PWR Today, 2-17-02

[jy3]

jordan the problem this year is this...
if there are no upsets in the tournaments for each of the conferences then you will get 5 bids. Now all of the conference leaders are in the top 12 in the computers EXCEPT mercyhurst, the maac leader. This means that if there are zero upsets, only numbers 1-11 plus mercyhurst will into the NCAAs.
BUT
for each tourney upset that does not result in a top 11 team dropping, then the top 11 drops one.
so if NEstern and wisconsin win their tourneys, then you have to be in the top 9 to get into the tourney. (12= mercyhurst, 11=wisconsin, 10-NEstern).
hope i explained it well (and accurately)
welcome to cornell and cornell hockey, eric!

[Robb]

Jordan,

The way I understand it (someone please correct me!) is that the PWR is a model of the real selection process, which occurs behind closed doors.  However, the committee has (intentionally) leaked enough information over the years for laymen to construct the PWR statistical model that mimics the behavior of the actual committee.  As best as I can recall, the PWR process has correctly predicted the 12 teams selected correctly for several years in a row now, so it's a pretty good model (but possibly NOT the actual process).  The much trickier part is the seeding, which is completely separate from the selection.  Seeding is not based strictly on PWR; it takes many other factors (travel, attendence, intra-conference matchups, etc) into account.

I apologize for not looking at the SCSUs and UMinns of the world - I had (wrongly) assumed that they would dominate us in the PWR just because they won so many more comparisons than we did.  However, as several people have pointed out, the insularity of scheduling allows a couple of bizarre results (read: Brown beating SCSU) to take on far too much significance in the grand scheme of things.  Keith - if you say that RPI can move .01 at this point in the season, I certainly can't argue with you.  I was thinking of it strictly from our point of view - our RPI is probably NOT going to go up by .01 given that most of the teams we have left to play are around .500, so I was thinking that we couldn't catch Maine.  However, if we go up .005 and they drop .005, we are in business...

Thanks for all the thanks - I figured as long as I was poring over the comparisons, I may as well share my thoughts.

[jtwcornell91]

The reason why finishing in the top 12 is not enough for Cornell to get an at-large bid is that neither anyone in the MAAC nor any ECAC team besides Cornell is in the top 12 according to the pairwise.  So if Cornell doesn't win the ECACs, the MAAC and ECAC champions will come from outside the top 12; even if there are no other upsets in conference tournaments, it will mean a top-ten finish is needed for an at-large bid.

The five selection criteria used to define pairwise comparisons between teams are spelled out in the NCAA D1 Hockey Championships Manual, available on line at
http://www.ncaa.org/library/handbooks/iceHockey/2002/2002_d1_m_icehockey.pdf
So no mystery there.  The part that is more complicated is how to use those comparisons to pick out the 7 at-large teams.  Sometimes you can find seven teams that win all the comparisons with everyone else (aside from each other and the teams with automatic bids), but since the pairwise comparisons are not transitive (e.g., right now Cornell win the comparison with Minnesota who win the comparison with Michigan State who win the comparison with Cornell), it can get complicated, and the NCAA has never spelled out how they sort it out when it's not obvious.

PWR is a name USCHO gave to the total number of comparisons won by a team, and ranking teams by the number of comparisons won will always give the right answer if things are simple, and usually even if they're somewhat complicated.  But I think USCHO oversells PWR to some extent, since there are conceivable situations where PWR does not give the same answer as we would expect from a consideration of the pairwise comparisons themselves.

So the "PWR has always predicted the tournament field" line (which is only true if you take out Quinnipiac for 1999 and 2000) is not so much a case of having constructed a rating that imitates some mysterious process as having chosen a simplification of the process which gives the same answer when things are simple, and getting lucky when they were not.

[RichS]

No...:-D

[JordanCS]

Thanks..I knew I was missing something obvious.  

[Keith K]

Simple reasoning about RPI movements.  Term #1 in the RPI is win pct, with 35% weight.  Our current Win% is .740 (18-6-1).  If we win out from here it will be .803 (26-6-1).  That's a delta of +0.063, which when weighted by .35 gives an increase of +.022.  Now, certainly adding games against 8 more ECAC teams will hurt the SOS portion of the statistic, but it probably won't hurt much. My rationale for saying that is that we'll be averaging more bas schedules into our already bad SOS number, so it shouldn't change much (as opposed to averaging 1.000 for wins into our current .740 win pct.)
The point is, I think, that at this point in the season changes in winning percentage drive the RPI more than the SOS factors, even though SOS is more highly weighted.