Dick Tuthill writes:
 
> > Well, in that case, why not use the HEAL ranking? That ranking had QC at
> > 10th. But of course, using the HEAL would not be consistent with the
> > unstated agenda.
 
I reply:
 
> I have no agenda.  I chose KRACH because I know it is designed with
> the same concepts in mind as RPI, but in a more rigorous way.  I don't
> know anything about HEAL.
 
As a followup, I dug up an old HOCKEY-L post on HEAL (thanks Wayne!)
and the HEAL rating is obtained, up to an overall multiplicative
factor, by multiplying the winning percentage of each of your
opponents by the number of points took from them and dividing by the
number of games you've played.  This system has the same weakness as
RPI, i.e., it assumes the winning percentages of one's opponents are a
good indicator of schedule strength.  This is usually true, but not if
most or all of one's opponents play easy schedules.  Perhaps if one
continued iterating this process until it converged (i.e., your HEAL+
ranking is the weighted average of your opponents' HEAL+ rankings,
where the weighting factor is the number of points taken from each
team divided by twice your total number of games) it would be more
robust.  At any rate, HEAL also has the possibly undesirable feature
of punishing teams which play strong schedules, in that a loss to any
team has the same effect on your rating.  (In KRACH, the strength of
the team you lost to is a serious mitigating factor:  losing to a team
ranked far ahead of you was pretty likely given the other information
available, so it doesn't tell the system anything it didn't already
know.)
                                          John Whelan, Cornell '91
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                                     http://www.amurgsval.org/joe/
 
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