These are a little late this week: I waited for Monday night's Beanpot
scores before recalculating everything.
Surprisingly enough, the top three is unchanged, despite CC's loss and
BU's two losses; the reason seems to be that most of the teams outside
the top three also lost. The big upward moves came from Harvard (not
surprisingly), up 6 places to 6th, and Wisconsin, up three to seventh.
Northeastern (losing to BC), New Hampshire (losing twice to Maine),
and Michigan State (losing to Ohio State!) all lost ground. NMU moved
up into fourth, not so much by their own performance (a split with St
Cloud) as by the performances of others; likewise, Minnesota hung on to
5th despite only splitting with Minn-Duluth.
I've added a new column to the table below which shows each team's
opponents for the week, and the results of the games against them.
For example, BU's results line reads "8:L 8:W 6:L", meaning that
BU played #8 Mass-Lowell twice, winning one and losing one, and also
played #6 Harvard, losing that game.
Rank Last Team W L T Rating Week's results
===================================================================
1. (1) Michigan 27- 2- 1 12.356 33:W 31:W
2. (2) Boston U 19- 7 11.268 8:L 8:W 6:L
3. (3) Colorado Coll 18- 8- 2 11.036 19:L 19:W
4. (6) Northern Mich 17-10- 1 11.012 11:W 11:L
5. (5) Minnesota 16- 9- 3 10.990 23:L 23:W
6. (12) Harvard 13- 3- 2 10.977 35:W 2:W
7. (10) Wisconsin 17-10- 1 10.904 32:W 32:W
8. (8) Mass-Lowell 16- 6- 5 10.878 2:W 2:L 43:W
9. (4) Northeastern 15- 7- 4 10.841 24:T 22:L
10. (11) Lake Superior 18- 9- 2 10.750
11. (13) St Cloud 14- 9- 3 10.729 4:L 4:W
12. (7) New Hampshire 16-10- 1 10.709 15:L 15:L
13. (9) Michigan State 16- 8- 3 10.708 40:L 39:W
14. (15) W Michigan 15- 9- 2 10.565 31:W 33:W
15. (17) Maine 14-11- 1 10.486 12:W 12:W
16. (14) RPI 13- 6- 2 10.448 36:L 25:W
17. (22) Denver 13-13- 2 10.392 28:W 28:W
18. (20) Miami 13-10- 1 10.298 34:W 34:W
19. (21) Alaska-Anchorage 11-13- 2 10.244 3:W 3:L
20. (16) Alaska-Fairbanks 15-10 10.220
21. (18) Brown 10- 6- 3 10.205 43:L 35:W
22. (19) Boston College 11-12- 3 10.133 30:L 30:L 9:W
23. (26) Minnesota-Duluth 10-15- 3 10.101 5:W 5:L
24. (24) Providence 11-12- 2 10.055 9:T
25. (25) Clarkson 9- 7- 4 9.989 38:W 16:L
26. (23) Bowling Green 11-12- 2 9.969 39:W 40:L
27. (31) Vermont 10- 8- 3 9.886 37:W 29:W
28. (27) North Dakota 8-18- 2 9.850 17:L 17:L
29. (28) Colgate 10- 8- 2 9.817 42:W 27:L
30. (32) Merrimack 9-13- 2 9.784 22:W 22:W 44:W
31. (29) Ferris State 10-17- 1 9.693 14:L 1:L
32. (30) Michigan Tech 7-19- 5 9.672 7:L 7:L
33. (33) Kent 9-17- 2 9.408 1:L 14:L
34. (34) Notre Dame 7-17- 4 9.324 18:L 18:L
35. (35) Princeton 6- 9- 3 9.175 6:L 21:L
36. (38) St Lawrence 8-14 9.132 16:W 38:L
37. (36) Cornell 4-10- 5 9.112 27:L 42:W
38. (39) Union 5- 9- 2 9.028 25:L 36:W
39. (37) Ill-Chicago 6-21- 1 8.979 26:L 13:L
40. (40) Ohio State 3-15- 4 8.938 13:W 26:W
41. (42) Air Force 4-14 8.279
42. (41) Dartmouth 3-15- 1 8.268 29:L 37:L
43. (44) Yale 3-16 7.966 21:W 8:L
44. (43) Mass-Amherst 1- 6 7.812 30:L
45. (45) Army 1-12 7.065
-----------------------------------------------------------
KRACH works along the following lines:
The key is the relationship between ratings and probability. Given the
ratings of two teams, first work out the difference d. The probability
of the higher-rated team winning a game on neutral ice is then:
Rating difference Probability
0.0 0.5
0.2 0.55
0.5 0.62
1.0 0.73
1.5 0.82
2.0 0.88
3.0 0.95
4.0 0.98
5.0 0.99
(or, as a formula: prob=1/(1+exp(-d))).
The ratings are then chosen so that the observed win percentage for each
team is equal to the expected win percentage, which is the average win
probability over all the team's opponents. The better a team's
opponents, the fewer games they will be expected to win.
As a result, a team can achieve a high rating by doing well against
average opposition, or by doing averagely against good opposition.
--
Ken Butler
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