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ECAC Projected Standings 2015-16

Re: ECAC Projected Standings 2015-16

Ralph Baer said:
For those who still think that Fortran is the ultimate in programming languages, although I did eventually switch to Matlab, could you explain what those two statements signify?
Click to expand...

The first is a meaningless expression (it would yield an integer, but not do anything with it), the second is equivalent to "wins[op] = wins[op] + 1" ('+=1' in python serving essentially the same purpose as '++' in C and similar languages). Basically, because of some careless coding, I wasn't crediting the away team with a win for the purpose of tiebreakers when simulating games. The same error wasn't present for a home team win, or for entering games that already happened (which is why the program worked as intended when I manually set the results of games).
 
Re: ECAC Projected Standings 2015-16

lugnut92 said:
The first is a meaningless expression (it would yield an integer, but not do anything with it), the second is equivalent to "wins[op] = wins[op] + 1" ('+=1' in python serving essentially the same purpose as '++' in C and similar languages). Basically, because of some careless coding, I wasn't crediting the away team with a win for the purpose of tiebreakers when simulating games. The same error wasn't present for a home team win, or for entering games that already happened (which is why the program worked as intended when I manually set the results of games).
Click to expand...

And I guess that the meaningless "wins[op] + 1" doesn't result in an error message, it is just ignored.
 
Re: ECAC Projected Standings 2015-16

Ralph Baer said:
And I guess that the meaningless "wins[op] + 1" doesn't result in an error message, it is just ignored.
Click to expand...

Yup. The program will just do the math and move on. I don't know if it would cause a hiccup in other languages, but Python is fine with it.
 
Re: ECAC Projected Standings 2015-16

lugnut92 said:
Yup. The program will just do the math and move on. I don't know if it would cause a hiccup in other languages, but Python is fine with it.
Click to expand...

It's perfectly OK in JS as well. It's essentially a method that returns something, but you don't catch it anywhere. I assume it'd be OK with C as well, seeing how that's what the most common Python compiler is using as a basis.
 
Re: ECAC Projected Standings 2015-16

lugnut92 said:
I don't! You misunderstood me. I was saying that assuming that Yale takes #1 1.6% of the time, for them to come up empty in 1.5 million simulations is effectively impossible (approximately 1 in 10^10500). There was a problem in my code.
Click to expand...

Thank you for the clarification !!!
 
Re: ECAC Projected Standings 2015-16

DeepRed72 said:
I did attempt a Monte Carlo and my numbers agree fairly well with yours. I think the main source of variance between the two is due to the assumption of the frequency of ties. I used 18.3% (22/120) because that is this year's empirical data to date, but I do offer that is probably historically high. That said, I show a slightly greater chance of attaining a first round bye, 22.5% to your 19.3%. And my output reveals that should we win both games this weekend we have approximately a 64% chance of getting the bye. A win and a tie, 25 points, get us the bye only 19% of the time. A 1-1 split gives us no chance at a bye, but that is easily determined by inspection as either Dartmouth or St. Lawrence, who play each other, have to finish with at least 24 points (as Flaggy has pointed out) and we would lose all tie-breakers for that fourth spot. On the other end of the spectrum you show a 2.0% chance of finishing 8th whereas I get 1.1%.
Click to expand...

I have to admit to a bug in my tie-break routine that I discovered only by looking at Lugnut's revised posting (#421 on the We want more banners thread). He showed a non-zero probability of Rensselaer finishing 4th if we ended with 24 points. So I used my challenge and upon further review I realized I had neglected the three-way possibility of a tie for 4th among only Cornell, St. Lawrence and Rensselaer. We win that three-way tie-break (1.5, 2.0, 2.5 respectively) if and only if the following results happen this coming weekend:

Rensselaer ties Colgate
Cornell Beats Union
St. Lawrence ties Dartmouth
Rensselaer ties Cornell
Harvard beats St. Lawrence
Clarkson beats Dartmouth

Since there are three ties in this scenario, the probability is in the neighborhood of 0.0004, which would nicely support Lugnut's non-zero output and would beat down my assertion above that it is 'easily determined by inspection' not to be the case. Mea Culpa.
 
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Re: ECAC Projected Standings 2015-16

I'm sorry that I didn't get back to post in between Friday and Saturday games, but I was busy watching the RPI women get beat by Quinnipiac yesterday. Anyway, it's playoff time! As with the regular season, I use KRACH to simulate the playoffs 1,000,000 times to see what is likely to happen. All of the same disclaimers hold, though we no longer have to worry about ties. Here we go:
Code: 
      KRACH |   1st    QF    SF     F
-------------------------------------
Qu |  731.0 |        94.4  77.7  [B]55.4[/B]
Ya |  373.4 |        81.7  [B]50.7[/B]  21.2
Ha |  268.6 |        [B]70.8[/B]  33.1  11.4
SL |  165.8 |        [B]52.3[/B]  14.0   4.1
Ck |  156.0 |  [B]92.4[/B]  44.1  11.4   3.2
RP |  152.0 |  [B]82.5[/B]  25.6   6.3   2.0
Da |  138.6 |  [B]80.5[/B]  16.4   3.3   1.2
Cr |  175.5 |  [B]61.1[/B]   9.8   2.5   1.1
Un |  129.8 |  38.9   4.1   0.8   0.3
Cg |   54.7 |  19.5   0.4   0.0   0.0
Br |   55.1 |  17.5   0.3   0.0   0.0
Pr |   31.7 |   7.6   0.0   0.0   0.0

Quarterfinal Matchups:
 QF|    Ck    RP    Da    Cr    Un    Cg    Br    Pr 
----------------------------------------------------
Qu |     x     x     x  [B]37.5[/B]  23.8  14.9  16.1   7.6
Ya |     x     x  [B]61.4[/B]  20.1  12.8   4.4   1.3     x
Ha |     x  [B]76.2[/B]  18.1   3.3   2.1   0.3     x     x
SL |  [B]92.4[/B]   6.3   1.1   0.2   0.1     x     x     x

Bold is each team's most likely outcome.
0.0 means the outcome occurred, but fewer than 500 times.
x means the outcome never occurred.

Union is the only upset that seems anywhere near likely to happen in the first round, though we know how quickly things can change in a three game series. With the benefit of the bye, Quinnipiac has better than 50/50 odds on taking the championship over the field.
 
Re: ECAC Projected Standings 2015-16

lugnut92 said:
I'm sorry that I didn't get back to post in between Friday and Saturday games, but I was busy watching the RPI women get beat by Quinnipiac yesterday. Anyway, it's playoff time! As with the regular season, I use KRACH to simulate the playoffs 1,000,000 times to see what is likely to happen. All of the same disclaimers hold, though we no longer have to worry about ties. Here we go:
Code: 
      KRACH |   1st    QF    SF     F
-------------------------------------
Qu |  731.0 |        94.4  77.7  [B]55.4[/B]
Ya |  373.4 |        81.7  [B]50.7[/B]  21.2
Ha |  268.6 |        [B]70.8[/B]  33.1  11.4
SL |  165.8 |        [B]52.3[/B]  14.0   4.1
Ck |  156.0 |  [B]92.4[/B]  44.1  11.4   3.2
RP |  152.0 |  [B]82.5[/B]  25.6   6.3   2.0
Da |  138.6 |  [B]80.5[/B]  16.4   3.3   1.2
Cr |  175.5 |  [B]61.1[/B]   9.8   2.5   1.1
Un |  129.8 |  38.9   4.1   0.8   0.3
Cg |   54.7 |  19.5   0.4   0.0   0.0
Br |   55.1 |  17.5   0.3   0.0   0.0
Pr |   31.7 |   7.6   0.0   0.0   0.0

Quarterfinal Matchups:
 QF|    Ck    RP    Da    Cr    Un    Cg    Br    Pr 
----------------------------------------------------
Qu |     x     x     x  [B]37.5[/B]  23.8  14.9  16.1   7.6
Ya |     x     x  [B]61.4[/B]  20.1  12.8   4.4   1.3     x
Ha |     x  [B]76.2[/B]  18.1   3.3   2.1   0.3     x     x
SL |  [B]92.4[/B]   6.3   1.1   0.2   0.1     x     x     x

Bold is each team's most likely outcome.
0.0 means the outcome occurred, but fewer than 500 times.
x means the outcome never occurred.

Union is the only upset that seems anywhere near likely to happen in the first round, though we know how quickly things can change in a three game series. With the benefit of the bye, Quinnipiac has better than 50/50 odds on taking the championship over the field.
Click to expand...

I ran a decision tree analysis for the first two rounds so assuming the KRACH numbers are significant to four digits, here are the 'exact' probabilities for each team winning the first two rounds of the ECACs to that same accuracy:

Team - 1st - QF

Quin - Bye - .9439
Yale - Bye - .8171
Harv - Bye - .7078
StLa - Bye - .5239
Clar - .9241 - .4409
RPI - .8253 - .2561
Dart - .8051 - .1637
Corn - .6114 - .0976
Unio - .3886 - .0414
Colg - .1949 - .0042
Brow - .1747 - .0029
Prin - .0759 - .0004

So your simulation is spot on. The only slight difference I found was in the possible quarterfinal matchup between Harvard and RPI, you show 76.2% while I calculate .7626. (every little bit helps you know) :)
 
Last edited:
Re: ECAC Projected Standings 2015-16

Game one is behind us, and despite being forced to OT in two of last night's games, the home team won each game and we're very likely to go chalk in this first round.

Code: 
      KRACH |   1st    QF    SF     F
-------------------------------------
Qu |  735.3 |        [B]91.4[/B]  [B]75.2[/B]  [B]53.6[/B]
Ya |  374.9 |        [B]80.7[/B]  [B]50.1[/B]  21.3
Ha |  271.0 |        [B]70.0[/B]  33.1  11.7
SL |  166.5 |        [B]52.0[/B]  14.4   4.3
Ck |  158.5 |  [B]97.5[/B]  46.8  12.5   3.6
RP |  155.6 |  [B]93.7[/B]  28.7   7.4   2.3
Da |  143.0 |  [B]92.9[/B]  18.1   3.6   1.4
Cr |  187.9 |  [B]84.4[/B]  11.0   3.4   1.7
Un |  122.5 |  15.6   1.1   0.2   0.1
Cg |   52.2 |   7.1   0.1   0.0   0.0
Br |   51.9 |   6.3   0.1   0.0   0.0
Pr |   30.1 |   2.5   0.0   0.0   0.0

Quarterfinal Matchups:
 QF|    Ck    RP    Da    Cr    Un    Cg    Br    Pr 
----------------------------------------------------
Qu |     x     x     x  [B]71.7[/B]  13.2   6.5   6.1   2.5
Ya |     x     x  [B]84.9[/B]  12.1   2.3   0.6   0.2     x
Ha |     x  [B]91.4[/B]   7.9   0.6   0.1   0.0     x     x
SL |  [B]97.5[/B]   2.3   0.1   0.0   0.0     x     x     x

Bold is each team's most likely outcome.
0.0 means the outcome occurred, but fewer than 500 times.
x means the outcome never occurred.

Union is the road team most likely to come back and win their first round series, but there's a reason the games aren't played in a random number generator. If the home teams want to advance, they'll have to go out and take it.
 
Re: ECAC Projected Standings 2015-16

Three series are over, but Dartmouth and Colgate will battle for the privilege of coming to New Haven County next weekend.

Code: 
      KRACH |   1st    QF    SF     F
-------------------------------------
Qu |  730.7 |        [B]91.5[/B]  [B]75.0[/B]  [B]53.6[/B]
Ya |  373.2 |        [B]80.2[/B]  [B]49.9[/B]  21.3
Ha |  268.5 |        [B]68.9[/B]  32.6  11.4
SL |  164.2 |        [B]51.0[/B]  14.1   4.1
Ck |  160.1 |   [B]100[/B]  49.0  13.3   3.8
RP |  158.3 |   [B]100[/B]  31.1   8.2   2.6
Cr |  196.7 |   [B]100[/B]  16.5   4.7   2.4
Da |  128.7 |  [B]69.3[/B]  11.4   2.1   0.8
Cg |   56.8 |  30.7   0.5   0.1   0.0

Quarterfinal Matchups:
 QF|    Ck    RP    Da    Cr    Cg 
----------------------------------
Qu |     x     x     x  [B]69.3[/B]  30.7
Ya |     x     x  [B]69.3[/B]  30.7     x
Ha |     x   [B]100[/B]     x     x     x
SL |   [B]100[/B]     x     x     x     x

Bold is each team's most likely outcome.
0.0 means the outcome occurred, but fewer than 500 times.
x means the outcome never occurred.

Looking forward to the two set series, SLU-Clarkson is basically a coin flip, and Harvard is about a 2:1 favorite.
 
Re: ECAC Projected Standings 2015-16

And the first round goes chalk. Will round two? Who knows? Despite being fourth in the league in KRACH, Cornell gets the "prize" of playing the Bobcat juggernaut in Hamden this weekend, where KRACH says they will likely fall in a sweep. A few miles south, Yale is predicted to easily handle Dartmouth.

Code: 
      KRACH |    QF    SF     F
-------------------------------
Qu |  730.1 |  [B]88.3[/B]  [B]72.8[/B]  [B]51.9[/B]
Ya |  372.6 |  [B]83.0[/B]  [B]51.6[/B]  22.3
Ha |  268.1 |  [B]69.0[/B]  32.6  11.6
SL |  164.0 |  [B]51.0[/B]  14.1   4.2
Ck |  159.9 |  49.0  13.3   3.9
RP |  157.5 |  31.0   8.2   2.7
Da |  132.5 |  17.0   3.2   1.3
Cr |  197.6 |  11.7   4.3   2.2

Semifinal Matchups:
 SF|    Ha    SL    Ck    RP    Da    Cr
----------------------------------------
Qu |     x  25.8  24.8  22.7  15.0     x
Ya |  50.6  11.6  11.1     x     x   9.7
Ha |     x   8.7   8.4     x     x   1.4
SL |     x     x     x   3.9   0.7   0.3
Ck |     x     x     x   3.8   0.7   0.3
RP |     x     x     x     x   0.6     x

Bold is each team's most likely outcome.
0.0 means the outcome occurred, but fewer than 500 times.
x means the outcome never occurred.
 
Last edited:
lugnut92 said:
And the first round goes chalk. Will round two? Who knows? Despite being fourth in the league in KRACH, Cornell gets the "prize" of playing the Bobcat juggernaut in Hamden this weekend, where KRACH says they will likely fall in a sweep. A few miles south, Yale is predicted to easily handle Clarkson.

Code: 
      KRACH |    QF    SF     F
-------------------------------
Qu |  730.1 |  [B]88.3[/B]  [B]72.8[/B]  [B]51.9[/B]
Ya |  372.6 |  [B]83.0[/B]  [B]51.6[/B]  22.3
Ha |  268.1 |  [B]69.0[/B]  32.6  11.6
SL |  164.0 |  [B]51.0[/B]  14.1   4.2
Ck |  159.9 |  49.0  13.3   3.9
RP |  157.5 |  31.0   8.2   2.7
Da |  132.5 |  17.0   3.2   1.3
Cr |  197.6 |  11.7   4.3   2.2

Semifinal Matchups:
 SF|    Ha    SL    Ck    RP    Da    Cr
----------------------------------------
Qu |     x  25.8  24.8  22.7  15.0     x
Ya |  50.6  11.6  11.1     x     x   9.7
Ha |     x   8.7   8.4     x     x   1.4
SL |     x     x     x   3.9   0.7   0.3
Ck |     x     x     x   3.8   0.7   0.3
RP |     x     x     x     x   0.6     x

Bold is each team's most likely outcome.
0.0 means the outcome occurred, but fewer than 500 times.
x means the outcome never occurred.
Click to expand...

Huh, you mean SLU doesn't have to play our mutually hated rival after all?
 
Re: ECAC Projected Standings 2015-16

Despite winning game one of their series, KRACH says Dartmouth has just better than a coin flip's chance of advancing to the semifinal, where they will almost definitely face Quinnipiac.

Code: 
      KRACH |    QF    SF     F
-------------------------------
Qu |  757.5 |  96.0  79.7  [B]59.3[/B]
Ha |  280.0 |  87.8  [B]48.2[/B]  16.6
Ya |  326.0 |  48.0  26.7  10.1
SL |  172.9 |  [B]78.6[/B]  24.6   7.0
Da |  144.4 |  [B]52.0[/B]   9.0   3.5
Ck |  149.0 |  21.4   6.1   1.6
RP |  150.5 |  12.2   4.1   1.1
Cr |  190.3 |   4.0   1.6   0.8

Semifinal Matchups:
 SF|    Ha    SL    Ck    RP    Da    Cr
----------------------------------------
Qu |     x  31.7   8.7   5.7  49.9     x
Ya |  40.4   4.4   1.2     x     x   1.9
Ha |        35.8   9.7     x     x   1.8
SL |     x           x   5.0   1.4   0.2
Ck |     x     x         1.3   0.4   0.1
RP |     x     x     x         0.3     x

Bold is each team's most likely outcome.
0.0 means the outcome occurred, but fewer than 500 times.
x means the outcome never occurred.
 
Re: ECAC Projected Standings 2015-16

Sorry I didn't give an update between games 2 and 3 of the Quinnipiac-Cornell series. I wasn't really feeling it. Basically, Quinnipiac is going to be the favorite here until they're not. We're in one-and-done territory now so pretty much anything can happen.

Code: 
  F|    Ha    SL    Da
---------------------- 
Qu |  49.7  31.3     x
Ha |           x  11.6
SL |     x         7.3

      KRACH |    SF     F
-------------------------
Qu |  676.9 |  81.1  [B]59.3[/B]
Ha |  293.1 |  [B]61.3[/B]  22.6
SL |  184.3 |  38.7  10.6
Da |  159.1 |  18.9   7.5
 
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