2011 ECAC Playoff Possibilities Time

[Give My Regards]

I await Bill Fenwick's analysis. ;-)

Allrightallright, it's up on HOCKEY-L.  I hate deadlines.

Have at it.

[Trotsky]

I await Bill Fenwick's analysis. ;-)

Allrightallright, it's up on HOCKEY-L.  I hate deadlines.

Have at it.

I haven't seen HOCKEY-L since about 1998.  Could you also post it here?

[Give My Regards]

Yup, here it is:


Back again with the ECAC's annual monument to confusion, not to mention
sadism -- the Playoff Permutations!  This year's "final weekend" has the
added attraction of a Tuesday night game between Harvard and Brown,
rescheduled from the beginning of February.  Despite that extra little
complication, the ECAC has split itself neatly into three groups.  Union
and Yale will finish 1-2 in some order; Cornell, Dartmouth, Rensselaer, and
Princeton will fight it out for the #3 through #6 spots, and then there are
The Rest:  Clarkson, Quinnipiac, Brown, St. Lawrence, Colgate, and Harvard
get to divvy up the remaining six seeds.

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://69.31.82.90/~whelan/tbrw/tbrw.cgi?ecac.cgi

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

THIS WEEKEND:  The team's weekend games, its last two (or three) 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 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.


And now onto How Things Could Shake Out in the ECAC:

Union:
     THIS WEEKEND:  Quinnipiac, Princeton.
     ON THEIR OWN:  The Dutchmen clinch the top spot with a sweep.
     BEST CASE:  First.
     WORST CASE:  Finishes second if Yale gets at least one more point than
     they do.
     TIEBREAKERS:  Loses to Yale.

Yale:
     THIS WEEKEND:  Colgate, Cornell.
     ON THEIR OWN:  Has already wrapped up second place and can do no better
     without help.
     BEST CASE:  Climbs to first if they get at least one more point than
     Union does.
     WORST CASE:  Second.
     TIEBREAKERS:  Beats Union.

Cornell:
     THIS WEEKEND:  At Brown, at Yale.
     ON THEIR OWN:  Finishes third with two wins.
     BEST CASE:  Third.
     WORST CASE:  Falls to sixth if they lose twice, Dartmouth does not get
     swept, Princeton beats Rensselaer and does not lose to Union, and
     Rensselaer beats Quinnipiac.
     TIEBREAKERS:  Beats Dartmouth and Rensselaer; could win or lose against
     Princeton.

Dartmouth:
     THIS WEEKEND:  St. Lawrence, Clarkson.
     ON THEIR OWN:  Clinches fourth place with a pair of wins.
     BEST CASE:  Would finish third with a sweep if Cornell does not win
     twice.
     WORST CASE:  Drops to sixth with two losses if Rensselaer gets at least
     one point and Princeton gets at least three.
     TIEBREAKERS:  Beats Princeton; loses to Cornell and Rensselaer.

Rensselaer:
     THIS WEEKEND:  Princeton, Quinnipiac.
     ON THEIR OWN:  Beating Princeton guarantees the Engineers fifth place.
     BEST CASE:  Clinches third with a sweep if Dartmouth does not win twice
     and Cornell gets no more than two points.
     WORST CASE:  Would end up in sixth place if Princeton sweeps.
     TIEBREAKERS:  Beats Dartmouth and Princeton; loses to Cornell.

Princeton:
     THIS WEEKEND:  At Rensselaer, at Union.
     ON THEIR OWN:  Gets the #5 seed with two wins.
     BEST CASE:  Rises to third with a sweep if Cornell and Dartmouth each get
     no more than one point.
     WORST CASE:  Finishes sixth if they lose to Rensselaer and Cornell does
     not get swept.
     TIEBREAKERS:  Loses to Dartmouth and Rensselaer; could win or lose
     against Cornell.

Clarkson:
     THIS WEEKEND:  At Harvard, at Dartmouth.
     ON THEIR OWN:  A sweep wraps up seventh place.
     BEST CASE:  Seventh.
     WORST CASE:  Would fall to ninth if they lose twice, Quinnipiac does not
     get swept, and Brown gets at least four points.
     TIEBREAKERS:  Beats Quinnipiac, Brown, and St. Lawrence.

Quinnipiac:
     THIS WEEKEND:  At Union, at Rensselaer.
     ON THEIR OWN:  Guarantees eighth place with two wins.
     BEST CASE:  Finishes seventh with a sweep if Clarkson does not win twice.
     WORST CASE:  Drops to tenth if they lose twice, Brown gets at least three
     points (with at least one win), and St. Lawrence sweeps.
     TIEBREAKERS:  Loses to Clarkson and St. Lawrence; could win or lose
     against Brown.

Brown:
     THIS WEEKEND:  Harvard (Tuesday), Cornell, Colgate.
     ON THEIR OWN:  Four points would clinch ninth place.
     BEST CASE:  Climbs to seventh with three wins if Clarkson gets no more
     than two points and Quinnipiac does not sweep.
     WORST CASE:  Finishes twelfth if they lose three times, Harvard wins
     their other two games, Colgate also beats Yale, and St. Lawrence beats
     Dartmouth.
     TIEBREAKERS:  Beats St. Lawrence; loses to Clarkson; could win or lose
     against Quinnipiac, Colgate, and Harvard.

St. Lawrence:
     THIS WEEKEND:  At Dartmouth, at Harvard.
     ON THEIR OWN:  Wraps up tenth place by beating Harvard.
     BEST CASE:  Would finish eighth with a sweep if Quinnipiac loses twice
     and Brown gets no more than two points.
     WORST CASE:  Falls to twelfth if they lose twice, Colgate sweeps, and
     Harvard wins at least one of their other two games.
     TIEBREAKERS:  Beats Colgate and Quinnipiac; loses to Clarkson, Brown, and
     Harvard.

Colgate:
     THIS WEEKEND:  At Yale, at Brown.
     ON THEIR OWN:  Can do no better than twelfth without help.
     BEST CASE:  Rises to ninth place if they win twice, Brown loses their
     other two games, St. Lawrence gets swept, and Harvard does not beat
     Clarkson.
     WORST CASE:  Twelfth.
     TIEBREAKERS:  Loses to St. Lawrence; could win or lose against Brown and
     Harvard.

Harvard:
     THIS WEEKEND:  At Brown (Tuesday), Clarkson, St. Lawrence.
     ON THEIR OWN:  Three wins would give Harvard tenth place.
     BEST CASE:  Clinches ninth with three wins if Brown gets no more than one
     point.
     WORST CASE:  Finishes twelfth if they lose all three games.
     TIEBREAKERS:  Beats St. Lawrence; could win or lose against Brown and
     Colgate.

[Jim Hyla]

Yup, here it is:

Thanks.

[Robb]

Well, a loss @Yale seems pretty likely, but even if we get swept this weekend, there are lots of scenarios that give us a bye.  The only other games that matter (to first order) are the ones played by Dartmouth, Princeton, and RPI (assuming no tiebreakers will come down to who is in the top .  Since Princeton and RPI play each other there are only 5 games, which means there are 3^5 = 243 interesting possibilities, 27 of which still give us a bye (7.8%):

Code Select Expand


Dartmouth     Princeton                            RPI                    # of possibilities covered
Swept         Beats RPI, any vs. Union             tie or loss to QU      6
Swept         Ties RPI, tie or loss vs. Union      any vs. QU             6
Swept         Loses to RPI, any vs. Union          any vs. QU             9
1 pt.         Beats or ties RPI, loses to Union    loses to QU            4
1 pt.         Ties RPI, Ties Union                 loses to QU            2


Of course, they all pretty much rely on Dartmouth forgetting to show up vs. CCT and SLU, which makes sense - RPI and Princeton play each other, so one or both of them will pick up some points.  If Dartmouth does, too, then game over for us (if we get swept).

Picking up a single point in our games improves the situation immensely:

Code Select Expand


Dartmouth     Princeton                            RPI                    # of possibilities covered
Swept         any vs. RPI, any vs. Union           any vs. QU             27
1 pt.         any vs. RPI, any vs. Union           any vs. QU             27
2 pts.        beats RPI, ties or loses to Union    any vs. QU             18
2 pts.        ties RPI, any vs. Union              ties or loses to QU    18
2 pts.        loses to RPI, any vs. Union          loss to QU             9
3 or 4 pts.   beats RPI, tie or loss to Union      any vs. QU             18
3 or 4 pts.   ties RPI, any vs. Union              tie or loss to QU      18
3 or 4 pts.   loses to RPI, any vs. Union          loss to QU             9


So that's 144/243 = 59% of the scenarios.

If we get 2 points (even with a loss to Yale), then it's easier to start looking for scenarios where we DON'T get a bye, and the only ones are:

Code Select Expand


Dartmouth     Princeton                            RPI                    # of possibilities covered
3 or 4 pts.   loses to RPI, any vs. Union          beats QU               9


That's only 9 out of 243 (3.7%) of scenarios where we DON'T get a bye for picking up 2 points.

So, for all practical purposes, we're playing for a bye on Friday - win, and we should have a bye.  Tie, and we still have a decent shot.  Lose, and we'll have less than an 8% shot at a bye unless we can pick up a point at Yale.

[Beeeej]

Thanks for the analysis, Robb - I'm more optimstic after that post than I was before it, and the numbers support me.  I feel like I need the extra week off almost as much as the team does.

[JDeafv]

If we get 2 points (even with a loss to Yale), then it's easier to start looking for scenarios where we DON'T get a bye, and the only ones are:

Code Select Expand


Dartmouth     Princeton                            RPI                    # of possibilities covered
3 or 4 pts.   loses to RPI, any vs. Union          beats QU               9


That's only 9 out of 243 (3.7%) of scenarios where we DON'T get a bye for picking up 2 points.

So, for all practical purposes, we're playing for a bye on Friday - win, and we should have a bye.  Tie, and we still have a decent shot.  Lose, and we'll have less than an 8% shot at a bye unless we can pick up a point at Yale.

Robb - great analysis!

From this, if Cornell beats Brown, to clinch a bye on Friday Cornell is rooting for one of the following:

• SLU(t) win
• Princeton win or tie

[Trotsky]

If any of the cognoscenti see this tonight -- do we have any preference in the Brown-Harvard game (aside from rooting for large numbers of DQs)?

[Jeff Hopkins '82]

Thanks for the analysis, Robb - I'm more optimstic after that post than I was before it, and the numbers support me.  I feel like I need the extra week off almost as much as the team does.

I hate to rain on the parade, but Robb's analysis seems to treat things as random possibilities.  If we deal with probable outcomes, we can see that it all really comes down to the Princeton-RPI game.

Mind you, I'd rather we took 4 points this weekend, but I'm not holding my breath.

[Rita]

Thanks for the analysis, Robb - I'm more optimstic after that post than I was before it, and the numbers support me.  I feel like I need the extra week off almost as much as the team does.

I hate to rain on the parade, but Robb's analysis seems to treat things as random possibilities.  If we deal with probable outcomes, we can see that it all really comes down to the Princeton-RPI game.

Mind you, I'd rather we took 4 points this weekend, but I'm not holding my breath.

What?!!? Do you mean to tell me that hockey games aren't played on/inside computers? ::panic::  ;-)

[jtwcornell91]

Thanks for the analysis, Robb - I'm more optimstic after that post than I was before it, and the numbers support me.  I feel like I need the extra week off almost as much as the team does.

I hate to rain on the parade, but Robb's analysis seems to treat things as random possibilities.  If we deal with probable outcomes, we can see that it all really comes down to the Princeton-RPI game.

Mind you, I'd rather we took 4 points this weekend, but I'm not holding my breath.

What?!!? Do you mean to tell me that hockey games aren't played on/inside computers? ::panic::  ;-)

Really have to work out the Bayes factors for the different Bradley-Terry models including ties...

[Trotsky]

What?!!? Do you mean to tell me that hockey games aren't played on/inside computers? ::panic::  ;-)

Sure they are.  Whole damn universe is a computer, and entropy is its God.

Please refer all further questions to Dr. Whelan and/or the Pope.

[Robb]

Thanks for the analysis, Robb - I'm more optimstic after that post than I was before it, and the numbers support me.  I feel like I need the extra week off almost as much as the team does.

I hate to rain on the parade, but Robb's analysis seems to treat things as random possibilities.  If we deal with probable outcomes, we can see that it all really comes down to the Princeton-RPI game.

Mind you, I'd rather we took 4 points this weekend, but I'm not holding my breath.

I certainly didn't go to the trouble of calculating the probabilities of each scenario (say, according to KRACH).  Notice that I was careful to say only what percentage of the scenarios were covered by each situation, which is not the same thing as the probability that the situation would occur - unless all of the outcomes are equally likely (i.e. that there's a 1/3 chance that every game ends in a win, tie, or loss).

The only time I mentioned the likeliness of an outcome was that if we "Lose (to Brown), and we'll have less than an 8% shot at a bye unless we can pick up a point at Yale."  I'm fairly confident in that one - Dartmouth surely has more than an 8% chance to pick up 2 points this weekend, which alone would sink our shot at a bye if we lose to Brown.

[Trotsky]

Beat Brown, then worry.  

Hopefully the Bears will be tired from having had a Tuesday game.

[Towerroad]

Beat Brown, then worry.  

Hopefully the Bears will be tired from having had a Tuesday game.

Amen, the next game is the only one that matters.