Just a couple of quick notes, since Wayne and Ken have discussed many
of the significant issues.
 
First, the principal point of my original post was not to say that
HEAL was an inherently bad way to do things, but to illustrate that
some of the "corrections" it performs would also apply to a balanced
schedule, so you could non-trivially apply it to HE as well as ECAC
this year.
 
It's true that a tournament seeding body might have other criteria
besides overall performance when ranking teams; for instance,
something like PWR (or KPWR) would also give different results than
W-L-T record after a balanced schedule, since it weights recent games,
and those against teams with winning records, more highly.  And the
ECAC and WCHA tiebreakers reward teams who performed better against
the upper parts of the leage, assuming their overall record is the
same.
 
[Wayne on my four-team mini-league]
 
> HEAL considers the Team D ties with powerhouse Team A as more
> important than the Team B win over lowly Team C.
 
To be precise, it also thinks that D's loss to C and B's loss to A are
equally irrelevant.  I.e., that tying a powerhouse and losing to a
bottom-feeder is "better" than losing to a powerhouse and beating a
bottom-feeder.  One of the major impacts of this system is that it
makes the results of games against weak teams unimportant, and greatly
reduces the possibility of a "spoiler" influencing the playoff race.
 
[More Wayne]
 
> Team A and Team B were close in the standings.  Team A played a top
> team and lost.  Team B played a poor team and won.  Team A charged
> into the (RPI) ranking lead, just because they scheduled a top team.
 
This sort of thing used to happen not infrequently with the old
25-50-25 weighting for RPI, and I think it's one of the reasons Hockey
now weights their RPI 35-50-15 unlike the rest of the NCAA.
 
[Ken proposes one scheme for seeding a tournament based on performance
against good teams]
 
> 1. Use KRACH (or your favourite rating system) to rank all the teams.
> 2. Eliminate the lowest-rated team (and thus all games involving that
> team).
> 3, Repeat 1 and 2 for the remaining teams until there are as many
> remaining as you have places in the tournament.
 
This is actually rather similar to the automatic algorithm "You Are
the Committee" <http://www.slack.net/~whelan/cgi-bin/tbrw.cgi?tourney>
uses for interpreting the NCAA's principle that pairwise comparisons
among teams in competition for something (at large bid, bye, default
berth in their own region) are the relevant ones, except of course
that games are replaced by PWCs and results against teams above as
well as below the pack are ignored.  Namely:
 
        1. Rank the teams by number of comparisons won.
        2. Remove the team (or teams if they've won the same number of
comparisons) with the most or fewest comparisons won from the
"bubble", declaring that they definitely do or don't qualify as
appropriate.  Whether you remove them from the top, bottom, or both
depends on whether there are more or less than half as many teams on
the bubble as remaining spots.
        3. Start over from step 1 with the remaining teams (ignoring
all comparisons against teams which have been removed from either end
of the list).
 
Both Ken's algorithm and mine suffer from the "Niagara percolation
effect" we saw last season: if game results/PWCs are more or less
transitive, a team which beat a couple of teams at (or above in Ken's
case) the tournament cutoff can remain a spot or two away from the
bottom of the list at each iteration and end up making the playoffs
despite being far down in the overall rankings.  (This is basically
what team C does in Ken's example.)
 
Incidentally I'll repeat a suggest I made last year on how HEAL could
be Quinnipiac-proofed: Instead of saying that a team's Tournament
Index is (up to an overall factor) the weighted (by number of games
against that opponent) sum of the Preliminary Indices of the teams
it's beaten [counting each tie as half a win] divided by the number of
games, why not recursively define the TI as the weighted sum of the
TIs of the teams you've beaten, divided by your number of games?  (I
propose "REAL" for "Recursive-HEAL" as the pseudo-acronym for this
system.  Or how about a recursive acronym like ELPASO, for "ELPASO
Look at Performance Against Strong Opposition"?)  The KRACH-like
nonlinearity should ensure that a conference whose members play most
of their games against each other but don't beat any strong teams out
of conference are judged as appropriately weak.  Of course, some
fiddling might have to be done to make sure a solution always exists;
for instance, if game results are completely transitive, the only
solution is for all the teams to have a REAL/ELPASO of zero.  KRACH
will also look a little funny in that situation as well, and in fact,
the condition for all teams to have a finite KRACH on the same scale
(that it's impossible to split the teams into two groups where no one
in the second group has beaten--or tied--anyone in the first) seems
like a necessary condition for REAL/ELPASO to be well-defined.
 
                                          John Whelan, Cornell '91
                                                 [log in to unmask]
                                     http://www.amurgsval.org/joe/
 
It's ECAC playoff possibilities time!
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