2011 ECAC Playoff Possibilities Time

[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...

[Jim Hyla]

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.::bolt::

[BigRedHockeyFan]

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:

Code Select Expand


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:

http://www.dailygazette.com/weblogs/schott/2011/feb/24/ecac-hockey-predictions-2010-11-week-20/

[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


In other words, just win baby.

[Give My Regards]

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.

[Give My Regards]

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

[andyw2100]

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.

[jkahn]

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.

[nyc94]

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.

[Robb]

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.

[Jim Hyla]

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.

[BigRedHockeyFan]

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

[Al DeFlorio]

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?

[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.

[Jim Hyla]

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.