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
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