2011 ECAC Playoff Possibilities Time

The ECAC schedule makers have been less elegant than usual this year, what with late Tuesday games and Sunday games, and travel partnerships squaring off late in the season. But finally every team has played every other team, and it's ECAC Playoff Possibilities Time!

Here are this year's goodies:

• ECAC Race in a Nutshell
• ECAC Playoff Possibilties Script

(slack.net and its alias fly.net seem to be having DNS issues, so I'm linking directly to the IP address.)

Please PM or email if you find any errors or problems.

Thanks for the site! I'm going to waste a few hours playing around with this instead of doing my homework!

bump. With the weekend coming this should be closer to the top.

If Cornell comes up with 2 points next weekend, they will need cooperation from either RPI (tie or loss) or Dartmouth (two ties or a loss) to remain in the top 4 of the ECAC. Princeton could complicate things if they run the table, but they will have to beat both Yale and Union.

BigRedHockeyFan
If Cornell comes up with 2 points next weekend, they will need cooperation from either RPI (tie or loss) or Dartmouth (two ties or a loss) to remain in the top 4 of the ECAC. Princeton could complicate things if they run the table, but they will have to beat both Yale and Union.

Yeah, our best chance if we only get 2 points, would seem to be PU losing to Yale and Union and beating RPI. We can't count on Dartmouth losing at home. But it would be nice if our fellow NYers could help.

FWIW, if RPI only picks up 3 points, we make top 4. OTOH, if Dartmouth only gets 3, we still have the possibility of finishing 5th.

I await Bill Fenwick's analysis.

Yale 1, Princeton 3, 1st period

BigRedHockeyFan
Yale 1, Princeton 3, 1st period

now 3-3 end of 1st.
Princeton scored the first 3, then Yale with 3 straight. The first two Yale goals both shorthanded.

jkahn

BigRedHockeyFan
Yale 1, Princeton 3, 1st period

now 3-3 end of 1st.
Princeton scored the first 3, then Yale with 3 straight. The first two Yale goals both shorthanded.

Yale almost got SHG #3 but the puck didn't have enough "oopmh" to get across the goal line.

This does not bode well for us and our inept PP.

Princeton just scores to make it 4-3. Crap. 14:52 left in the 2nd.

Rita

jkahn

BigRedHockeyFan
Yale 1, Princeton 3, 1st period

now 3-3 end of 1st.
Princeton scored the first 3, then Yale with 3 straight. The first two Yale goals both shorthanded.

Yale almost got SHG #3 but the puck didn't have enough "oopmh" to get across the goal line.

This does not bode well for us and our inept PP.

Princeton just scores to make it 4-3. Crap. 14:52 left in the 2nd.

4 - 4 at the end of 2 periods.

Late 3rd period goal from Yale leads to a 5-4 Bulldog victory over the Tigers and keeps Princeton 2 points behind us heading into the weekend.

Yale wins 5-4, helps Cornell's top 4 chances.

Princeton was leading 3-0 during the first period. I think that on a good night, Cornell could beat Yale. It's too bad that the game is in New Haven, where Yale is 14-0. On the road, they are 8-5.

Cornell's playoff possibilities fall into two groups.

Bad. Finish 5th or 6th, have to play the bye week (tradtionally a Cornell bye week), at home, probably win, then go on the road and play a winnable series to advance to Atlantic City.

Less bad. Finish 3rd or 4th, get the bye, play a winnable series at home, probably win, go to Atlantic City, face death by firing squad or by hanging, depending on whether we draw Union or Yale. Right now everyone's going to say that based on getting 9 shots at Union, we're better off facing Yale. We'll know a week from now if that's so. Maybe Iles has a career night next Saturday and a miracle happens. Or someone leaves the door to the Yale swimming pool unlocked and more Yale players get hurt.

All kinds of things could happen such as our messing up in the first round (not unthinkable) or Yale and/or Union flopping in the first round (unlikely for one, impossible for both).

Our chances for the NCAAs boil down to: Have to win the ECACs.

jtwcornell91
I await Bill Fenwick's analysis.

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

Have at it.

Give My Regards

jtwcornell91
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?

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
[69.31.82.90]

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.

Give My Regards
Yup, here it is:

Thanks.

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 8). 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%):

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:

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:

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.

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.

Robb

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:

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

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)?

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.

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.

Jeff Hopkins '82

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.

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?

Rita

Jeff Hopkins '82

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.

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?

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

Rita
What?!!? Do you mean to tell me that hockey games aren't played on/inside computers?

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.

Jeff Hopkins '82

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.

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.

Beat Brown, then worry.

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

Trotsky
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.

Robb

Jeff Hopkins '82

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.

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.

Robb,

I wasn't criticizing your analysis. It's actually quite valuable. And I'm not saying you suggested our real odds are any different because of your analysis. But if someone interpreted it that way, it would be an unrealistic way to look at things.

Jeff Hopkins '82

Robb

Jeff Hopkins '82

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.

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.

Robb,

I wasn't criticizing your analysis. It's actually quite valuable. And I'm not saying you suggested our real odds are any different because of your analysis. But if someone interpreted it that way, it would be an unrealistic way to look at things.

No worries - I didn't take it that way at all. Just clarifying!

So....I just happened to have some old code lying around for KRACH and some for figuring out ECAC standings possibilities (who doesn't?), so I linked 'em up, threw a Monte Carlo wrapper around them, and voila! After a million trials, here are the approximate* probabilities for each team finishing in each place, sorted to the most likely order of finish:

	1	2	3	4	5	6	7	8	9	10	11	12
Union	81.0%	19.0%										
Yale	19.0%	81.0%										
Cornell			83.1%	14.7%	2.2%							
Dartmouth		9.8%	36.2%	42.7%	11.3%						
Rensselaer		2.5%	29.5%	25.3%	42.7%						
Princeton		4.6%	19.6%	29.8%	46.0%						
Quinnipiac						68.0%	30.6%	1.3%	0.1%		
Clarkson						32.0%	68.0%				
St. Lawrence							0.8%	54.9%	44.2%		
Brown								0.6%	43.8%	45.9%	9.7%	
Colgate										9.7%	73.2%	17.0%
Harvard											17.0%	83.0%

It is theoretically possible for Cornell to finish in 6th, but it didn't happen in a single one of the million trials I ran.

*my ECAC tiebreaker code is out of date - I don't have total wins in there as the second tie-breaker, etc, but I'm not going to have time to update it before Friday, so this is the best you get.

Thank you, Robb. That is terrific.

And people think there is no real world use of math beyond calculating 18% of the check. The breakout makes it a lot clearer that Cornell with a weekend split is in pretty good shape. Thank you!

You certainly are a lot more productive at 5:30 AM, when I posted my Playoff Poll, than I am.

Wow. Just wow.

Jim Hyla
You certainly are a lot more productive at 5:30 AM, when I posted my Playoff Poll, than I am.

11h30 ici a Geneve...

Robb

Jim Hyla
You certainly are a lot more productive at 5:30 AM, when I posted my Playoff Poll, than I am.

11h30 ici a Geneve...

So, I see now.

Robb
So....I just happened to have some old code lying around for KRACH and some for figuring out ECAC standings possibilities (who doesn't?), so I linked 'em up, threw a Monte Carlo wrapper around them, and voila! After a million trials, here are the approximate* probabilities for each team finishing in each place, sorted to the most likely order of finish:

	1	2	3	4	5	6	7	8	9	10	11	12
Union	81.0%	19.0%										
Yale	19.0%	81.0%										
Cornell			83.1%	14.7%	2.2%							
Dartmouth		9.8%	36.2%	42.7%	11.3%						
Rensselaer		2.5%	29.5%	25.3%	42.7%						
Princeton		4.6%	19.6%	29.8%	46.0%						
Quinnipiac						68.0%	30.6%	1.3%	0.1%		
Clarkson						32.0%	68.0%				
St. Lawrence							0.8%	54.9%	44.2%		
Brown								0.6%	43.8%	45.9%	9.7%	
Colgate										9.7%	73.2%	17.0%
Harvard											17.0%	83.0%

It is theoretically possible for Cornell to finish in 6th, but it didn't happen in a single one of the million trials I ran.

*my ECAC tiebreaker code is out of date - I don't have total wins in there as the second tie-breaker, etc, but I'm not going to have time to update it before Friday, so this is the best you get.

Thanks Robb! Now I can tell my family there is a 97.8% chance they will see me next weekend . Life is so much more predictable when hockey games are played inside computers.

Rita
Life is so much more predictable when hockey games are played inside computers.

Unfortunately, they all are for me... I haven't even managed to go see the local Swiss league team this year.

Robb

Rita
Life is so much more predictable when hockey games are played inside computers.

Unfortunately, they all are for me... I haven't even managed to go see the local Swiss league team this year.

Me too. Reason #483 why they need to get to Atlantic City. I have a 29-year streak of seeing at least one game on the line.

Robb
So....I just happened to have some old code lying around for KRACH and some for figuring out ECAC standings possibilities (who doesn't?), so I linked 'em up, threw a Monte Carlo wrapper around them, and voila! After a million trials, here are the approximate* probabilities for each team finishing in each place, sorted to the most likely order of finish:

	1	2	3	4	5	6	7	8	9	10	11	12
Union	81.0%	19.0%										
Yale	19.0%	81.0%										
Cornell			83.1%	14.7%	2.2%							
Dartmouth		9.8%	36.2%	42.7%	11.3%						
Rensselaer		2.5%	29.5%	25.3%	42.7%						
Princeton		4.6%	19.6%	29.8%	46.0%						
Quinnipiac						68.0%	30.6%	1.3%	0.1%		
Clarkson						32.0%	68.0%				
St. Lawrence							0.8%	54.9%	44.2%		
Brown								0.6%	43.8%	45.9%	9.7%	
Colgate										9.7%	73.2%	17.0%
Harvard											17.0%	83.0%

It is theoretically possible for Cornell to finish in 6th, but it didn't happen in a single one of the million trials I ran.

*my ECAC tiebreaker code is out of date - I don't have total wins in there as the second tie-breaker, etc, but I'm not going to have time to update it before Friday, so this is the best you get.

Fanfreakin'tastic.

Robb
So....I just happened to have some old code lying around for KRACH and some for figuring out ECAC standings possibilities (who doesn't?), so I linked 'em up, threw a Monte Carlo wrapper around them, and voila!

What probability did you assign to a tie in any given game?

Robb

Rita
Life is so much more predictable when hockey games are played inside computers.

Unfortunately, they all are for me... I haven't even managed to go see the local Swiss league team this year.

Tant pis. Presumably you would have had more incentive when Knoepfli (sorry, Knöpfli) was still playing for Genève-Servette.

jtwcornell91

Robb
So....I just happened to have some old code lying around for KRACH and some for figuring out ECAC standings possibilities (who doesn't?), so I linked 'em up, threw a Monte Carlo wrapper around them, and voila!

What probability did you assign to a tie in any given game?

I was wondering how long it would take you to ask - since you already brought it up.

I used 0.13 for each game, since 13% of games nationally have been ties. However, that's wrong, of course - the probability of a tie should change with the ratio of the KRACH ratings - teams that have the same rating should be much more likely to tie than teams with widely different ratings. I didn't have time to think about how to make that happen while making the total proportion of ties be 13%.... Needs work...

Robb

jtwcornell91

Robb
So....I just happened to have some old code lying around for KRACH and some for figuring out ECAC standings possibilities (who doesn't?), so I linked 'em up, threw a Monte Carlo wrapper around them, and voila!

What probability did you assign to a tie in any given game?

I was wondering how long it would take you to ask - since you already brought it up.

I used 0.13 for each game, since 13% of games nationally have been ties. However, that's wrong, of course - the probability of a tie should change with the ratio of the KRACH ratings - teams that have the same rating should be much more likely to tie than teams with widely different ratings. I didn't have time to think about how to make that happen while making the total proportion of ties be 13%.... Needs work...

So does the Cornell PP, but I certainly don't expect either to be done by tomorrow night.

Robb
So....I just happened to have some old code lying around for KRACH and some for figuring out ECAC standings possibilities (who doesn't?), so I linked 'em up, threw a Monte Carlo wrapper around them, and voila! After a million trials, here are the approximate* probabilities for each team finishing in each place, sorted to the most likely order of finish:

	1	2	3	4	5	6	7	8	9	10	11	12
Union	81.0%	19.0%										
Yale	19.0%	81.0%										
Cornell			83.1%	14.7%	2.2%							
Dartmouth		9.8%	36.2%	42.7%	11.3%						
Rensselaer		2.5%	29.5%	25.3%	42.7%						
Princeton		4.6%	19.6%	29.8%	46.0%						
Quinnipiac						68.0%	30.6%	1.3%	0.1%		
Clarkson						32.0%	68.0%				
St. Lawrence							0.8%	54.9%	44.2%		
Brown								0.6%	43.8%	45.9%	9.7%	
Colgate										9.7%	73.2%	17.0%
Harvard											17.0%	83.0%

It is theoretically possible for Cornell to finish in 6th, but it didn't happen in a single one of the million trials I ran.

*my ECAC tiebreaker code is out of date - I don't have total wins in there as the second tie-breaker, etc, but I'm not going to have time to update it before Friday, so this is the best you get.

A subjective concurrence:

[www.dailygazette.com]

So am I correct in assessing that for a first round by we need to either:

1) Win

2) Tie and have Princeton tie/lose

3) Lose and have Princeton lose and RPI lose


In other words, just win baby.

Jordan 04
So am I correct in assessing that for a first round by we need to either:

1) Win

2) Tie and have Princeton tie/lose

3) Lose and have Princeton lose and RPI lose

1) Yup.

2) Yup.

3) In this case, RPI could either tie or lose.

And the flip side is that if Cornell loses, RPI wins, and Princeton wins or ties, the Big Red finishes... sixth.

Give My Regards
And the flip side is that if Cornell loses, RPI wins, and Princeton wins or ties, the Big Red finishes... sixth.

Apparently the end of a scenario that Robb's computer never encountered in a million trials.

andyw2100

Give My Regards
And the flip side is that if Cornell loses, RPI wins, and Princeton wins or ties, the Big Red finishes... sixth.

Apparently the end of a scenario that Robb's computer never encountered in a million trials.

I think there were some programming flaws there. The additive probability of all teams finishing 2nd was well over 100%, and the same for 3rd and 4th. On the other hand the total for 6th place was only 75% and only 32% for eighth.

Give My Regards
And the flip side is that if Cornell loses, RPI wins, and Princeton wins or ties, the Big Red finishes... sixth.

Sixth would play 11th place which would be the loser of tonight's St Lawrence v. Harvard game (both currently have 13 points). If Colgate wins tonight they would also have 13 points. SLU swept the season series with Colgate and wins a tiebreaker. Colgate and Harvard split but Harvard has two more wins that Colgate and would also win the tiebreaker.

jkahn

andyw2100

Give My Regards
And the flip side is that if Cornell loses, RPI wins, and Princeton wins or ties, the Big Red finishes... sixth.

Apparently the end of a scenario that Robb's computer never encountered in a million trials.

I think there were some programming flaws there. The additive probability of all teams finishing 2nd was well over 100%, and the same for 3rd and 4th. On the other hand the total for 6th place was only 75% and only 32% for eighth.

The programming was good - the HTML formatting was bad for some people, apparently, so the columns didn't line up. Unfortunately, I'm away on business now and forgot to bring that with me, so I can't re-try.

Robb

jkahn

andyw2100

Give My Regards
And the flip side is that if Cornell loses, RPI wins, and Princeton wins or ties, the Big Red finishes... sixth.

Apparently the end of a scenario that Robb's computer never encountered in a million trials.

I think there were some programming flaws there. The additive probability of all teams finishing 2nd was well over 100%, and the same for 3rd and 4th. On the other hand the total for 6th place was only 75% and only 32% for eighth.

The programming was good - the HTML formatting was bad for some people, apparently, so the columns didn't line up. Unfortunately, I'm away on business now and forgot to bring that with me, so I can't re-try.

I think you're right, as mine all added up correctly.

RPI's tie against Q gives Cornell 4th place for the regular season and a bye, despite the Yale and Brown losses.

BigRedHockeyFan
RPI's tie against Q gives Cornell 4th place for the regular season and a bye, despite the Yale and Brown loses.

Is this what they call "backing in?" In any case, it's a welcome development.

Good grief...I just heard a replay of Yale's goals and they've installed an obnoxious train horn a la Clarkson. What's the world coming to?

Al DeFlorio

BigRedHockeyFan
RPI's tie against Q gives Cornell 4th place for the regular season and a bye, despite the Yale and Brown loses.

Is this what they call "backing in?" In any case, it's a welcome development.

Good grief...I just heard a replay of Yale's goals and they've installed an obnoxious train horn a la Clarkson. What's the world coming to?

I guess the good news is that the next two games will be in Ithaca, most likely against Princeton.

BigRedHockeyFan

Al DeFlorio

BigRedHockeyFan
RPI's tie against Q gives Cornell 4th place for the regular season and a bye, despite the Yale and Brown loses.

Is this what they call "backing in?" In any case, it's a welcome development.

Good grief...I just heard a replay of Yale's goals and they've installed an obnoxious train horn a la Clarkson. What's the world coming to?

I guess the good news is that the next two games will be in Ithaca, most likely against Princeton.

If top seeds win next weekend, it's RPI.

1. Union
2. Yale
3. Dartmouth
4. Cornell --- Cornell wins tiebreaker with RPI (head to head) Cornell wins tiebreaker with Princeton (record vs. top 4 teams in league)
5. RPI --- RPI wins tiebreaker with Princeton (Record vs. top 4 teams)
6. Princeton
7. Clarkson --- Clarkson wins tiebreaker with Quinnipiac (More league wins)
8. Quinnipiac
9. Brown
10. Harvard
11. SLU
12. Colgate

Meaning...

12.Colgate @ 5.RPI
11.SLU @ 6.Princeton
10.Harvard @ 7.Clarkson
9.Brown @ 8.Quinnipiac

This what others come up with? The ECAC site standings are not correctly updated yet.

See Post Season thread.

LGRye
1. Union
2. Yale
3. Dartmouth
4. Cornell --- Cornell wins tiebreaker with RPI (head to head) Cornell wins tiebreaker with Princeton (record vs. top 4 teams in league)
5. RPI --- RPI wins tiebreaker with Princeton (Record vs. top 4 teams)
6. Princeton
7. Clarkson --- Clarkson wins tiebreaker with Quinnipiac (More league wins)
8. Quinnipiac
9. Brown
10. Harvard
11. SLU
12. Colgate

Meaning...

12.Colgate @ 5.RPI
11.SLU @ 6.Princeton
10.Harvard @ 7.Clarkson
9.Brown @ 8.Quinnipiac

This what others come up with? The ECAC site standings are not correctly updated yet.

Actually, Cornell gets fourth place because they win the three-way tiebreaker over Princeton and RPI (Cornell has 6 pts in games among the three teams, Princeton has 4 and RPI has 2). Cornell would have beaten Princeton on record vs the top 4 (3 in this case) if RPI lost, but since it's a 3-way tie, they don't need to go that far. The rest is correct, though.