This week, Harvard managed to win twice and *still* fall two places!
KRACH was rather more impressed with Wisconsin's duo of wins over
NMU and CC's three-out-of-four with St Cloud. Lowell, and to a lesser
extent LSSU, also move up after successful weekends. Curiously,
Michigan State's impressive win over UM moved them up only one place.
(The reason probably is that out of the five teams immediately ahead
of MSU last week, four also met with success this time around).
Down in the cellar, Dartmouth's surprise defeat of Brown moves them
up two to 41st; after that loss, Brown slips seven places and out of
the top 20.
 
Rank  Last Team                 W  L  T   Rating   Week's results
===================================================================
   1.  (1) Michigan            28- 3- 1   12.145   23:W 10:L
   2.  (2) Boston U            21- 7- 1   11.367   15:T 15:W
   3.  (4) Colorado Coll       20- 9- 3   11.047   13:W 13:T
   4.  (7) Wisconsin           20-11- 1   11.039    8:W  8:W
   5.  (3) Harvard             17- 4- 2   10.948   41:W 29:W
   6. (10) Mass-Lowell         18- 6- 7   10.946   27:W 27:W
   7.  (9) Lake Superior       20- 9- 4   10.868   14:T 14:W
   8.  (6) Northern Mich       18-13- 1   10.797    4:L  4:L
   9.  (5) Minnesota           17-11- 4   10.792   16:L 16:L
  10. (11) Michigan State      17- 9- 4   10.780    1:W
  11.  (8) Northeastern        17- 9- 5   10.775   26:L 26:W
  12. (14) New Hampshire       17-11- 2   10.646   20:T 20:W
  13. (12) St Cloud            15-11- 4   10.604    3:L  3:T
  14. (13) W Michigan          17-10- 3   10.533    7:T  7:L
  15. (15) Maine               14-12- 4   10.524    2:T  2:L
  16. (18) Alaska-Anchorage    14-14- 2   10.455    9:W  9:W
  17. (16) RPI                 15- 6- 4   10.416   43:T 38:W
  18. (20) Alaska-Fairbanks    16-10      10.246   45:W
  19. (22) Bowling Green       15-12- 2   10.237   35:W 23:W
  20. (23) Boston College      12-13- 4   10.217   12:T 12:L
  21. (21) Denver              14-16- 2   10.196   22:W 22:L
  22. (24) Minnesota-Duluth    12-17- 3   10.131   21:L 21:W
  23. (19) Miami               14-13- 1   10.121    1:L 19:L
  24. (17) Brown               12- 7- 4   10.100   29:T 41:L
  25. (25) Clarkson            12- 8- 4   10.003   39:L 31:W
  26. (27) Merrimack           11-14- 2    9.997   11:W 11:L
  27. (26) Providence          11-15- 3    9.954    6:L  6:L
  28. (30) North Dakota        10-19- 3    9.928   30:W 30:W
  29. (28) Vermont             10- 9- 6    9.844   24:T  5:L
  30. (29) Michigan Tech        9-21- 5    9.740   28:L 28:L
  31. (31) Colgate             11-11- 2    9.650   40:W 25:L
  32. (32) Ferris State        11-20- 1    9.505   36:L 36:W
  33. (38) Union                8- 9- 3    9.307   38:W 43:W
  34. (36) Ill-Chicago          9-21- 2    9.288   37:W 37:W
  35. (33) Notre Dame           7-20- 4    9.212   19:L
  36. (37) Ohio State           5-16- 5    9.163   32:W 32:L
  37. (34) Kent                 9-21- 2    9.106   34:L 34:L
  38. (35) Princeton            7-12- 3    9.051   33:L 17:L
  39. (39) Cornell              5-13- 5    9.048   25:W 40:L
  40. (40) St Lawrence          9-17       8.931   31:L 39:W
  41. (43) Dartmouth            4-18- 1    8.385    5:L 24:W
  42. (41) Air Force            4-14       8.304
  43. (42) Yale                 4-18- 1    8.192   17:T 33:L
  44. (44) Mass-Amherst         1- 6       7.780
  45. (45) Army                 1-13       7.034   18:L
 
-----------------------------------------------------------
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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