The recent threads discussing HEAL, CHODR, etc prompted me to resurrect my
attempt at a computer rating system.  I reviewed my groundrules, made some
changes, and rewrote the program.  Here are the tennets of my system:
 
1.  Wins always add to your raw score.
2.  Losses always subtract from your raw score.
3.  Beating a good team is better than beating a bad team.
4.  Losing to a bad team is worse than losing to a good team.
5.  Ties count a half a win and half a loss.
 
Some implementation rules:
 
1.  Total score is determined by dividing raw score by number of games.
2.  Beating a team with a .800 winning percentage yields 4 times the raw
score contribution as beating a .200 team.
3.  Losing to a .200 team yields 4 times the raw score decrement as losing
to an .800 team.
4.  Only games vs other Div 1 schools count (i.e., only those with NC, WC,
CC, EC, or HE from the composite schedule).
 
The algorithm looks something like this:
 
1.  Determine each team's winning percentage (win %) to date.
2.  For each game played:
     a) add to the winner's raw score the current win % of the losing team.
     b) subtract from the loser's raw score the quantity (1 minus the
current win % of the winning team).
     c) for ties, calculate the contribution to raw score if each team had
won and lost, then divide by 2
          (this is equivalent to adding the opponent's win % and subtracting
0.5.  I'll leave the math to you.)
3.  Divide raw score by games played to come up with the first approximation
(which I'll call X).
4.  Using X in place of win %, redo steps 2 and 3 to arrive at second
approximation (which I'll call Y).
 
The value X is equivalent to only looking at win % and opp win %.  The value
Y is equivalent to taking opp opp % into account.  I set out to determine Y,
which I think is the better gauge of a team.  I'll show X too, since it
bears some merit, and it seems to approximate the HEAL rankings (Y
approximates RPICH).
 
Results: (games through 18 Dec 95):
              ranked by X                                  ranked by Y
      Boston University                       Boston University
      Minnesota                                    Colorado College
      Michigan                                       Minnesota
      Maine                                             Maine
      Vermont                                        Michigan
      Western Michigan                      Western Michigan
      Colorado College                        Vermont
      Lake Superior St.                        Denver
      Clarkson                                       Michigan State
      Michigan State                            Providence
      Denver                                          Lake Superior St.
      Providence                                   Clarkson
      Mass-Amherst                            Minnesota-Duluth
      Bowling Green                            Bowling Green
      Mass-Lowell                                Mass-Lowell
      Minnesota-Duluth                       Mass-Amherst
      St. Lawrence                                St. Lawrence
 
Comments welcome (privately, unless you want the whole list to know!)
Source code available.
 
Steve G
 
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