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! http://www.slack.net/~whelan/cgi-bin/tbrw.cgi?ecac.cgi HOCKEY-L is for discussion of college ice hockey; send information to [log in to unmask], The College Hockey Information List.