PWR after Saturday

[Al DeFlorio]

As long as we're gonna win, we might as well play the Red Wings. ::nut::

Really boost our RPI.  (But are they a TUC?)::rolleyes::

[tml5]

That's exactly my point.  As long as Cornell wins, who really cares?  Bring on Denver!  But only if Cornell wins. . .  :-)

[DeltaOne81]

Hmmm, ok...

I was getting most of my information from USCHO. For instance this quote:

"Teams are then ranked by PWR point total, with ties broken by looking at the Ratings Percentage Index (RPI). Note:  this tiebreaking procedure is used solely for convenience in displaying the PWR, and will not necessarily match the committee's process. This is especially true near the end of the top 12, where the committee looks more closely at head-to-head comparisons when selecting the last few teams."

from http://uscho.com/FAQs/?data=pwrexplanation

and then the whole example under "Can you give an example?" from their selection FAQ (http://uscho.com/FAQs/?data=selection).

That first one seems to be directly disagreed with by the NCAA selection procedure (though technically, the NCAA only says it's used as the tie-breaker in individual comparisons, not overall - but that messes with the PWR).

The NCAA's instructions are interestingly vague (though not on that point). For instance, no where does it say (as far as I saw) that the selected teams are the one that win's the most comparisons. In fact, I saw no direct comment on how to pick teams overall, only how to compare two individually, which leads me to think that the "example" from USCHO is probably still accurate, except that you *do* break individual ties with RPI.

Last comment: That puts us in an interesting situation right now, because when you break individual ties by RPI, you have to do all the way down to 13 before a 'higher' teams outright loses a comparison to a 'lower' one. Meaning 1-12 should be automatically in (if the season ended now)... but the MAAC winner won't be 1-12, so they'll have to kick at least one out (12, obviously), but it just sorta messes with the system a bit. The 'above the bubble' group right now is simply too big.

Oh, and before someone tells me that none of the matters because the season *doesn't* end today, I know... it's just a statistical game which I'm enjoying and which is undoubtedly more fun than studying ;-)

-Fred, DeltaOne81 '03

[jtwcornell91]

I think the confusion is between using RPI as a tiebreaker to decide an individual comparison and using RPI as a tiebreaker when ranking teams based on the number of comparisons won (after you've worked out who wins each comparison).

When deciding who wins a comparison, RPI is definitely used as a tiebreaker if each team wins the same number of criteria.

OTOH, when deciding how to rank teams based on the outcome of their comparisons, well as has been pointed out, the NCAA doesn't actually calculate a PWR per se, but  they look at all the comparisons among the teams they're trying to sort out.  Presumably they do something like a "local pairwise rating" (lPWR) which totals a subset of the comparison wins.  When sorting out teams that are tied in number of relevant comparisons won, the NCAA first looks at the individual comparisons, and if those don't resolve it, then they go to RPI as a tiebreaker.  To give an example, suppose you have the following pairwise comparisons:

* Denver beats Minnesota, New Hampshire, and Michigan
* Minnesota beats New Hampshire, Michigan, and Cornell
* New Hampshire beats Michigan and Cornell
* Michigan beats Cornell
* Cornell beats Denver

Denver and Minnesota win three comparisons each, UNH wins two, and Cornell and Michigan win one each.  But Denver is ranked ahead of Minnesota and Michigan ahead of Cornell because they win the head-to-head comparison in each case.

On the other hand, suppose we have this scenario:

* Denver beats Minnesota, New Hampshire, and Michigan
* Minnesota beats New Hampshire and Cornell
* New Hampshire beats Michigan and Cornell
* Michigan beats Minnesota and Cornell
* Cornell beats Denver

Now the total number of comparisons won are three for Denver, two each for Minnesota, New Hampshire, and Michigan, and one for Cornell.  This time, individual comparisons can't resolve the Minesota-New Hampshire-Michigan tie (it's a rock-scissors-paper situation), so we have to compare the three teams' RPI.

USCHO's PWR table would break the ties in both cases by RPI, without trying to look at the head-to-head comparisons, presumably because it's easier to write the program that generates the tables that way.  My PWC table does break ties by head-to-head comparisons if possible, because I'm a geek.

As a complement to USCHO's tournament selection materials, you may want to look at my perspective on the process at http://slack.net/~whelan/tbrw.cgi?pairwise or try the "You Are The Committee" script I wrote to help simulate the process at http://slack.net/~whelan/tbrw.cgi?tourney

[Al DeFlorio]

>"[What JTW said above.]"

Would someone email me an Excedrin, please. ::yark::

[DeltaOne81]

JTW-

Do you agree then, that the way it currently is now, the typical "above the bubble" group is "too large" - or do you think that USCHO's description of the bubble group (and hence above and below) aren't valid?

[littleredfan]

Question:

I heard a rumor that the selection committee isolates themselves in a small wooden lodge near a frozen pond and keeps a fire burning in a fireplace. When white smoke appears, they've chosen who will go to the tournament. If black smoke, they have not decided yet. Is there any truth to this rumor? :-D

Note: I've actually found out that the procedure to elect the Pope has now slightly changed:

"In the age of the bullet-proof popemobile, electing a new pope has gone modern. The Sacred College of Cardinals, the electoral body which chooses the pope, will continue to meet and vote in the Sistine Chapel. Breaking with tradition, though, they won't be locked in. Instead they'll live in nearby Casa Santa Marta, new hotel-style facilities in the Vatican, and will be bused the short distance to the chapel where Michelangelo painted the ceiling and Last Judgement frescoes."

whats the world coming to???

[CowbellGuy]

You submit the question, I'll answer it :-)

[Josh '99]

Looking at JTW's You Are The Committee scripts, it looks like there's actually a conceivable set of events (that is to say, not requiring tournament wins by Notre Dame, Wisconsin, and Lowell) that would result in a bye for Cornell.

I don't have the patience to try ALL the possibilities (I can't imagine the MAAC tourney is gonna have a whole lot of bearing on this, since Cornell hasn't played any MAAC teams this year, and I've conservatively (I think) assumed that UAH and Niagara both lose their first games in the CHA tourney), but from what I've tried, this is one reasonable set of events that could lead to a bye for Cornell:

Cornell over Dartmouth, Clarkson over Harvard
Cornell over Clarkson, Harvard over Dartmouth

Denver over CC, Minnesota over St. Cloud
Minnesota over Denver, St. Cloud over CC

Michigan over UAF, Michigan State over Northern Mich.
Michigan State over Michigan

UNH over Lowell, Maine over BU
UNH over Maine

Generalizations:
-  Cornell needs their opponent in the final to be Clarkson, not Harvard.
-  UNH is more or less assured of a bye, and either BU or Maine would likely earn one with a win over UNH; BU could also do so with a win over Maine and a loss to UNH
-  Michigan likely cannot earn a bye even with a CCHA tournament championship, but an appearance in the final appears to assure Michigan State of one
-  Minnesota, Denver, SCSU, and CC all could earn byes depending on the way things shake down in the WCHA tourney

OK, to close on an optimistic note:  If the top seed wins every game in every tournament (yes, I know, not all THAT likely), JTW's script predicts byes will go to UNH, Denver, Minnesota, and...  Cornell.  How about that, it still could happen.  Everyone repeat after me:   "THANK YOU, BROWN."  :-D

[Greg Berge]

> I don't think UAH can help Cornell. If Huntsville wins the CHA tourney, then that's nice and all, but since there's no CHA auto-bid to the NCAAs the TUC status of UAH does not change.

True.  That was a pure brainfart on my part.