Final Weekend Playoff Possibilities

I'll let Bill Fenwick do his usual breakdown of everyone's prosepects, but I went through and worked out which teams will definitely win tiebreakers against which other teams, and which could go either way. Here's what I got (this has been incorporated into the magic numbers at [slack.net] and [slack.net] ; first team listed wins the tiebreaker):

Cg Bn
Cg Da
Cg Cr
Bn Cr
Da RP
Da Bn
Da Cr
Ya RP
Ha Ya
Ya Ck
Ha SL
Ya SL
Ck Pn
SL Ck
Un SL
Pn Un
# Undecided:
# Bn/RP
# Cr/RP
# RP/Ha
# Ha/Ck
# SL/Vt
# Ck/Un
# Ck/Vt
# Un/Vt
# Vt/Pn

Post Edited (02-22-04 11:08)

Well, Cornell possibilities are pretty simple. We can finish 1st through 5th. Without any help we can guarantee 3rd with two wins, since Brown and Dartmouth play on Saturday.

From the "ain't gonna matter" department....

When using the "record against top 4" criteria between Cornell and RPI, do you include RPI in Cornell's record (currently 5th, but Cornell's in the top 4), or do you use a winning percentage based on the number of games played against true top 4 teams (i.e. 6 games for Cornell, 8 games for RPI).

When I calculated it on Friday night, I had Cornell winning the tiebreaker against RPI based on record against top 8 -- I had assumed that RPI would lose to Colgate, which made both teams 2-5-1 against top 4 teams. But to calculate that, I included RPI in Cornell's "top 4 opponents." Actually, at the time, there was a three-way tie for third.

Anyway, thanks for clearing it up.

Cornell can't be 4th and RPI 5th if they finish tied (well, at least not until the tie is broken). Let's say they finish tied for 4th behind Dartmouth, Bornw and Colgate. Then record vs. Top 4 is record vs. Colgate, Brown and Dartmouth. If they finish tied for 3rd (say ahead of Dartmouth) then it's record against top 2.

The Top 4 tiebreaker with RPI can go either way. If Dartmouth is 5th, RPI would win 2-1. If Brown is 5th, Cornell wins 2-1. If the tie is for 4th then it's a wash, 3-3 and we go to Top 8. Cornell looks pretty good on that one, but I don't think it's certain yet (just by visual inspection).

Posted this on USCHO, but it fits here too (some of it has been updated). All tiebreakers are assumed to be only 2 teams. 3+ team tiebreakers I can't go through every single permutation.

(And FYI, Dartmouth plays Brown on Friday, not Saturday - I notice TBRW has it switched around)

Colgate has clinched a first round bye, and needs only a win to clinch the regular season title.

Brown needs a tie vs. Dartmouth OR a win vs. Vermont to clinch a first round bye. If they tie Vermont AND lose to Dartmouth and RPI ties them with a 4 point weekend, Brown falls to 5th if Clarkson winds up as the 8th seed. If SLU or Union winds up in 8th, then Brown wins the tiebreaker and takes 4th.

Dartmouth clinches a first round bye with a 2 point weekend (either a win or 2 ties), and can win the regular season title with 2 wins and Colgate losing twice.

Cornell clinches a first round bye by getting at least 2 points as well. If Cornell and RPI end up tied, I believe Cornell has the tiebreaker via record vs. Top 8.

Everyone else (RPI and Yale) needs help to get a first round bye.



Post Edited (02-22-04 17:40)

Ben Flickinger wrote:

Everyone else (RPI and Yale) needs help to get a first round bye.

Post Edited (02-22-04 17:38)

Being five points or more behind four teams, Yale will need a lot of help.

Why did I think they were only 3 behind Dartmouth and Cornell? Oh well, then the race for the 4 byes is down to 5 teams, with only RPI needing help to get one.

Keith K '93 wrote:

Cornell can't be 4th and RPI 5th if they finish tied (well, at least not until the tie is broken). Let's say they finish tied for 4th behind Dartmouth, Bornw and Colgate. Then record vs. Top 4 is record vs. Colgate, Brown and Dartmouth. If they finish tied for 3rd (say ahead of Dartmouth) then it's record against top 2.

The Top 4 tiebreaker with RPI can go either way. If Dartmouth is 5th, RPI would win 2-1. If Brown is 5th, Cornell wins 2-1. If the tie is for 4th then it's a wash, 3-3 and we go to Top 8. Cornell looks pretty good on that one, but I don't think it's certain yet (just by visual inspection).

Oh yeah. Duh.

But you did answer my question.

[q]Cornell clinches a first round bye by getting at least 2 points as well.[/q]

Not correct for multiple ties.

Say Cornell gets 2 points -- that means they have 27. Doesn't the following scenario deny them a bye?

+ RPI sweep (27)
+ Brown 1 point (27)
+ Dartmouth 2 points (27)

Then we get a 4-way tie for second, and I think Cornell is dead last in the h2h and finishes 5th.

Put Dartmouth in 2nd and assume a 3-way tie for third (Cornell, RPI, and Brown), and I think Cornell loses that h2h and finishes 5th.

Therefore, we need at least 3 points to clinch a bye (and with 3 we will clinch at least 3rd at the same time).



Post Edited (02-23-04 08:49)

Greg Berge '85 wrote:

[q]Cornell clinches a first round bye by getting at least 2 points as well.[/q]

Not correct for multiple ties.

Say Cornell gets 2 points -- that means they have 27. Doesn't the following scenario deny them a bye?

+ RPI sweep (27)
+ Brown 1 point (27)
+ Dartmouth 2 points (27)

Then we get a 4-way tie for second, and I think Cornell is dead last in the h2h and finishes 5th.

That's not how the head-to-head tiebreaker works. If you have a three-way tie with Brown and RPI, it goes like this:
Head-to-head points: Brown 5, RPI 4, Cornell 3; Brown wins tiebreaker
Now start over with a 2-team tiebreaker between Cornell and RPI.
Head-to-head points: 2 each
Points vs. Top 4: 3 each (assuming Dartmouth is in the top three and Cornell and RPI are tied for 4th)
Points vs. Top 8: depends whether SLU is in the top 8 or not.

It is possible for Cornell to take 2 points and not get a bye, but SLU needs to finish in the bottom four.

A) I said all my tiebreakers assumed 2 teams only. I don't have time to figure out 3/4 team ties and what combination leaves which teams on top.

B) The scenario where all 4 teams end up tied for 2nd is remote. For Brown to get one point and Dartmouth 2 means a lot of very wierd results need to happen all at the same time.

... but you never know

Ben F.:

You might want to try [slack.net] and fiddle with the standings there.



Post Edited (02-23-04 14:54)

[q]If you have a three-way tie with Brown and RPI, it goes like this:
Head-to-head points: Brown 5, RPI 4, Cornell 3; Brown wins tiebreaker[/q]

Oops. I knew that, I was just being dumb. Or, rather, I was being rational and not remebering that the tie breaker is dumb. Except in this case, where it benefits us.



Post Edited (02-23-04 15:33)

Why would dropping the bottom team make more logical sense than advancing the top team?

And why would dropping the bottom team *and* advancing the top team at the same time make more logical sense than reapplying?

I've had to work through tiebreaker systems for bizarre summer league tournament formats, and what I found was that the weird reapplication of tiebreaker rules that the ECAC uses usually produces the same effect, while resolving some other issues (mainly reducing the amount of whining coming from the peanut gallery, at least as far as summer league formats are concerned).

For example, suppose Brown, Cornell, Dartmouth, and RPI are tied. Let's further suppose that Cornell took 0 points from Brown and Dartmouth, and 3 points from RPI. RPI took 1 each from Cornell and Brown, and 2 from Dartmouth. Dartmouth took 2 from RPI, 1 from Brown, and 4 from Cornell. Brown is the clear winner, losing just 1 point each from RPI and Dartmouth.

With me so far? Tiebreaker yields:

Brown - 10 of 12 points
Dartmouth - 7 of 12 points
RPI - 5 of 12 points
Cornell - 3 of 12 points

Using this as the final standings puts Cornell at the bottom and Brown at the top. It even resolves the RPI/Dartmouth split. But here's the issue - Cornell and RPI finished with the same total number of points in the overall standings, and Cornell took 3 of 4 points from RPI. Why is RPI now ahead of Cornell?

You can argue that applying tiebreakers straight down makes just as much logical sense as the re-application method that the ECAC uses, but I don't think that it's logical while the ECAC system is dumb. It's far more elegant, and in most cases it's a simpler way to get the same results, but it's not necessarily a more logical, more fair, or even a better system.

I've just defended the ECAC tiebreakers. I think maybe I should go lie down for a bit. . .



Post Edited (02-23-04 15:55)

Not that weird...

It means Dartmouth needs to tie Brown and Harvard, and Brown needs to lose to UVM. Given Dartmouth's propensity for ties this year, that's not that impossible and Brown losing to UVM is not nearly as improbable as one would have thought a month ago either.

It's the ECAC...it ain't over 'til it's over.

JH

Would you use the standings to determine the #1 team, then figure out head to head among the remaining 11 teams to determine #2, then figure out head to among among the remaining 10...?

I've just attacked an ECAC policy. I think I'm on solid ground here.

Starting over with the remaining N-1 teams after you've isolated the top team from an N-way tie is also the way the NFL does things, or at least the way they did the last time I checked. It's a common practice to reduce the chance that a team which wins a two-team tiebreaker will lose a three-way tie-breaker thanks to the inclusion of an otherwise irrelevant third team.

The thing that the ECAC does slightly differently is that if the top two or more teams are tied in head-to-head, they get separated from the top of the group and then have their individual tie broken, but all of them finish ahead of the teams that were lower down. To quote one of the league's examples:

Suppose teams A, B, C and D are all tied with an equal number of points. Teams A is 1-1-0 vs Team B, 1-1-0 vs Team C and 2-0-0 vs Team D. Team B is 1-1-0 vs Team A, 1-1-0 vs Team C, and 2-0-0 vs Team D. Team C is 1-1-0 vs Team A, 1-1-0 vs Team B and 0-1-1 vs Team D. Team D is 0-2-0 vs Team A, 0-2-0 vs Team B, and 1-0-1 vs Team C. The head-to-head records among all four teams are 4-2-0 for Teams A and B, 2-3-1 for Team C and 1-4-1 for Team D. Teams A and B are thus separated from Teams C and D and the tie-breakers are re-applied in each group. Teams A and B tied head-to-head so additional tie-breakers are needed. Team D won the series against Team C 1-0-1 so Team D would be seeded ahead of Team C despite the fact that Team D was behind Team C in the 4-way tie-breaker.

In the NFL method (at least as of circa 1995), the loser of the tiebreaker between Team A and Team B would be thrown back into a three-way tie with Team C and Team D.

BTW, I worked out part of the question of whether we get the bye with a split. If we split, RPI sweeps, Brown doesn't get swept, and Dartmouth does no worse than a split, we end up tied for 4th with RPI. The one case I looked at was where we beat SLU and lose to Clarkson. This is the worst version of the split for us, since we want SLU (who swept RPI) to stay in the top 8. Anyway, in that circmustance, we get home ice if SLU beats Colgate, Clarkson doesn't beat Colgate, and Union gets no more than one point, OR if SLU ties Colgate, Clarkson loses to Colgate, and Union gets swept.

Point being, even if we beat SLU Friday, we'll only clinch the bye that night if RPI ties or loses.

Still will be MUCH simpler at 9:30 on Friday night.

The inherent stupidity of most ECAC policies aside. . .

Would you use the standings to determine the #1 team, then figure out head to head among the remaining 11 teams to determine #2, then figure out head to among among the remaining 10...

No, I wouldn't, but now you're mixing overall standings with tiebreaking procedures. They have a method for determining the standings, and then a separate method for resolving situations that the standings cannot settle - i.e. when there are tied teams.

My point was not that the ECAC tiebreaking system is perfect (it isn't), nor that it is inherently more logical than the system you are advocating (I think they're equally justifiable). My point was that, just this once, the ECAC was not merely being dumb, but applied a certain logic to the tiebreaking procedure. JTW's post clearly summarizes the ECAC's reasoning:

It's a common practice to reduce the chance that a team which wins a two-team tiebreaker will lose a three-way tie-breaker thanks to the inclusion of an otherwise irrelevant third team.

You may not agree with their argument, but it makes sense to me. It makes even more sense if you're up at 2 in the morning trying to find a way to set up a tournament tiebreaker system that will prevent a bunch of whiny athletes (and their fans) from bitching and moaning when they beat a team that ends up advancing over them.

John T. Whelan '91 wrote:

I'll let Bill Fenwick do his usual breakdown of everyone's prosepects

And now he has. See [slack.net]