2018 ECAC Permutations

[Give My Regards]

Here we go again, folks.  First the short version:

Possible ECAC tournament seedings (the number in parentheses is the best
seed the team can get with no help):

Cornell        1-2    (1)
Union          1-3    (2)
Clarkson       2-4    (3)
Harvard        3-4    (4)
Dartmouth      5-9    (5)
Colgate        5-9    (6)
Yale           5-9    (7)
Princeton      5-9    (7)
Quinnipiac     5-9    (9)
Brown         10-11   (10)
Rensselaer    10-12   (11)
St. Lawrence  11-12   (12)

[Give My Regards]

...and now the grotesquely long version:

Once again, it's time for the ECAC Playoff Permutations!  Oddly enough,
this year the teams have slotted themselves nicely into three tiers; there
are four teams that can finish in first through fourth, five that can
finish from fifth through ninth, and three that can finish from tenth
through twelfth.  If you love drama, the final ECAC weekend is a little
short of if this year, although it makes things a lot easier to figure out.

Going into the final weekend of league play, here's a breakdown of where
each team in the ECAC could finish.  As always, I'm greatly indebted to
John Whelan's excellent playoff possibilities script at http://www.elynah.com/tbrw/2018/ecac.cgiframe.shtml


For each ECAC team, I've listed the following:

THIS WEEKEND:  The team's weekend games, its last two of the season.
ON THEIR OWN:  The highest the team could finish with no help from the
      competition.  Generally, this involves a weekend sweep.
BEST CASE:  The highest the team could finish if everything goes right.
WORST CASE:  The lowest the team could finish if everything goes wrong.
      This generally involves getting swept while teams nearby in the
      standings win.
TIEBREAKERS:  How the team would fare if they finished the season tied with
      some other team which is currently close (i.e. within 4 points) in the
      standings.  Note that there may be cases in which Team A "could win or
      lose" the tiebreaker against Team B, depending on whether there are
      more than just those two teams tied.  For instance, Colgate wins the
      head-to-head tiebreaker against Princeton with a 1-0-1 record; however,
      in a four-way tie involving these two, Yale, and Dartmouth, Colgate
      would actually be seeded lower than Princeton.  If a listed tiebreaker
      result depends on more than just those two teams being tied, it is
      marked with an asterisk:

           Colgate could win or lose* against Princeton

For two or more teams tied in the standings, the ECAC tiebreakers are:

1.   Head-to-head record in ECAC games (non-conference meetings, such as in
     tournaments, do not count).
2.   League wins.
3.   Record against the top four teams in the conference.
4.   Record against the top eight teams in the conference.
5.   Goal differential (net goals) head-to-head.
6.   Goal differential against the top four teams in the conference.
7.   Goal differential against the top eight teams in the conference.

Note that if the tie is among three or more teams, the tiebreaking steps are
used in order until a team, or multiple teams, is/are separated from the
"pack".  Once that happens, the process starts all over to break the remaining
ties.  For example, when the above steps are applied to a four-way tie, once
one team is separated out leaving a three-way tie, the procedure goes back to
the first step with the three remaining tied teams.


Without further ado, here's how the final weekend looks:

Cornell:
      THIS WEEKEND:  At Rensselaer, at Union.
      ON THEIR OWN:  Wraps up first place with one point on the weekend.
      BEST CASE:  First.
      WORST CASE:  Will finish second with two losses if Union also beats
      Colgate.
      TIEBREAKERS:  Loses to Union.

Union:
      THIS WEEKEND:  Colgate, Cornell.
      ON THEIR OWN:  One point will clinch second place.
      BEST CASE:  Finishes first with a sweep if Cornell also loses to
      Rensselaer.
      WORST CASE:  Drops to third if they lose twice and Clarkson sweeps.
      TIEBREAKERS:  Beats Cornell; loses to Clarkson.

Clarkson:
      THIS WEEKEND:  Princeton, Quinnipiac.
      ON THEIR OWN:  Clinches third with a pair of wins.
      BEST CASE:  Climbs to second with two wins if Union loses twice.
      WORST CASE:  Falls to fourth with two losses if Harvard gets at least
      one point.
      TIEBREAKERS:  Beats Union; loses to Harvard.

Harvard:
      THIS WEEKEND:  At Brown, at Yale.
      ON THEIR OWN:  Has already wrapped up fourth place and can do no 
      better without help.
      BEST CASE:  Takes third with a sweep if Clarkson gets no more than three
      points.
      WORST CASE:  Fourth.
      TIEBREAKERS:  Beats Clarkson and Dartmouth.

Dartmouth:
      THIS WEEKEND:  At Yale, at Brown.
      ON THEIR OWN:  Will guarantee fifth place with a sweep.
      BEST CASE:  Fifth.
      WORST CASE:  Would slide to ninth with two losses if Quinnipiac wins
      twice and Colgate and Princeton each get at least two points.
      TIEBREAKERS:  Beats Quinnipiac; loses to Princeton; could win or lose
      against Colgate and Yale.

Colgate:
      THIS WEEKEND:  At Union, at Rensselaer.
      ON THEIR OWN:  A sweep wraps up sixth place.
      BEST CASE:  Rises to fifth with two wins if Dartmouth does not sweep.
      WORST CASE:  Would finish ninth with two losses if Yale gets at least
      one point, Princeton gets at least two points, and Quinnipiac gets at
      least three points.
      TIEBREAKERS:  Loses to Yale; could win or lose against Dartmouth and
      Quinnipiac; could win or lose* against Princeton.

Yale:
      THIS WEEKEND:  Dartmouth, Harvard.
      ON THEIR OWN:  Clinches seventh with a pair of wins.
      BEST CASE:  Climbs to fifth if they win twice, Dartmouth does not beat
      Brown, and Colgate does not sweep.
      WORST CASE:  Falls to ninth if they lose twice, Princeton does not get
      swept, and Quinnipiac gets at least two points.
      TIEBREAKERS:  Beats Colgate and Quinnipiac; could win or lose against
      Dartmouth and Princeton.

Princeton:
      THIS WEEKEND:  At Clarkson, at St. Lawrence.
      ON THEIR OWN:  Guarantees seventh with two wins.
      BEST CASE:  Would finish fifth with a sweep if Colgate gets no more
      than two points and the Dartmouth-Yale winner loses its other game
      (or if they tie, Dartmouth does not win its other game).
      WORST CASE:  Slides to ninth if they lose twice and Quinnipiac gets
      at least two points.
      TIEBREAKERS:  Beats Dartmouth; could win or lose against Yale and
      Quinnipiac; could win* or lose against Colgate.

Quinnipiac:
      THIS WEEKEND:  At St. Lawrence, at Clarkson.
      ON THEIR OWN:  Has clinched ninth and can do no better without help.
      BEST CASE:  Takes fifth with a sweep if Dartmouth loses twice, Colgate
      gets no more than one point, Princeton gets no more than two points,
      and Yale loses to Harvard.
      WORST CASE:  Ninth.
      TIEBREAKERS:  Loses to Dartmouth and Yale; could win or lose against
      Colgate and Princeton.

Brown:
      THIS WEEKEND:  Harvard, Dartmouth.
      ON THEIR OWN:  Guarantees tenth with a three-point weekend.
      BEST CASE:  Tenth.
      WORST CASE:  Drops to eleventh if they lose twice and Rensselaer
      gets at least two points.
      TIEBREAKERS:   Beats Rensselaer and St. Lawrence.

Rensselaer:
      THIS WEEKEND:  Cornell, Colgate.
      ON THEIR OWN:  One point would give the Engineers eleventh place.
      BEST CASE:  Gets tenth with a sweep if Brown gets no more than two
      points.
      WORST CASE:  Would finish twelfth if they lose twice and St. Lawrence
      wins twice.
      TIEBREAKERS:  Beats St. Lawrence; loses to Brown.

St. Lawrence:
      THIS WEEKEND:  Quinnipiac, Princeton.
      ON THEIR OWN:  Can do no better than twelfth without help.
      BEST CASE:  Finishes eleventh with a sweep if Rensselaer loses twice.
      WORST CASE:  Twelfth.
      TIEBREAKERS:  Loses to Brown and Rensselaer.

[Jim Hyla]

...and now the grotesquely long version:

Wow, impressed and thankful, but how long did it take you?

[scoop85]

Not strictly ECAC related, but this seems to confirm we're in the NCAA's regardless of what happens the rest of the way:

https://twitter.com/chnews/status/965582957078556672

[KenP]

Not strictly ECAC related, but this seems to confirm we're in the NCAA's regardless of what happens the rest of the way:

https://twitter.com/chnews/status/965582957078556672

. Also shows 91% likelihood of being a #1 seed.

[upprdeck]

but this doesn show what happens if we do lose the next 4. just the likelihood of that are low.. even 2-4 probably keeps us high.

[imafrshmn]

but this doesn show what happens if we do lose the next 4. just the likelihood of that are low.. even 2-4 probably keeps us high.

This is true. As well, there's reason to believe that the CHN simulations don't really capture the low-probability outcomes as well as they should (which is to say it's all a little bit overconfident). Because KRACH ratings are assumed to be (1) constant,  (2) unbiased, and (3) not-uncertain, there is no way to account for recent trends (like Clarkson tanking, for example), variations in luck, and inherent uncertainty/variability of a team's strength. Of course, these assumptions simplify this exercise to a point where it's easily understood.

[adamw]

... there's reason to believe that the CHN simulations don't really capture the low-probability outcomes as well as they should (which is to say it's all a little bit overconfident). Because KRACH ratings are assumed to be (1) constant,  (2) unbiased, and (3) not-uncertain, there is no way to account for recent trends (like Clarkson tanking, for example), variations in luck, and inherent uncertainty/variability of a team's strength. Of course, these assumptions simplify this exercise to a point where it's easily understood.

repeating: anyone wants to help write a better algorithm, be my guest.

All of the above is true.   1. can be solved easily, but requires a lot of additional computing time - way too much to be worth it.  3. there's a lot packed there. Some would be good to adjust for, others have more dubious value

[upprdeck]

wouldnt it require the ability to run the 20K simulations with the 1 know result?

[adamw]

wouldnt it require the ability to run the 20K simulations with the 1 know result?

You could do it where the KRACH gets re-computed after each 'day' in the simulation ... but that would require like 20 KRACH computations per simulation - multiplied by 20,000

[upprdeck]

you mean like the power of mining for crypto currancy

[Jeff Hopkins '82]

if we have to finish #2, I'd like it to be behind St. Cloud or Mankato.  Extra likelihood of us being in Allentown.

[BearLover]

... there's reason to believe that the CHN simulations don't really capture the low-probability outcomes as well as they should (which is to say it's all a little bit overconfident). Because KRACH ratings are assumed to be (1) constant,  (2) unbiased, and (3) not-uncertain, there is no way to account for recent trends (like Clarkson tanking, for example), variations in luck, and inherent uncertainty/variability of a team's strength. Of course, these assumptions simplify this exercise to a point where it's easily understood.

repeating: anyone wants to help write a better algorithm, be my guest.

All of the above is true.   1. can be solved easily, but requires a lot of additional computing time - way too much to be worth it.  3. there's a lot packed there. Some would be good to adjust for, others have more dubious value

adamw, I wish I had the mathematical or computing background to help improve the algorithm. I can only say that the 59% chance the model gives us of winning the ECAC tournament has to be wrong. 40% would already be pushing it. Someone want to go back and check how often a team whom this model gave a "60% chance" of winning an 8-team tournament didn't end up winning it?

[abmarks]

... there's reason to believe that the CHN simulations don't really capture the low-probability outcomes as well as they should (which is to say it's all a little bit overconfident). Because KRACH ratings are assumed to be (1) constant,  (2) unbiased, and (3) not-uncertain, there is no way to account for recent trends (like Clarkson tanking, for example), variations in luck, and inherent uncertainty/variability of a team's strength. Of course, these assumptions simplify this exercise to a point where it's easily understood.

repeating: anyone wants to help write a better algorithm, be my guest.

All of the above is true.   1. can be solved easily, but requires a lot of additional computing time - way too much to be worth it.  3. there's a lot packed there. Some would be good to adjust for, others have more dubious value

adamw, I wish I had the mathematical or computing background to help improve the algorithm. I can only say that the 59% chance the model gives us of winning the ECAC tournament has to be wrong. 40% would already be pushing it. Someone want to go back and check how often a team whom this model gave a "60% chance" of winning an 8-team tournament didn't end up winning it?

The frigging model is 100% correct, BearLover.   TLDR version: Bearlover doesn't understand instructions.

Bearlover, If you'd read the explanation of the model, it clearly states that:

These are the results of 20,000 Monte Carlo simulations of the remaining games prior to Selection Day. The winner of each game in the simulation was determined randomly, weighted by KRACH.

The simple translation of this is that, based on the relative value of the KRACH ratings, IN THE LONG RUN (when variance is removed) We are expected to win 59% of the time. I.e. we'd be expected to win 11,800 of the 20,000 times.  So, as defined, the model is accurate.  

This model can't possibly be used to tell you the likelihood of wining the tournament when the tournament is only played out once, not 20,000 times. Because, variance.

Please stop shitting on the model as wrong. It's not. It is what it is.

[Dafatone]

I think it's easy to believe that we are worse than our record, given that we've slowed down a little bit as of late, we're beaten up, and that all year, we seem to win a lot of close games.

But KRACH goes by record, not recent record or margin of victory. And our record is really, really, REALLY good.

I'd expect the 2nd best team in the country to win its tournament often, especially given that the next best teams are 8th and 21st. And KRACH says we're #2.

Are we actually #2? I have no idea. I haven't been watching other teams all that often. I have to figure that the extreme difference between conferences is at least a little bit flukey, and that the ECAC isn't as far behind the others as the results have said. But that really works in our favor, not against.

We've given up 38 goals in 27 games. That's absurd. Maybe we aren't as good as our performance, but our performance has been fantastic.