50.98 22
12 21 Alaska-Anchorage 2 0 0 64.22 31.52 38
13 5 Northeastern 2 1 0 63.95 56.11 13
14 9 Michigan Tech 2 3 1 60.96 65.29 6
15 11 Northern Michigan 3 3 2 56.35 54.81 19
16 16 Minnesota-Duluth 3 5 0 56.18 67.00 5
17 15 Miami 5 1 0 55.75 30.14 39
18 14 Minnesota 4 4 0 55.18 50.56 25
19 28 Boston College 2 4 1 52.47 67.14 4
20 17 Merrimack 3 2 0 51.30 41.73 31
21 22 Brown 0 0 0 51.00 0.00 40
22 23 Cornell 0 0 0 51.00 0.00 41
23 24 Dartmouth 0 0 0 51.00 0.00 42
24 25 Harvard 0 0 0 51.00 0.00 43
25 26 Princeton 0 0 0 51.00 0.00 44
26 27 Yale 0 0 0 51.00 0.00 45
27 19 Air Force 1 3 0 50.05 67.94 3
28 32 Providence 4 2 0 49.86 36.26 36
29 36 Western Michigan 3 2 1 48.21 39.47 32
30 20 Notre Dame 1 3 0 45.44 70.24 2
31 4 North Dakota 5 3 0 44.73 34.59 37
32 42 St Cloud 2 4 0 44.13 56.56 12
33 34 Alabama-Huntsville 1 2 0 39.77 45.90 27
34 35 Colgate 0 2 0 38.06 75.33 1
35 18 Colorado College 2 3 1 36.95 42.28 30
36 33 UMass-Lowell 1 3 0 36.53 54.97 17
37 37 Ohio State 2 4 1 32.92 42.77 29
38 30 Alaska-Fairbanks 1 5 0 31.52 54.90 18
39 39 Bowling Green 1 5 0 31.18 57.52 10
40 40 Union 0 2 0 30.28 62.60 8
41 43 Kent 0 3 0 29.14 57.50 11
42 38 Ferris State 1 4 1 25.99 43.41 28
43 31 Denver 2 6 0 25.76 46.68 26
44 44 Army 0 2 0 15.86 50.58 24
45 45 Illinois-Chicago 0 3 1 9.31 37.10 34
Based on 98 Division I games.
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