> From: Keith Instone <[log in to unmask]>
>
> The NEW College Hockey Computer Ranking
> by Keith Instone
>
> 1989-90, including all games up to the NCAA tournament (3/12/90)
> [Discussion below]
>
> Rank  Team                  Overall   Div. I   Rating  Old Rank
>  33   Brown                10 16  3  10 15  3   36.76    32
 
Any system which lowers the rank of Brown is obviously a crock :-)
 
> [interesting description of methodology deleted ]
 
I assume you'd get the same results by putting the NCAA champions at 100 and
working down instead of selecting a bad team and working up.
 
Although your method seems to be objective, I can see one problem.
The graph of teams is really several loosely connected cliques (see Figure 1).
 
        HE               ECAC
       0---0            0---0
       |› /|            |› /|
       | O |------------| O |
       |/ ›|     |      |/ ›|
       0---0     |      0---0
          |       |        |
          |-------+--------|
          |       |        |
       0---0     |      0---0
       |› /|     |      |› /|
       | O |------------| O |
       |/ ›|            |/ ›|
       0---0            0---0
       WCHA             CCHA
 
Figure 1.  Some loosely connected cliques (ignoring independents)
 
If you ground a single team (Yale, in your case), you'll get a reliable
measure within its clique (ECAC), but you'll be on much shakier ground
outside the ECAC because of the relative rarity of interleague play.
 
I don't know if it will make a difference, but you might want to get relative
ratings within each clique (using 4 different ground teams).  Then treat each
clique as a single "team" and run the program again with only four teams
to interrelate the cliques and get the relative measure of the leagues
(and, hence, the teams in those leagues).
 
Algorithmically:
 
  1. Find a ground team in each league
  2. Run algorithm N times (N = number of leagues [+1 for independents?])
  3. Treat each league as a single team - ground one of the leagues
  4. Run algorithm for "leagues"
  5. Normalize the results from step 2 using the results from step 4
 
-- Matthew
 
Matthew Merzbacher     ARPA:   [log in to unmask]
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tthew
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