Clinching

[Beeeej]

So, is it my imagination, or is there mathematically no way for us to finish lower then 3rd place?  Someone like Greg, John, or Robb who's much more adept at such theoretical mathematics can hopefully demonstrate what's at work here.

Beeeej

[Josh '99]

I THINK I can handle this one...

Harvard can win out and tie us in points, and I guess depending on tiebreakers can finish ahead of us.

Clarkson needs 8 points to tie us; Dartmouth needs 7.  However, they play each other to close out the season, so it's impossible for both of those to happen.

Therefore, only Harvard and either Dartmouth OR Clarkson can catch us, so even if we lose all the tiebreakers, we still can't finish lower then 3rd.

Now, by speaking of finishing third, are you anti-woofing, Beeeej?  :-P

[Greg Berge]

You're right, Beeeej.

Current standings:

29 Cornell
22 Dartmouth
21 Harvard
21 Clarkson

Everybody has 8 points (4 games) remaining.  Worst case is obviously that Cornell gets 0, Harvard gets 8.  Clarkson plays Dartmouth, so both cannot get 8.    If Clarkson wins, then Dartmouth can get at most 28 points.  If the game is a tie, then Clarkson can get at most 28 points.  

Therefore, we have clinched 3rd place.

I posted 1 second after Josh -- his post says the same thing (and uses fewer words).

[Beeeej]

Thanks very kindly for the explanation, gents.

I am indeed anti-woofing, but the question occurred to me more because I was pondering Placid.  Not to get all ahead of myself or anything, but we've just guaranteed ourselves (one way or another, natch) that we won't be in the Thursday night play-in game.

Beeeej

[Greg Berge]

Yes, we will not be in the PIG.  So to speak.

[Robb]

I've been working on for determining possibilities (including taking tiebreakers into account - bleah).  Unfortunately, I started working on it from the optimistic point of view ("what's the best a certain team can finish"), and planned to adapt it later for finding the worst a team could do.  Haven't gotten that far yet....  My algorithm tells me that the best we can finish is first!  Whoo-hoo!  Not bad for 30-40 hours work, eh?

[DeltaOne81]

LOL

Now, if you wouldn't mind working a bit more for us, Robb, I'm sure we'd all be interested in the burning question on everyone's mind... what's the worst UVM can do?  ::yark:: ( I don't know what Yark is, this would just be my second post in a row w/o smileys, so I had to pick one ;-) - ah, much beetter)

[jtwcornell91]

I have a range of possible finishes that another ECAC watcher worked out if you want to compare your results (email me).  UVM can finish anywhere from 9th to 12th.