Maine Loses? Cornell #2 in PWR?

[jtwcornell91]

DeltaOne81 '03 wrote:

The most likely thing for the committee to use to break a tie is the head-to-head pairwise comparison, but that's just an educated guess. After that (if it's tied w/o the RPI tiebreaker), I'd say head-to-head record.

That would only be necessary in the phenomenally unlikely scenario of the two teams having exactly the same RPI.  Because (repeat after me) THERE IS NO SUCH THING AS A TIED PAIRWISE COMPARISON, a decision between two teams can always be made on the basis of the direct pairwise comparison.

Now, if it's a decision among three teams, each of which wins one PWC and loses one, they break that tie with RPI.  That's how they decided to send Cornell West instead of Vermont and UHN in 1997.

[Greg Berge]

John:

2 team league, teams A and B.
They split two games.
Is that a tied pairwise comparison?

[jtwcornell91]

Greg wrote:

2 team league, teams A and B.
They split two games.
Is that a tied pairwise comparison?

In that situation, RPI itself is not even defined (because neither team has an "opponents' winning percentage" once head-to-head games are left out). Suffice it to say that a PWC can only be tied if two teams have identical RPIs, which is a situation which will, practically speaking, never happen, and which was not the situation Fred was describing.

[nyc94]

Wow.  I can see into the future.

http://uscho.com/news/2003/02/26_006291.php

[ugarte]

Bringing the worst ice in the NHL to the NCAA.

But I'm not complaining - I would love to have the tournament in my backyard.

[ZooeyDog]

So who's figured out what our RPI's gonna be if and when we've beaten Princeton? How much does it drop us, relative to, say, a BU win at Orono tonight?



ZD

[Greg Berge]

You can't figure out what the RPI will be without also factoring in all the other results, though you can figure out what adding a W or L will do, given a hypothetical set of other results.  IIRC, the penalty for beating RPI was around .004

But ooo, ooo (I hope I spelled Horshack correctly), here is a question for the mathematicati.  

DEFINE every possible permutation of outcomes in tonight's game other than the Cornell game as p1, p2, p3, .... pn.

DEFINE Cornell's RPI after a win tonight for the xth permutation of other games as wx, their RPI after a loss tonight for the xth permutation as lx, for a tie as tx.

THEN, is (wx - lx) the same for all x?

In longer words, is the difference between our RPI after a win tonight as opposed to a loss the same no matter what else happens around the NCAA?