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Mon, 31 Jan 1994 21:15:30 PST |
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Big gainers this week were Northeastern (with their duo of wins against
Maine) and Minnesota (ditto against Northern Michigan, who fall from
3rd to 6th. The Gophers are in fact only a tiny distance out of 3rd.
Mass-Lowell slip into the top 10 after defeating Brown and taking three
of four points off BC. Further down, Clarkson's two wins over Cornell
are worth a five-place jump; meanwhile, Mass-Amherst's first win of the
season against Div. I opposition (against now-definitely-last Army!)
takes them to the dizzy heights of 43rd :-)
The ratings follow; below that is a short description of how the system
works. If you would like more information, by all means e-mail me.
1. (1) Michigan 25- 2- 1 12.380
2. (2) Boston U 18- 5 11.475
3. (4) Colorado Coll 17- 7- 2 11.058
4. (8) Northeastern 15- 6- 3 11.040
5. (9) Minnesota 15- 8- 3 11.026
6. (3) Northern Mich 16- 9- 1 11.022
7. (5) New Hampshire 16- 8- 1 10.933
8. (11) Mass-Lowell 14- 5- 5 10.882
9. (10) Michigan State 15- 7- 3 10.877
10. (7) Wisconsin 15-10- 1 10.823
11. (6) Lake Superior 18- 9- 2 10.789
12. (12) Harvard 11- 3- 2 10.707
13. (13) St Cloud 13- 8- 3 10.642
14. (14) RPI 12- 5- 2 10.554
15. (18) W Michigan 13- 9- 2 10.511
16. (15) Alaska-Fairbanks 16- 9 10.444
17. (16) Maine 12-11- 1 10.348
18. (17) Brown 9- 5- 3 10.334
19. (19) Boston College 10-10- 3 10.247
20. (22) Miami 11-10- 1 10.245
21. (21) Alaska-Anchorage 10-12- 2 10.172
22. (23) Denver 10-14- 2 10.133
23. (20) Bowling Green 10-11- 2 10.127
24. (24) Providence 11-12- 1 10.024
25. (30) Clarkson 8- 6- 4 9.980
26. (26) Minnesota-Duluth 9-14- 3 9.961
27. (27) North Dakota 8-16- 2 9.940
28. (25) Colgate 9- 7- 2 9.881
29. (28) Ferris State 10-15- 1 9.811
30. (29) Michigan Tech 7-17- 5 9.725
31. (32) Vermont 8- 8- 3 9.677
32. (33) Merrimack 6-13- 2 9.504
33. (31) Kent 9-15- 2 9.492
34. (34) Notre Dame 7-15- 4 9.453
35. (37) Princeton 6- 7- 3 9.257
36. (38) Cornell 3- 9- 5 9.123
37. (35) Ill-Chicago 6-19- 1 9.096
38. (36) St Lawrence 7-13 9.028
39. (39) Union 4- 8- 2 8.945
40. (40) Ohio State 1-15- 4 8.487
41. (41) Dartmouth 3-13- 1 8.362
42. (42) Air Force 4-14 8.248
43. (44) Mass-Amherst 1- 5 7.965
44. (43) Yale 2-15 7.594
45. (45) Army 1-12 7.081
-----------------------------------------------------------
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
[log in to unmask]
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