Last year I was trying to devise a computer ranking scheme.  I started with
fundamental thoughts like:
 
        winning is better than losing
        beating a weak team is not as good as beating a strong team
        lowing to a strong team is not as bad as losing to a weak team
        tieing a strong team is better than tieing a weak team
 
The problem with this is how to _QUANTIFY_ "weak" and "strong".  The only
objective evidence is their record.  I tried to make a logical case for
score, but that got too cumbersome because all 2-goal losses aren't equal
(the ever popular ENG).  The same can be said of shots on goal (having seen
games where one team gets 30 blue-line blasts and loses to a team with 15
tic-tac-toe or sniper shots from point blank).  I came up with a scheme and
immediately noticed that it was *horrible* early in the season, but was
quite good at the end.
 
The reason?  with a small number of games played, you get a higher
probability of *wierd distribution* of games played.  For example, Team A
plays Michigan twice, Minnesota, Maine, and BU in its first five games
whereas Team B plays Air Force, Amherst, Dartmouth twice and Wisconsin in
its first five games; Team A is 0-4-1 and Team B is 4-0-1.  Are both teams
equal (assuming the usual performance out of those 8 opponents)?  No, but
there is a case where that tie for Team A may be worth more than the wins
for Team B.  The bottom line is WAIT.  By year's end, I'm sure you'll be
much more in agreement with HEAL than you are now.  Just let the schedules
balance out.
 
Steve G
 
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