> Heal Point System Rank for Men's ECAC D-I College Hockey, through 2000-02-12.
 
I assume that Wayne is calculating this as a way to correct for the
different in the number of games played by ECAC teams this season, and
the unbalanced nature of the schedule.  However, HEAL seems like a
strange choice of rating system for this job, for the following
reason:
 
If a group of teams play a balanced schedule, each team playing each
other team an equal number of times, I think we'd all agree that the
correct way to rank the teams based on those results is by their
overall won-lost-tied record.  (Whether you refer to total points or
winning percentage, the results are the same, since winning percentage
is just points divided by twice the number of games played.)  KRACH
(as one of the defining properties of the system) and RPI (because all
teams' "Opponents' Winning Percentage" are equal after a balanced
schedule) are both guaranteed to give the same ranking as
won-lost-tied record if the schedule is balanced.  HEAL lacks this
very desirable property, since wins over good and bad teams are rated
differently, while losses to any team are rated the same.  So if HEAL
ratings were calculated for last season's ECAC race, or this season's
Hockey East race, which both used a balanced schedule, there's no
guarantee that the results would reproduce the final standings.
 
To give an example of how this can happen, imagine a league with four
teams, A, B, C and D, who each play each other once each, with the
following results:
 
head2head               ____HEAL____
  A B C D   W-L-T  Pts  P.I.    T.I.   Pct   RPI  KRACH
A   W W T   2-0-1   5  33.33  133.33  .833  .617  350.2
B L   W T   1-1-1   3  20.00   66.67  .500  .500  100.0
C L L   W   1-2-0   2  13.33   44.44  .333  .442  56.51
D T T L     0-1-2   2  13.33   88.89  .333  .442  56.51
 
The teams have played a balanced schedule, so there is nothing to
correct for, but while team D's won-lost-tied record of 0-1-2 is worse
than team B's record of 1-1-1, they have the higher HEAL rating
(Tournament Index).  As shown above, both RPI and KRACH give the same
rankings as winning percentage for this balanced schedule.
 
Incidentally (and I've actually had this going since long before the
whole UVM business, to get a snapshot of teams' performances given the
unbalanced nature of their partial schedules while the season was in
progress) I've got an intraconference KRACH rating for the ECAC on the
web at http://www.slack.net/~whelan/cgi-bin/tbrw.cgi?ecac.rrwp
 
                                          John Whelan, Cornell '91
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                                     http://www.amurgsval.org/joe/
 
It's playoff possibilities time!
        http://www.slack.net/~whelan/cgi-bin/tbrw.cgi?ecac.cgi
 
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