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Ralph Baer
03-15-2011, 03:35 PM
It would also be nice to go to a regional that starts on SATURDAY, not that other day of the week.

(oops, back to lurking)

Good to see that people are still jumping the bandwagon. :D

Ralph Baer
03-15-2011, 03:37 PM
Glad to hear they're still going strong. Not sure what to expect, but if we do make the tourney we could easily be the most rested team there. Hard to say whether that would be a good thing or a bad thing. Maybe RPI and Union can scrimmage against each other while everyone else is in AC next weekend to prepare. :D

Would that be legal? Somehow I think that we wouldn't do that even if it is.

fr joe
03-15-2011, 04:30 PM
What would be so bad about potentially a part six?

RPI 2010-2011 VI: We Like to Post! :D

RPI 2010-2011 VI: Digital posters!

jmhusker
03-15-2011, 05:40 PM
Been looking into our tournament chances some more and it's really going to be a nail biter this weekend from an expected outcome point of view. Here's why:


We've got 15 PWR points now.
17 points will get anyone in barring a number of lower seeds making it. Who are those folks? Surprisingly not many: Bemidji, Cornell, Colgate and Northeastern. If AA runs the table in the WCHA they earn their way in anyhow.
16 point is clearly the bubble with most teams getting in with that total (tougher for us though because RPI's RPI is not so RPI-riffic)
There are 7 PWR comparisons that can flip for us: 5 UP in order of likelihood are CC, UWM, NtD, DC and ME and 2 down UNH and AA.
Using KRACH to determine probability of certain outcomes gives us some feel for what our chances of gaining PWR are. The downside for us is not too bad.

AA needs to win the WCHA to flip the PWR, the chances of that are about 4% and if they do then we gain a PWR from CC anyhow.
WE lose one PWR to UNH if they win HE, chances of that are 20%
Net all of that, we can expect to lose about .24 PWR points but this is more than made up for by some positive scenarios that create PWR flips in our direction, including:

Likelihood of CC losing to AA and AA not winning WCHA gets us an expected .425 points
Probability of Notre Dame or West Mich losing two in the CCHA is 61.6% which flips one PWR and gets us .616 points (note that it is possible to flip both but really unlikely).
Probability of Dartmouth losing both games is 27% and gets us an expected .27 PWR points
The ME PWR can be flipped if Colgate can win a game, especially against Yale, and NDAK is upset. Chances here are only about 5% or so but it's possible - call that a .05 point gain


Net of all of this is we can expect to gain about 1.5 points. That means 16 (bubble) or 17 points (in!) There are other ways to gain more ground (2 Cornell losses for instance) but we are playing at the margins and relying on indirect effects there. What does this mean? If we are on the bubble and there are upsets or there is a log jam at 16 we lose tie breakers. I'd say we have a 40% shot with only 16 PWR points (gut feel). At 17 we are in. Our likelihood of being at 17 seems a bit higher, maybe 55%. Which yields my estimate... 73% likelihood to dance.

Let's see what the program says when it comes out. I think 73% is reasonable and conservative but I've done the math in rather inelegant fashion.

realet
03-15-2011, 05:57 PM
There are 7 PWR comparisons that can flip for us: 5 UP in order of likelihood are CC, UWM, NtD, DC and ME and 2 down UNH and AA.

Do you mean WMU here? I haven't seen a scenario where we flip the WMU comparison, though I'd love to be proven wrong.

We also have to bear in mind that other teams are potentially gaining/losing comparison wins, too. We don't necessarily need to flip our own comparisons to move up the ranks.

RHamilton
03-15-2011, 06:29 PM
Fantastic! I knew someone out there would have the ability and wherewithal to undertake a project like this.

I don't want to be presumptuous or anything, but I know a pretty easy error would be to forget the possibility of ties in the CCHA and ECAC consolation games. Those included?

Added them in today. They're weighted wrong though probability-wise, as KRACH doesn't seem to have a good way to estimate ties. I used the probability of a split when two games are played, but that's no where near the probability of a tie. It shouldn't matter too much for the actual analysis though, as the probability associated with each outcome are secondary to the result of RPI in that outcome for this. It'll also be easy/quick to re-generate my probabilities if someone has a better idea about how to predict ties.

After running for about an hour, the program is predicting that we have an 84.2463% chance of making the playoffs (+/- ~4%). The margin of error accounts for a number of probability-based biases. I have one computer calculating the result of each permutation in highest-to-least-likely order, and another randomly picking permutations. The random one is converging to around 82%, which is inline with the probability based method.

I'm glad the results "agree" with RPI92's pen-and-paper based 86% estimate.

Here's a data dump for the data processed so far, accounting for the 30.5% most probable permutations:

Ranking if we're "in" the tournament (84.2463% of total):
15 - 34.930720271277%
13 - 18.091683732382%
14 - 25.354367457376%
12 - 5.8607277621524%
11 - 0.0088531694667127%
Ranking if we're out of the tournament (15.7537% of total):
16 - 12.705547353595%
17 - 2.1967289450045%
15 - 0.85137130874607%

Rankings of 14 and lower where we don't make it will be found eventually, it simply hasn't processed scenarios where there are more than two outside-the-top 16 auto-bids. I'm also bemused it hasn't found any #10 rankings where we're in yet.

GRussinko
03-15-2011, 06:39 PM
Only on an RPI thread...loving the analysis! Keep it coming! :)

jmhusker
03-15-2011, 06:45 PM
Do you mean WMU here? I haven't seen a scenario where we flip the WMU comparison, though I'd love to be proven wrong.

We also have to bear in mind that other teams are potentially gaining/losing comparison wins, too. We don't necessarily need to flip our own comparisons to move up the ranks.
Yes I meant WMU not the University of Wisconsin at Milwaukee. I've seen a few - including the scenario that RHamilton suggested earlier. That said you're right in that the UWM flip is not easy and I've overstated the situation in our favor - that is certainly offset by the negative effect 2 losses has on other WMU comparisons. Of course, now that the computer has spoken I can stop playing around with estimating.

troyboy
03-15-2011, 06:53 PM
Added them in today. They're weighted wrong though probability-wise, as KRACH doesn't seem to have a good way to estimate ties. I used the probability of a split when two games are played, but that's no where near the probability of a tie. It shouldn't matter too much for the actual analysis though, as the probability associated with each outcome are secondary to the result of RPI in that outcome for this. It'll also be easy/quick to re-generate my probabilities if someone has a better idea about how to predict ties.

After running for about an hour, the program is predicting that we have an 84.2463% chance of making the playoffs (+/- ~4%). The margin of error accounts for a number of probability-based biases. I have one computer calculating the result of each permutation in highest-to-least-likely order, and another randomly picking permutations. The random one is converging to around 82%, which is inline with the probability based method.

I'm glad the results "agree" with RPI92's pen-and-paper based 86% estimate.

Here's a data dump for the data processed so far, accounting for the 30.5% most probable permutations:

Ranking if we're "in" the tournament (84.2463% of total):
15 - 34.930720271277%
13 - 18.091683732382%
14 - 25.354367457376%
12 - 5.8607277621524%
11 - 0.0088531694667127%
Ranking if we're out of the tournament (15.7537% of total):
16 - 12.705547353595%
17 - 2.1967289450045%
15 - 0.85137130874607%

Rankings of 14 and lower where we don't make it will be found eventually, it simply hasn't processed scenarios where there are more than two outside-the-top 16 auto-bids. I'm also bemused it hasn't found any #10 rankings where we're in yet. Am I the only guy feeling inferior here !!!!

AspyDad
03-15-2011, 07:01 PM
Am I the only guy feeling inferior here !!!!

No

LTsatch
03-15-2011, 07:02 PM
Am I the only guy feeling inferior here !!!!

I am lucky to understand the selection show;), this stuff is mind boggling, either way good luck to you guys, the more ECAC teams the better!

AspyDad
03-15-2011, 07:02 PM
Great job Tom, RH and the rest of you. Your work is appreciated.

DrDemento
03-15-2011, 07:08 PM
Am I the only guy feeling inferior here !!!!

I have been out of school way too long! I was attempting to do this on my slide rule.;)

burgie12
03-15-2011, 07:34 PM
They're weighted wrong though probability-wise, as KRACH doesn't seem to have a good way to estimate ties. I used the probability of a split when two games are played, but that's no where near the probability of a tie. It shouldn't matter too much for the actual analysis though, as the probability associated with each outcome are secondary to the result of RPI in that outcome for this. It'll also be easy/quick to re-generate my probabilities if someone has a better idea about how to predict ties.
How about the method used by LynahFan in this post (http://board.uscho.com/showthread.php?94182-ECAC-Home-Stretch-A-mathematical-approach-to-Byes-and-Home-ice-(2010-2011)&p=5048525&viewfull=1#post5048525)?

Basically, if it's Dartmouth v Yale in the ECAC consolation game, KRACH says (going into the weekend) that the Elis have a 70.7% chance of winning the game. So, using a RNG, any result between 0.642 and 0.772 would be regarded as a tie, below 0.642 would be a Yale win, and above 0.772 would be a Dartmouth win.

vizoroo
03-15-2011, 07:50 PM
Just to help ou I'm rooting for a cc loss to UAA on thursday.
Go Engineers!

DrDemento
03-15-2011, 08:28 PM
Just to help ou I'm rooting for a cc loss to UAA on thursday.
Go Engineers!

That alone deserves a positive rep from me!

engineerhockeyfan
03-15-2011, 09:54 PM
Added them in today. They're weighted wrong though probability-wise, as KRACH doesn't seem to have a good way to estimate ties. I used the probability of a split when two games are played, but that's no where near the probability of a tie. It shouldn't matter too much for the actual analysis though, as the probability associated with each outcome are secondary to the result of RPI in that outcome for this. It'll also be easy/quick to re-generate my probabilities if someone has a better idea about how to predict ties.

After running for about an hour, the program is predicting that we have an 84.2463% chance of making the playoffs (+/- ~4%). The margin of error accounts for a number of probability-based biases. I have one computer calculating the result of each permutation in highest-to-least-likely order, and another randomly picking permutations. The random one is converging to around 82%, which is inline with the probability based method.

I'm glad the results "agree" with RPI92's pen-and-paper based 86% estimate.

Here's a data dump for the data processed so far, accounting for the 30.5% most probable permutations:

Ranking if we're "in" the tournament (84.2463% of total):
15 - 34.930720271277%
13 - 18.091683732382%
14 - 25.354367457376%
12 - 5.8607277621524%
11 - 0.0088531694667127%
Ranking if we're out of the tournament (15.7537% of total):
16 - 12.705547353595%
17 - 2.1967289450045%
15 - 0.85137130874607%

Rankings of 14 and lower where we don't make it will be found eventually, it simply hasn't processed scenarios where there are more than two outside-the-top 16 auto-bids. I'm also bemused it hasn't found any #10 rankings where we're in yet.

You guys are amazing, I thought my head was spinning before, now it just fell off. :eek:

Ralph Baer
03-15-2011, 10:00 PM
Added them in today. They're weighted wrong though probability-wise, as KRACH doesn't seem to have a good way to estimate ties. I used the probability of a split when two games are played, but that's no where near the probability of a tie. It shouldn't matter too much for the actual analysis though, as the probability associated with each outcome are secondary to the result of RPI in that outcome for this. It'll also be easy/quick to re-generate my probabilities if someone has a better idea about how to predict ties.

After running for about an hour, the program is predicting that we have an 84.2463% chance of making the playoffs (+/- ~4%). The margin of error accounts for a number of probability-based biases. I have one computer calculating the result of each permutation in highest-to-least-likely order, and another randomly picking permutations. The random one is converging to around 82%, which is inline with the probability based method.

I'm glad the results "agree" with RPI92's pen-and-paper based 86% estimate.

Here's a data dump for the data processed so far, accounting for the 30.5% most probable permutations:

Ranking if we're "in" the tournament (84.2463% of total):
15 - 34.930720271277%
13 - 18.091683732382%
14 - 25.354367457376%
12 - 5.8607277621524%
11 - 0.0088531694667127%
Ranking if we're out of the tournament (15.7537% of total):
16 - 12.705547353595%
17 - 2.1967289450045%
15 - 0.85137130874607%

Rankings of 14 and lower where we don't make it will be found eventually, it simply hasn't processed scenarios where there are more than two outside-the-top 16 auto-bids. I'm also bemused it hasn't found any #10 rankings where we're in yet. Do you mean that in about an hour you ran 30.5% of the permutations or however many permutations it takes to have a total of a 30.5% chance of happening. The latter, since you started with the most likely ones, would represent much less than 30.5% of all of the permutations, however if you meant the former, it means that it only takes between 3 and 4 hours to run all of them.

fr joe
03-15-2011, 10:13 PM
It's also not over until Hokymom sings. :D

I'd rather hear Princeton SuperMOM sing. :D I'm sure Babo has a wondeful signing voice. I know I don't! ;)

Ralph Baer
03-15-2011, 10:41 PM
I'd rather hear Princeton SuperMOM sing. :D I'm sure Babo has a wondeful signing voice. I know I don't! ;)

me neither :)