I have been trying to stay clear of recent discussions about various
computer rating systems, but a couple of items have been posted
recently that deserve further comment.  Robin Lock noted that SLU moved
up five spots in the RPICH rankings although it lost both games to
Maine.  He went on to state that a team that only played Maine and lost
every game would still have an RPI rating good enough to make the NCAA
Tournament.  This is correct and illustrates the peculiar nature of the
.25, .50, .25 weights that are used -- as I have stated several times,
.50, .25, .25 would be much more appropriate mathematically.  It does
make sense for a team to have its losses count differently depending
upon the quality of the opponent, but .25, .50, .25 is just too high a
weight on opp%.  [By the way, it is also possible that SLU's rating
went up despite the two losees due to what happened to the other teams
that it played earlier this season.  If most of them won than there
opp% would increase, however the primary reason is almost certainly the
inclusion of Maine twice in the opp%]
 
 
Wayne Smith introduced a new system (at least new to Hockey-L) called
the HEAL system which if you eliminate all of the extraneous calculation
of normalization factors gives each team credit for each win based upon
the quality of the team that it beats (measured by the loser's record).
Interestingly, no such correction is made for losses.  To be consistant
one would subtract for loses based upon the record of the team that
won.  If that had been done, then the HEAL system would be equivalent
to .50, .50, 0.0 weights.  .(I have eliminated the fact that Wayne
states that the minimum PI is 1, which says that if a team has a worse
record than 1-39, still gave them this record.  All that does is make
games against teams with no wins not totally meaningless.)
 
I suppose that rooting for RPI I should say that the HEAL system makes
a lot of sense.  :-)  RPI will get the benefit of its apparent upset
wins vs Clarkson, Harvard, and Brown, but won't lose more for its loss
to Army than it loses for its loss to Maine.  (Note to the reader: in
no way am I trying to disparage Army, I am just using it as an example
of a team with a currently low winning percentage.)
 
Despite my feeling that the HEAL system is lacking due to its
noninclusion of weighted losses, it still makes more sense that the RPI
rating which has no apparent mathematical basis.
 
Ralph Baer
RPI '68, '70, '74