On Mar 1, 10:08, John T. Whelan wrote:
> Major bragging rights for the first person to resolve the
>possible six-way tie (which would cover fourth through eighth
>places!).
OK, I'll bite... especially since this scenario comes the closest of anything
I've ever seen to the ECAC's famed unresolvable infinite loop.
The six-way tie comes about if: Brown and Colgate are swept, Cornell and
Princeton get two points each, and Dartmouth and Vermont sweep. Harvard is
also currently four points behind Brown and Colgate, and thus in theory could
pull into a tie with a weekend sweep, but since they're playing Dartmouth and
Vermont (as is Brown), there won't be a seven-way tie. Thank God for small
favors.
So the six teams involved are Brown, Colgate, Cornell, Princeton, Dartmouth,
and Vermont, and they would all be tied for fourth place with 21 points. The
first tiebreaker is head-to-head record, and here's how the teams have (will
have) done against each other:
Brn Col Cor Prn Drt Vt
Brn --- 1-1 1-1 1-1 1-1 0-2
Col 1-1 --- 1-1 1-1 1-0-1 2-0
Cor 1-1 1-1 --- 2-0 1-1 1-0-1
Prn 1-1 1-1 0-2 --- 2-0 0-1-1
Drt 1-1 0-1-1 1-1 0-2 --- 1-0-1
Vt 2-0 0-2 0-1-1 1-0-1 0-1-1 ---
So the head-to-head records among these six teams are:
Brn: 4-6
Col: 6-3-1
Cor: 6-3-1
Prn: 4-5-1
Drt: 3-5-2
Vt: 3-4-3
This means that Colgate and Cornell remain tied for the #4 seed, with the rest
being eliminated. Now we start over and try to break the tie between Colgate
and Cornell. The two teams split the regular-season series, so we move on to
the next tiebreaker, record against the top 4. Yale, Clarkson, and Rensselaer
would be the top three teams.
Yal Cla RPI
Col 0-2 0-1-1 1-0-1 = 1-3-2
Cor 0-2 1-0 0-2 = 1-4 (pending the game against Clarkson)
If Cornell fails to get two points against Clarkson, then Colgate wins the
record-against-top-4 tiebreaker and the #4 seed, relegating Cornell to #5.
However, if Cornell does beat Clarkson, they would tie Colgate in this
tiebreaker and we would have to move on to the next one, record against the top
8. Which presents a problem, because with an as-yet-unresolved four-way tie
for sixth, we don't have a top 8. So let's set aside for now the
Colgate-Cornell tie in the case that Cornell beats Clarkson, and move on to
breaking the tie among the remaining four teams.
In the battle for the #6 seed, the head-to-head shapes up like this:
Brn: 2-4
Prn: 3-2-1
Drt: 2-3-1
Vt: 3-1-2
So Vermont is seeded sixth. Looking at the record among the three remaining
teams, we get:
Brn: 2-2
Prn: 3-1
Drt: 1-3
So Princeton gets the seventh seed.
On to 8th and the only two left. Brown and Dartmouth went 1-1 against each
other, so we have to look at the record against the top 4. Oh, [expletive
deleted], we don't have a top 4, because we need a top 8 to break the
fourth-place tie between Colgate and Cornell (in one case), and we've got a tie
for eighth here!
Fortunately, it doesn't matter which of Cornell or Colgate is in fourth place.
Brown and Dartmouth's records against the top three (Yale, Clarkson, and
Rensselaer) and Colgate and Cornell are:
Yal Cla RPI Col Cor
Brn 1-1 0-2 1-0-1 1-1 1-1
Drt 1-0-1 0-2 0-2 0-1-1 1-1
Whichever team finishes fourth, Brown would be 3-4-1 against the top 4 while
Dartmouth would be either 1-5-2 or 2-5-1. So Brown wins the tiebreaker and is
seeded eighth.
Knowing this, we can now go back and break the tie between Colgate and Cornell
in the case that Cornell beats Clarkson. The respective records against the
top 8 are:
Yal Cla RPI Vt Prn Brn
Col 0-2 0-1-1 1-0-1 2-0 1-1 1-1 = 5-5-2
Cor 0-2 2-0 0-2 1-0-1 2-0 1-1 = 6-5-1
giving Cornell the #4 seed.
So to sum up, the seedings in the six-way tie are:
4. Cornell 4. Colgate
5. Colgate 5. Cornell
6. Vermont 6. Vermont
7. Princeton 7. Princeton
8. Brown 8. Brown
9. Dartmouth 9. Dartmouth
if Cornell beats Clarkson otherwise
--
Disclaimer -- Unless otherwise noted, all opinions expressed above are
strictly those of:
Bill Fenwick
Cornell '86 and '95 DJF 5/27/94
LET'S GO RED!! JCF 12/2/97
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