I have written a program similar to Keith Instone's TCHCR and have
used it to rate the twelve teams in the Olympic Hockey tournament.
The results of that (through the first 20 games - Canada vs. Czech.)
still in progress.)  Note that there is no real connection between
the ratings of the Pool A teams and the Pool B teams since there is
no cross pool schedule.  Thus, as you might expect, the relative
ratings are fairly randomly distributed.
 
 
 
 
 
 
(Some results from today are to follow, so if you don't wish to see the team's
records, you should quit now . . .)
 
 
 
 
Rankings for Olympic Hockey Tournament
 
  Rank   Team Name            Record         Rating         Schedule
  ----   ---------            ------         ------         --------
    1    United States (A)    3 - 0 - 0       82.60          42.60
    2    Czechoslovakia(B)    3 - 0 - 0       78.28          39.28
    3    Sweeden       (A)    3 - 0 - 0       68.60          26.60
    4    Canada        (B)    3 - 0 - 0       67.35          25.35
    5    Unified Team  (B)    3 - 1 - 0       66.33          38.58
    6    Finland       (A)    2 - 1 - 0       57.00          40.00
    7    Italy         (A)    1 - 2 - 0       42.40          53.40
    8    France        (B)    1 - 3 - 0       38.13          59.12
    9    Germany       (A)    0 - 3 - 0       28.40          69.40
   10    Switzerland   (B)    1 - 3 - 0       24.54          46.29
   11    Norway        (B)    0 - 4 - 0       13.38          59.12
   12    Poland        (A)    0 - 3 - 0        9.00          56.00
 
Based on  20 games.
 
 
Now, consider a hypothetical game between Czechoslovakia and Poland
which is won by the Czechs by the score of 3-2.  The rankings now
look like this:
 
Rankings for Olympic Hockey Tournament
 
  Rank   Team Name            Record         Rating         Schedule
  ----   ---------            ------         ------         --------
    1    United States (A)    3 - 0 - 0       94.77          54.77
    2    Sweeden       (A)    3 - 0 - 0       80.77          38.77
    3    Finland       (A)    2 - 1 - 0       69.17          52.17
    4    Czechoslovakia(B)    3 - 0 - 0       66.11          27.11
    5    Canada        (B)    3 - 0 - 0       55.18          13.18
    6    Italy         (A)    1 - 2 - 0       54.57          65.57
    7    Unified Team  (B)    4 - 1 - 0       54.17          25.37
    8    Germany       (A)    0 - 3 - 0       40.57          81.57
    9    France        (B)    1 - 3 - 0       25.96          46.96
   10    Poland        (A)    0 - 4 - 0       21.17          64.67
   11    Switzerland   (B)    1 - 3 - 0       12.38          34.13
   12    Norway        (B)    0 - 4 - 0        1.21          46.96
 
Based on  21 games.
 
And since the weak Pool A team did fairly well against the strong
Pool B team, the rankings have become top heavy with Pool A teams.
Also, notice that the strength of schedule for the Pool A teams is
higher than that for the Pool B teams.
 
The take-home message here is that only one cross division game will
skew the relative rankings of the teams acording to the outcome of
that game.  And so it is in TCHCR.  The skewing of rankigs which
favors the western teams is due to the west's superiority in the very
limited sample of east-wast games.  Also, it is due to the west's
better performance against the independants relative to the east.
This has been Keith's contention all along and it is the correct
analysis.
 
 
Now, for fun, consider a different hypothetical game in which the USA
beats Norway 3-2.  The same effects should be observed as were
before.
 
Rankings for Olympic Hockey Tournament
 
  Rank   Team Name            Record         Rating         Schedule
  ----   ---------            ------         ------         --------
    1    Czechoslovakia(B)    3 - 0 - 0       96.39          57.39
    2    Canada        (B)    3 - 0 - 0       85.46          43.46
    3    Unified Team  (B)    3 - 1 - 0       84.44          56.69
    4    United States (A)    4 - 0 - 0       64.49          26.24
    5    France        (B)    1 - 3 - 0       56.24          77.24
    6    Sweeden       (A)    3 - 0 - 0       50.49           8.49
    7    Switzerland   (B)    1 - 3 - 0       42.66          64.41
    8    Finland       (A)    2 - 1 - 0       38.89          21.89
    9    Norway        (B)    0 - 5 - 0       31.49          74.69
   10    Italy         (A)    1 - 2 - 0       24.29          35.29
   11    Germany       (A)    0 - 3 - 0       10.29          51.29
   12    Antarctica    (C)    0 -12 - 0        0.00           0.00
 
Based on  21 games.
 
Now the schedule strength of the Pool A teams has plumetted.  Notice
too that Poland's rating has dipped below that of the mighty team
from Antarctica which I am using as a basis team.
 
Everybody beats the Antarcticans by a score of 10-0, but the games
against the lone Pool C team are given a weight seven orders of
magnitude lower than the actual games.  The efect of the basis team
is then to scale the ratings for everyone else, but the effect on the
rankings of the "games" involving the basis team drop out after only
one game is played.  However, it is possible to do worse than the
basis team when a limited sample of data is used!
 
     - Pat
.
 
- Patrick E. Fleming ---------------------------------------------------
- Department of Chemistry ------------ Pour un instant je suis content -
- The Ohio State University ---------- En l'air de la Liousianne -------
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