RPI 2011-12 season

[OnMAA]

Re: RPI 2011-12 season

Cornell 36 - 40 [1-1]
Harvard 31 - 35 [2-4]
Clarkson 30 - 34 [2-4]
--- Home Lock - 30+
St. Lawrence 28 - 32 [2-5]
Dartmouth 26 - 30 [4-5]
--- Home Eligible - 26+
Quinnipiac 22 - 26 [6-6]
Princeton 18 - 24 [7-8]
--- In - 18+
Brown 14 - 18 [8-10]
Rensselaer 14 - 18 [7-10]
Colgate 12 - 16 [8-10]
--- Out - 13
Union 6 - 10 [11-12]
Yale 3 - 7 [11-12]

Brown holds 8th place based on H2H record (1-0-1 vs 0-1-1).

Remaining League Schedules:

---------------------------------
|              |    |F2/17|S2/18|
---------------------------------
| Cornell      | CR |  CK |  SL |
| Harvard      | HA |  BN |  YA |
| Clarkson     | CK | @CR | @CG |
| St. Lawrence | SL | @CG | @CR |
| Dartmouth    | DA |  YA |  BN |
| Quinnipiac   | QN |  UN |  RP |
| Princeton    | PN |  RP |  UN |
| Brown        | BN | @HA | @DA |
| Rensselaer   | RP | @PN | @QN |
| Colgate      | CG |  SL |  CK |
| Union        | UC | @QN | @PN |
| Yale         | YA | @DA | @HA |
---------------------------------

Best-case scenarios:
Cornell (1st Place)
Already clinched

Harvard (2nd Place)
1) Win out
2) Earn one win and one tie
3) Earn two points (can be by a single win or two ties) AND have Clarkson NOT win out
4) Earn one point AND have Clarkson earn two or less points
5) Get swept AND have Clarkson earn zero or one points AND have SLU NOT win out

Clarkson (2nd Place)
1) Win out AND have Harvard earn two or less points
2) Earn one win and one tie AND have Harvard earn zero or one points
3) Earn two points (can be by a single win or two ties) AND have Harvard get swept AND have SLU NOT win out

St. Lawrence (2nd Place)
1) Win out AND have Harvard get swept AND have Clarkson earn two or less points

Dartmouth (4th Place)
1) Win out AND Cornell beats SLU AND Clarkson earns at least one point
2) Win out AND SLU ties Colgate AND SLU ties Cornell AND Clarkson earns at least one point
3) Win out AND SLU beats Cornell AND Colgate beats SLU AND Colgate finishes in 8th place AND Clarkson earns at least one point
4) Win out AND have SLU earn zero or one points
5) Earn one win and one tie AND SLU earns zero or one points
6) Earn exactly one win AND SLU gets swept

Quinnipiac (6th Place)
Already clinched

Princeton (7th Place)
1) Earn any point
2) Get swept AND Have RPI NOT win out
3) Get swept AND Have RPI win out AND Brown win out

Brown (8th Place)
1) Win out
2) Earn one win and one tie AND have RPI NOT win out
3) Earn two points (can be by a single win or two ties) AND have RPI earn two or less points
4) Earn one point AND have RPI earn zero or one points AND have Colgate NOT win out
5) Earn zero points AND have RPI earn zero points AND have Colgate earn two or less points

RPI (7th Place)
1) Win out AND Princeton gets swept AND have Brown NOT win out

Colgate (8th Place)
1) Win out AND Brown earns zero or one points AND RPI earns two or less points
2) Tie Clarkson AND beat SLU AND Brown gets swept AND RPI earns exactly one point AND SLU beats Cornell
3) Tie Clarkson AND beat SLU AND Brown gets swept AND RPI earns exactly one point AND SLU earns more points against Cornell than Dartmouth does against Yale (requires the near miracle of Yale beating Dartmouth)
4) Tie Clarkson AND beat SLU AND Brown gets swept AND RPI earns zero points
5) Beat Clarkson AND tie SLU AND Brown gets swept AND RPI earns zero or one points

Union (11th Place)
1) Earn any point
2) Have Yale NOT win out

Yale (11th Place)
1) Win out AND have Union get swept

Other intriguing scenarios:
St. Lawrence (Home-ice)
1) Win out
2) Earn one win and one tie
3) Beat Colgate AND lose to Cornell AND have Dartmouth NOT win out
4) Tie both Colgate and Cornell AND have Dartmouth NOT win out
5) Beat Cornell AND lose to Colgate AND have Dartmouth NOT win out
6) Beat Cornell AND lose to Colgate AND have Colgate not finish in 8th
7) Earn exactly one point AND have Dartmouth earn two or less points
8) Get swept AND have Dartmouth tie both Yale and Brown
9) Get swept AND have Dartmouth earn zero or one points

RPI (In)
1) Win out AND have Brown NOT win out
2) Earn one win and one tie AND have Brown earn two or less points
3) Earn two points (can be by a single win or two ties) AND have Brown earn zero or one points AND have Colgate NOT win out
4) Earn exactly one point AND have Brown get swept AND Colgate ties Clarkson AND Colgate beats SLU AND SLU does not beat Cornell AND Dartmouth earns at least as many points against Yale as SLU does against Cornell
5) Earn exactly one point AND have Brown get swept AND Colgate earns two or less points

Wow, do you have a computer program to spit all that out, or did you do this by hand.?

More importantly we need ODDS. For example the ODDS of the second last item happening must be miniscule.

 

[burgie12]

Re: RPI 2011-12 season

That fourth scenario for RPI getting in makes my head spin. I assume it boils down to us tying Colgate and Dartmouth staying in the top four?

Yes. If Colgate beats Clarkson, then RPI can't win the Points vs Top 4 criteria and as I said yesterday, Colgate wins the Points vs Top 8 criteria. If SLU beats Cornell, then a SLU / Dartmouth tie goes to Points vs Top 8. Since there would be a tie for both 4th and 8th place, the "Infinite Loop" (detailed here) starts. That means that both SLU and Dartmouth would be de facto Top 4 teams. RPI would then lose the Points vs Top 4 criteria.

Basically, it's a combination of Dartmouth's #3 and Colgate's #3.

All I can say is, you've used "less" where you should have used "fewer" unless there is a way that I don't know about to earn fractional points.

My apologies

Also, ask lugnut, he's been assigning fractional points to results for the past two weeks!

Wow, do you have a computer program to spit all that out, or did you do this by hand.?

More importantly we need ODDS. For example the ODDS of the second last item happening must be miniscule.

By hand. I have an Excel document where I can mess around with the scores and it'll generate standings and show the tiebreakers that were applied (if any), so I've just been messing around with that most of the weekend and I've spent a little bit of time just writing some stuff down.

It's difficult to use KRACH to guess the probability of ties. If we assume that there's a straight 13% probability of a tie in any women's college hockey game (terrible assumption because 1) that's the rate for men's games, women's is lower and 2) not every game has the same probability of a tie) and use the current KRACH, then:

-------------------------------------------------------
| Situation                                  |  Odds  |
-------------------------------------------------------
| RPI earns exactly one point                |        |
|   Ties Princeton, loses to Quinnipiac      | 0.0924 |
|   Ties Quinnipiac, loses to Princeton      | 0.0848 |
|   Total                                    | 0.1772 |
-------------------------------------------------------
| Brown gets swept                           | 0.5949 |
-------------------------------------------------------
| Colgate beats SLU and ties Clarkson        | 0.0053 |
-------------------------------------------------------
| Dartmouth earns at least as many           |        |
|  points against Yale as SLU does           |        |
|  against Cornell                           |        |
|    SLU-Cornell tie, Dartmouth beats Yale   | 0.1186 | 
|    SLU-Cornell tie, Dartmouth-Yale tie     | 0.0169 |
|    Cornell beats SLU, Dartmouth beats Yale | 0.6566 |
|    Cornell beats SLU, Dartmouth-Yale tie   | 0.0936 |
|    Cornell beats SLU, Yale beats Dartmouth | 0.0000 |
|    Total                                   | 0.8857 |
-------------------------------------------------------

| Overall likelihood                         | 0.0005 |

That's right... there's a 0.05% chance of the RPI #4 occurring. And that's an overestimation!!

 

[OnMAA]

Re: RPI 2011-12 season

Yes. If Colgate beats Clarkson, then RPI can't win the Points vs Top 4 criteria and as I said yesterday, Colgate wins the Points vs Top 8 criteria. If SLU beats Cornell, then a SLU / Dartmouth tie goes to Points vs Top 8. Since there would be a tie for both 4th and 8th place, the "Infinite Loop" (detailed here) starts. That means that both SLU and Dartmouth would be de facto Top 4 teams. RPI would then lose the Points vs Top 4 criteria.

Basically, it's a combination of Dartmouth's #3 and Colgate's #3.

My apologies

Also, ask lugnut, he's been assigning fractional points to results for the past two weeks!

By hand. I have an Excel document where I can mess around with the scores and it'll generate standings and show the tiebreakers that were applied (if any), so I've just been messing around with that most of the weekend and I've spent a little bit of time just writing some stuff down.

It's difficult to use KRACH to guess the probability of ties. If we assume that there's a straight 13% probability of a tie in any women's college hockey game (terrible assumption because 1) that's the rate for men's games, women's is lower and 2) not every game has the same probability of a tie) and use the current KRACH, then:

-------------------------------------------------------
| Situation                                  |  Odds  |
-------------------------------------------------------
| RPI earns exactly one point                |        |
|   Ties Princeton, loses to Quinnipiac      | 0.0924 |
|   Ties Quinnipiac, loses to Princeton      | 0.0848 |
|   Total                                    | 0.1772 |
-------------------------------------------------------
| Brown gets swept                           | 0.5949 |
-------------------------------------------------------
| Colgate beats SLU and ties Clarkson        | 0.0053 |
-------------------------------------------------------
| Dartmouth earns at least as many           |        |
|  points against Yale as SLU does           |        |
|  against Cornell                           |        |
|    SLU-Cornell tie, Dartmouth beats Yale   | 0.1186 | 
|    SLU-Cornell tie, Dartmouth-Yale tie     | 0.0169 |
|    Cornell beats SLU, Dartmouth beats Yale | 0.6566 |
|    Cornell beats SLU, Dartmouth-Yale tie   | 0.0936 |
|    Cornell beats SLU, Yale beats Dartmouth | 0.0000 |
|    Total                                   | 0.8857 |
-------------------------------------------------------

| Overall likelihood                         | 0.0005 |

That's right... there's a 0.05% chance of the RPI #4 occurring. And that's an overestimation!!

OK so now I'm really impressed. Do you have a day job?


According to your numbers, the chance of Brown getting swept is 60%, and the chance of RPI picking up a point is 17%. So the chance of RPI moving on with that combo is about 10% or so.

There are other combos like RPI winning one of two games over the weekend, that would hike that percentage up, but not by much.

So on the betting line about 1-10 odds of RPI making the playoffs, based on raw numbers.

Suspect the odds should be better for RPI to make it. IMHO the chance of Brown being swept is higher than 60%, and RPI picking up at least one point this weekend is reasonably good. There is not much at stake in this weekends games for Princeton and Quinnipiac. Dartmouth and Harvard are looking for points in a tight race for positions 2-5, so every point counts for them. Based on that I'd venture to guess, 90% chance Brown gets swept, and 30% chance RPI picks up at least one point. That would put RPI's chance to get in close to 30%.

Similarly there is about a 90%+ chance Harvard will take second place, as it is likely 90% plus chance they will sweep Brown and Yale this weekend.

 

[FlagDUDE08]

Re: RPI 2011-12 season

That's right... there's a 0.05% chance of the RPI #4 occurring. And that's an overestimation!!

Which means it'll probably happen, given how the ECAC usually is.

 

[lugnut92]

Re: RPI 2011-12 season

Case 1	
---------------------------------
/RPI takes 4            /0.06379/
/~(Brown wins both)     /0.97370/
---------------------------------
/           TOTAL       / 6.21% /
---------------------------------	

Case 2	
----------------------------------
/RPI takes 3             /       /
/    beats Q, ties P     /0.02063/
/    ties Q, beats P     /0.02597/
/	     SUBTOTAL	 /0.04661/
----------------------------------
/Brown takes ≤2	         /       /
/    loses H, loses D    /0.55306/
/    ties H, loses D     /0.06584/
/    loses H, ties D     /0.07058/
/    beats H, loses D    /0.09938/
/    loses H, beats D    /0.14632/
/    ties H, ties D	 /0.00840/
/         SUBTOTAL	 /0.94360/
----------------------------------
/              TOTAL     /4.40%  /
----------------------------------
	
Case 3	
----------------------------------
/RPI takes 2	         /       /
/    beats Q, loses P    /0.14066/
/    loses Q, beats P    /0.19363/
/    ties Q, ties P	 /0.00840/
/         SUBTOTAL	 /0.34270/
----------------------------------
/Brown takes ≤1	         /       /
/    loses H, loses D    /0.55306/
/    ties H, loses D     /0.06584/
/    loses H, ties D     /0.07058/
/         SUBTOTAL	 /0.68949/
----------------------------------
/Colgate takes <4	 /0.98816/
----------------------------------
/              TOTAL     /23.35% /
----------------------------------
	
Case 4	
--------------------------
/Burgie12's TOTAL  /0.05%/
--------------------------
	
Case 5
----------------------------------	
/RPI takes 1             /       /	
/     ties Q, loses P    /0.05728/
/     loses P, ties Q    /0.06263/
/          SUBTOTAL	 /0.11991/
----------------------------------
/Brown takes none	 /0.55306/
----------------------------------
/Colgate takes ≤2	 /       /
/     loses S, loses C   /0.63923/
/     ties S, loses C    /0.07318/
/     loses S, ties C    /0.07339/
/     beats S, loses C   /0.08594/
/     loses S, beats C   /0.08804/
/     ties S, ties C     /0.00840/
/          SUBTOTAL	 /0.96821/
----------------------------------
/               TOTAL    /6.42%  /
----------------------------------

--------------------
/      TOTALS      /
--------------------
/Case 1      /6.21%/
/Case 2      /4.40%/
/Case 3      /23.3%/
/Case 4      /0.05%/
/Case 5      /6.42%/
--------------------
/GRAND TOTAL /40.4%/
--------------------

In order to get all of the odds, I just expanded on what Burgie did for all 5 cases. I used 9.2% for ties (as that is what we've seen in the ECAC this season). Anyway, it all comes down to just over a 40% chance of RPI making the playoffs. Note: this is my first time using the code tags, so hopefully the formatting works...

 

[burgie12]

Re: RPI 2011-12 season

I used 9.2% for ties (as that is what we've seen in the ECAC this season)

Excellent formatting

Stupid question, but I have to say it because it's a common mistake... you subtracted 4.6% from the probability of each team winning, right? Otherwise, the total probability for a (for example) RPI - Princeton matchup would be 1.092, instead of 1.

 

[lugnut92]

Re: RPI 2011-12 season

I counted the chance of losing as 1-(winning chance)-(chance of tie), but I suppose your way would be more correct, wouldn't it... To the spreadsheet!

Okay, rather than copying everything again, just understand that I overestimated the chance of winning a given game and underestimated the chances of losing. As such, the chances of cases 1, 2, and 3 decreased, and 5 went up, leading to an overall 1.5% difference.

Here are the more accurate probabilities:

--------------------
/      TOTALS      /
--------------------
/Case 1      /4.20%/
/Case 2      /3.68%/
/Case 3      /23.1%/
/Case 4      /0.05%/
/Case 5      /7.88%/
--------------------
/GRAND TOTAL /38.9%/
--------------------

So our chances are a little under 40%, not a little over as was previously stated.

 

[jericho]

Re: RPI 2011-12 season

Two teams on the ice...50% chance of a win, 50% chance of a loss.


This is why I took statistics twice. I got an F and a D

 

[ARM]

Re: RPI 2011-12 season

They didn't cover ties in stats class?

 

[realet]

Re: RPI 2011-12 season

They didn't cover ties in stats class?

Thought you didn't have ties in the WCHA anymore...

 

[ARM]

Re: RPI 2011-12 season

Thought you didn't have ties in the WCHA anymore...

True, but there are still non-conference games and the NCAA picture, so I vaguely remember that the third number in a team's record is connected to some happening unrelated to a zamboni scraping the ice.

 

[burgie12]

Re: RPI 2011-12 season

Using a straight tie likelihood of 9.2% and subtracting 4.6% from the probability of each team winning (except when a team has less than a 4.6% chance of winning, then all 9.2% is deducted from the favored team), here are the expected places of all twelve teams after 1000 trials.

--------------------------------------------------------------------------------------------------------
|              |  1st  | 2nd  | 3rd  | 4th  | 5th  |  6th  | 7th  | 8th  | 9th  | 10th | 11th  | 12th  |
--------------------------------------------------------------------------------------------------------
| Cornell      | 100.0 |      |      |      |      |       |      |      |      |      |       |       |
| Harvard      |       | 98.0 |  2.0 |      |      |       |      |      |      |      |       |       |
| Clarkson     |       |  2.0 | 82.1 | 15.9 |      |       |      |      |      |      |       |       |
| St. Lawrence |       |      | 15.9 | 34.2 | 49.9 |       |      |      |      |      |       |       |
| Dartmouth    |       |      |      | 49.9 | 50.1 |       |      |      |      |      |       |       |
| Quinnipiac   |       |      |      |      |      | 100.0 |      |      |      |      |       |       |
| Princeton    |       |      |      |      |      |       | 99.6 |  0.4 |      |      |       |       |
| Brown        |       |      |      |      |      |       |      | 59.5 | 40.0 |  0.5 |       |       |
| Rensselaer   |       |      |      |      |      |       |  0.4 | 39.3 | 55.4 |  4.9 |       |       |
| Colgate      |       |      |      |      |      |       |      |  0.8 |  4.6 | 94.6 |       |       |
| Union        |       |      |      |      |      |       |      |      |      |      | 100.0 |       |
| Yale         |       |      |      |      |      |       |      |      |      |      |       | 100.0 |
--------------------------------------------------------------------------------------------------------

Note that despite the fact that it is possible for Yale to finish in 11th, it is extraordinarily unlikely.

 

[OnMAA]

Re: RPI 2011-12 season

Using a straight tie likelihood of 9.2% and subtracting 4.6% from the probability of each team winning (except when a team has less than a 4.6% chance of winning, then all 9.2% is deducted from the favored team), here are the expected places of all twelve teams after 1000 trials.

--------------------------------------------------------------------------------------------------------
|              |  1st  | 2nd  | 3rd  | 4th  | 5th  |  6th  | 7th  | 8th  | 9th  | 10th | 11th  | 12th  |
--------------------------------------------------------------------------------------------------------
| Cornell      | 100.0 |      |      |      |      |       |      |      |      |      |       |       |
| Harvard      |       | 98.0 |  2.0 |      |      |       |      |      |      |      |       |       |
| Clarkson     |       |  2.0 | 82.1 | 15.9 |      |       |      |      |      |      |       |       |
| St. Lawrence |       |      | 15.9 | 34.2 | 49.9 |       |      |      |      |      |       |       |
| Dartmouth    |       |      |      | 49.9 | 50.1 |       |      |      |      |      |       |       |
| Quinnipiac   |       |      |      |      |      | 100.0 |      |      |      |      |       |       |
| Princeton    |       |      |      |      |      |       | 99.6 |  0.4 |      |      |       |       |
| Brown        |       |      |      |      |      |       |      | 59.5 | 40.0 |  0.5 |       |       |
| Rensselaer   |       |      |      |      |      |       |  0.4 | 39.3 | 55.4 |  4.9 |       |       |
| Colgate      |       |      |      |      |      |       |      |  0.8 |  4.6 | 94.6 |       |       |
| Union        |       |      |      |      |      |       |      |      |      |      | 100.0 |       |
| Yale         |       |      |      |      |      |       |      |      |      |      |       | 100.0 |
--------------------------------------------------------------------------------------------------------

Note that despite the fact that it is possible for Yale to finish in 11th, it is extraordinarily unlikely.

Cool. What is the margin for error with 1000 trials. ?

Interesting paradox:
- Team with highest probability to finish fourth is Dartmouth.
- Team with highest probability to finish fifth is......Dartmouth.

Overall it shows that the 4/5 placing/order is the most unpredictable, followed closely by the contest for placings 8 and 9.

RPI has the largest variance, as they are the only team that can finish in four different spots.

 

[burgie12]

Re: RPI 2011-12 season

Cool. What is the margin for error with 1000 trials?

Large.
1) KRACH is not meant to be a predictive ranking, it's retrodictive.
2) There is not a straight 9.2% tie percentage (as evidenced by Cornell's 0 ties).
3) The 9.2% shouldn't come evenly from each side.
4) 1000 trials is really too small, but I just wanted to make sure it worked.

The best example of this is that straight KRACH (assuming lugnut's math is correct) says that RPI has a 38.9% chance of making the playoffs. The simulation gave RPI a 39.7% chance.

By the way, SLU can also finish in 2nd (giving them a 4-spot range, too), but it requires Harvard getting swept.

 

[Ralph Baer]

Re: RPI 2011-12 season

Large.
1) KRACH is not meant to be a predictive ranking, it's retrodictive.
2) There is not a straight 9.2% tie percentage (as evidenced by Cornell's 0 ties).
3) The 9.2% shouldn't come evenly from each side.
4) 1000 trials is really too small, but I just wanted to make sure it worked.

The best example of this is that straight KRACH (assuming lugnut's math is correct) says that RPI has a 38.9% chance of making the playoffs. The simulation gave RPI a 39.7% chance.

By the way, SLU can also finish in 2nd (giving them a 4-spot range, too), but it requires Harvard getting swept.

I would think that the closer a team is to a .500 record, the more likely it is to get ties (explains Cornell's 0 ties). More importantly, the closer that two teams' KRACH numbers are to each other, the more likely they are to tie. I suspect that a tie factor could be developed by calculating the distribution of ties as a function of the difference or the ratio of the KRACH of the two teams playing.

I hope that made some sense.

 

[Red Cloud]

Re: RPI 2011-12 season

I hope that made some sense.

None of this makes any sense.

 

[hab]

Re: RPI 2011-12 season

None of this makes any sense.

. Thank God! I had been thinking that it all came down to how badly the Engineers want to win on the weekend, but I was beginning to worry that I was missing something of great significance from the last page or two of this thread.

 

[Red Cloud]

Re: RPI 2011-12 season

. Thank God! I had been thinking that it all came down to how badly the Engineers want to win on the weekend, but I was beginning to worry that I was missing something of great significance from the last page or two of this thread.

In all reality, that's pretty much what it comes down to.

 

[Ralph Baer]

Re: RPI 2011-12 season

None of this makes any sense.

I never said that I knew how to write.

. Thank God! I had been thinking that it all came down to how badly the Engineers want to win on the weekend, but I was beginning to worry that I was missing something of great significance from the last page or two of this thread.

How does one quantify that?

 

[burgie12]

Re: RPI 2011-12 season

I would think that the closer a team is to a .500 record, the more likely it is to get ties (explains Cornell's 0 ties). More importantly, the closer that two teams' KRACH numbers are to each other, the more likely they are to tie. I suspect that a tie factor could be developed by calculating the distribution of ties as a function of the difference or the ratio of the KRACH of the two teams playing.

I hope that made some sense.

That is exactly what should be happening. And, in a perfect world, I'd be able to implement it. However, finding a sliding scale such that it comes out to the correct percentage (9.2 for women's ECAC, 13.2 for overall men's last year) is difficult. This same discussion came up last season in the ECAC Byes / Home-Ice thread when LynahFan tried to post some results and complained about KRACH's poor ability to predict ties (starting with Post #28).

If you're interested, there's an interesting website published by LakersFan / Michael Rutter that ranks women's college hockey teams by normal distributions (derived from the Mease College Football ratings) and can incorporate ties. However, he doesn't publish a ranking for men's hockey and I'm more interested in applying this to the men's ECAC race, so I need to be able to use a ranking system that I can calculate on my own. (Well, I could learn how to program the formula, but I'm pleased with the KRACH formula.)

If you want to start diving into this, I'd be interested in looking at it, too (obviously). Perhaps we'd even be able to come up with a suitable answer for KRACH. Ideally, this would be dealt with within the next couple of weeks. However, there's a long offseason coming up, so there will be plenty of time to look at it then, too.