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lugnut92
10-26-2015, 12:27 PM
Here we are again, hearts full of hope as we look forward at the clean slate of the ECAC standings, wondering where our teams will end up. Well, I'm here to put an end to that hope with cold, unfeeling math. Never mind that half the conference has yet to play a game, never mind that KRACH is still using the hypothetical tie, never mind that our sample size so far is smaller than small, it's time to make unfounded projections about what will happen at the end of this ECAC schedule.

Simulated Final Standings (1,000,000 simulations of 10^62.98 possibilities):

Quinnipiac
Clarkson
SLU
Union

Dartmouth
Harvard
Yale
Princeton
Cornell
Brown

Colgate
RPI


Reminder: KRACH doesn't do ties. KRACH doesn't do prediction, it does retrodiction. KRACH cares not about your momentum, injuries, home-ice, etc. KRACH thinks you're exactly as good as your record. This early in the season, it is necessary to have the aforementioned hypothetical tie to keep all of the ratings finite and non-zero.

Rank and Points breakdown:

| KRACH | 1 2 3 4 5 6 7 8 9 10 11 12 |Avg Rk |AvgPts
-----------------------------------------------------------------------------------------------------
Qu | 2590.7 | 92.2 7.5 0.3 0.0 0.0 x 0.0 x x x x x | 1.08 | 38.92
Ck | 570.1 | 7.3 72.4 15.5 3.6 0.9 0.3 0.1 0.0 0.0 0.0 0.0 x | 2.20 | 32.46
SL | 258.8 | 0.4 13.4 43.4 22.0 9.9 5.1 2.8 1.5 0.8 0.4 0.2 0.0 | 3.71 | 26.88
Un | 190.0 | 0.1 4.9 22.9 28.5 16.5 10.3 6.7 4.4 2.8 1.7 0.9 0.3 | 4.75 | 24.31
Da | 100.0 | 0.0 0.3 2.8 7.1 11.1 12.4 13.0 12.9 12.4 11.6 10.0 6.4 | 7.76 | 18.66
Ha | 100.0 | 0.0 0.3 2.8 7.1 11.0 12.5 13.0 12.9 12.5 11.6 10.0 6.4 | 7.76 | 18.66
Ya | 100.0 | 0.0 0.3 2.8 7.1 11.0 12.5 12.9 12.9 12.5 11.7 9.9 6.4 | 7.76 | 18.66
Pr | 100.0 | 0.0 0.3 2.8 7.1 11.0 12.4 12.9 13.0 12.5 11.6 10.0 6.4 | 7.76 | 18.65
Cr | 100.0 | 0.0 0.3 2.8 7.1 11.0 12.4 13.0 12.8 12.5 11.6 10.1 6.4 | 7.77 | 18.65
Br | 100.0 | 0.0 0.3 2.8 7.1 10.9 12.4 12.8 12.9 12.5 11.7 10.1 6.4 | 7.77 | 18.65
Cg | 77.4 | 0.0 0.1 0.9 2.9 5.4 7.5 9.4 11.4 13.4 15.7 17.9 15.4 | 9.03 | 16.42
RP | 51.6 | x 0.0 0.1 0.4 1.2 2.1 3.5 5.3 8.0 12.4 20.9 45.9 | 10.66 | 13.07

| KRACH | x 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 |AvgPts
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Qu | 2590.7 | x x x x x x x x x x x x x x x x x x x x x x x x 0.0 0.0 0.0 0.0 0.0 0.0 0.1 0.2 0.5 1.2 2.4 4.3 7.1 10.5 13.9 16.1 16.1 13.3 8.8 4.2 1.1 | 38.92
Ck | 570.1 | x x x x x x x x x x x x x x 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.1 0.2 0.3 0.7 1.2 2.0 3.2 4.7 6.5 8.4 10.2 11.4 11.7 11.1 9.6 7.5 5.2 3.2 1.7 0.8 0.3 0.1 0.0 0.0 | 32.46
SL | 258.8 | x x x x x x x x 0.0 0.0 0.0 0.0 0.0 0.0 0.1 0.1 0.2 0.5 0.8 1.3 2.2 3.2 4.6 6.0 7.5 8.9 9.9 10.3 10.0 9.1 7.7 6.1 4.5 3.1 1.9 1.1 0.5 0.2 0.1 0.0 0.0 0.0 0.0 x x | 26.88
Un | 190.0 | x x x x x x 0.0 0.0 0.0 0.0 0.0 0.0 0.1 0.2 0.4 0.7 1.2 1.9 2.9 4.1 5.5 6.9 8.3 9.3 9.9 9.8 9.3 8.1 6.7 5.1 3.7 2.5 1.6 0.9 0.5 0.2 0.1 0.0 0.0 0.0 0.0 0.0 x x x | 24.31
Da | 100.0 | x 0.0 0.0 0.0 0.0 0.0 0.1 0.1 0.3 0.5 1.0 1.7 2.6 3.8 5.2 6.6 8.0 9.0 9.7 9.7 9.3 8.2 7.0 5.5 4.1 3.0 1.9 1.2 0.7 0.4 0.2 0.1 0.0 0.0 0.0 0.0 0.0 0.0 x 0.0 x x x x x | 18.66
Ha | 100.0 | 0.0 0.0 0.0 0.0 0.0 0.0 0.1 0.1 0.3 0.6 1.0 1.7 2.6 3.8 5.2 6.6 8.0 9.0 9.7 9.7 9.2 8.2 7.0 5.5 4.2 2.9 1.9 1.2 0.7 0.4 0.2 0.1 0.0 0.0 0.0 0.0 0.0 0.0 x 0.0 x x x x x | 18.66
Ya | 100.0 | x x 0.0 0.0 0.0 0.0 0.1 0.1 0.3 0.6 1.0 1.7 2.6 3.8 5.2 6.6 8.0 9.1 9.6 9.7 9.2 8.2 6.9 5.6 4.2 2.9 1.9 1.2 0.7 0.4 0.2 0.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 x x x x x x | 18.66
Pr | 100.0 | x x 0.0 0.0 0.0 0.0 0.1 0.1 0.3 0.6 1.0 1.7 2.6 3.8 5.2 6.7 8.0 9.1 9.7 9.7 9.2 8.2 6.9 5.5 4.1 2.9 1.9 1.2 0.7 0.4 0.2 0.1 0.0 0.0 0.0 0.0 0.0 x 0.0 x x x x x x | 18.65
Cr | 100.0 | x 0.0 0.0 0.0 0.0 0.0 0.1 0.1 0.3 0.6 1.0 1.7 2.6 3.8 5.2 6.6 8.0 9.0 9.7 9.7 9.2 8.2 6.9 5.5 4.2 2.9 2.0 1.2 0.7 0.4 0.2 0.1 0.0 0.0 0.0 0.0 0.0 0.0 x x x x x x x | 18.65
Br | 100.0 | x 0.0 0.0 0.0 0.0 0.0 0.1 0.1 0.3 0.6 1.0 1.7 2.6 3.8 5.2 6.6 8.1 9.0 9.7 9.7 9.2 8.2 6.9 5.5 4.2 2.9 2.0 1.2 0.7 0.4 0.2 0.1 0.0 0.0 0.0 0.0 0.0 0.0 x x x x x x x | 18.65
Cg | 77.4 | 0.0 0.0 0.0 0.0 0.0 0.1 0.3 0.6 1.1 1.8 2.8 4.1 5.7 7.1 8.5 9.5 9.9 9.7 9.0 7.9 6.5 5.1 3.8 2.6 1.7 1.1 0.6 0.3 0.2 0.1 0.0 0.0 0.0 0.0 0.0 0.0 x x x x x x x x x | 16.42
RP | 51.6 | 0.0 0.0 0.1 0.2 0.5 1.0 1.9 3.0 4.6 6.3 8.0 9.3 10.2 10.4 9.9 8.8 7.4 5.9 4.4 3.1 2.1 1.3 0.8 0.4 0.2 0.1 0.1 0.0 0.0 0.0 0.0 0.0 x x x x x x x x x x x x x | 13.07

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.

lugnut92
11-01-2015, 08:38 PM
The first weekend is in the books. We have ten undefeated teams and ten winless teams. There is some overlap.

Simulated Final Standings (1,000,000 simulations of 10^61.07 possibilities):

Quinnipiac
Clarkson
Yale
SLU
—————
Harvard
Cornell
Princeton
RPI
-----
Colgate
Union
Dartmouth
Brown


Reminder: KRACH doesn't do ties. KRACH doesn't do prediction, it does retrodiction. KRACH cares not about your momentum, injuries, home-ice, etc. KRACH thinks you're exactly as good as your record. This early in the season, it is necessary to have the aforementioned hypothetical tie to keep all of the ratings finite and non-zero.

Rank and Points breakdown:

| KRACH | 1 2 3 4 5 6 7 8 9 10 11 12 |Avg Rk |AvgPts
-----------------------------------------------------------------------------------------------------
Qu | 3691.5 | 87.7 10.4 1.8 0.2 0.0 0.0 x x x x x x | 1.15 | 38.68
Ck | 815.9 | 6.4 41.8 33.2 12.2 4.6 1.6 0.3 0.0 0.0 0.0 0.0 x | 2.73 | 32.21
Ya | 773.9 | 5.5 38.1 35.3 13.4 5.3 1.8 0.3 0.1 0.0 0.0 x x | 2.82 | 31.90
SL | 312.7 | 0.2 3.9 11.2 25.6 26.2 20.5 8.7 3.0 0.6 0.1 0.0 0.0 | 4.90 | 25.97
Ha | 275.1 | 0.1 3.4 10.2 24.8 26.8 21.6 9.2 3.1 0.6 0.1 0.0 0.0 | 4.97 | 25.72
Cr | 270.1 | 0.1 2.3 7.6 19.7 25.4 25.9 12.6 4.8 1.2 0.3 0.0 0.0 | 5.30 | 24.91
Pr | 132.6 | 0.0 0.1 0.5 2.7 6.8 14.8 30.7 25.8 11.8 4.8 1.5 0.4 | 7.33 | 19.58
RP | 93.0 | 0.0 0.0 0.2 1.4 4.3 11.3 27.8 33.3 14.5 5.2 1.6 0.4 | 7.61 | 18.70
Cg | 60.5 | x 0.0 0.0 0.1 0.3 1.5 5.8 14.3 27.8 26.2 16.0 8.0 | 9.50 | 13.84
Un | 71.7 | x 0.0 0.0 0.0 0.2 0.8 3.6 10.9 27.5 29.4 18.3 9.2 | 9.72 | 13.27
Da | 36.3 | x x x 0.0 0.0 0.1 0.6 2.7 8.9 18.5 32.7 36.5 | 10.89 | 9.90
Br | 29.3 | x x x 0.0 0.0 0.0 0.4 1.9 6.9 15.3 29.8 45.5 | 11.09 | 9.33

| KRACH | 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 |AvgPts
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Qu | 3691.5 | x x x x x x x x x x x x x x x x x x x x x x x x 0.0 0.0 0.0 0.0 0.0 0.0 0.1 0.3 0.7 1.5 2.9 5.0 8.0 11.3 14.4 16.0 15.2 12.2 7.7 3.6 1.0 | 38.68
Ck | 815.9 | x x x x x x x x x x x x x x x x 0.0 0.0 0.0 0.0 0.0 0.1 0.2 0.3 0.7 1.2 2.1 3.5 5.1 7.1 9.2 10.9 11.8 11.9 10.9 8.9 6.7 4.5 2.7 1.3 0.6 0.2 0.1 0.0 0.0 | 32.21
Ya | 773.9 | x x x x x x x x x x x x x x x 0.0 0.0 0.0 0.0 0.0 0.0 0.1 0.2 0.4 0.8 1.5 2.5 3.9 5.8 7.8 9.7 11.2 11.9 11.6 10.3 8.2 6.0 3.9 2.2 1.1 0.5 0.2 0.0 0.0 0.0 | 31.90
SL | 312.7 | x x x x x x x x x 0.0 0.0 0.0 0.0 0.0 0.1 0.1 0.3 0.6 1.1 1.8 2.9 4.3 6.0 7.7 9.2 10.4 10.8 10.5 9.5 7.9 6.1 4.4 2.9 1.7 0.9 0.5 0.2 0.1 0.0 0.0 0.0 0.0 0.0 x x | 25.97
Ha | 275.1 | x x x x x x x x x 0.0 0.0 0.0 0.0 0.0 0.1 0.1 0.3 0.6 1.1 2.0 3.2 4.7 6.4 8.2 9.8 10.7 11.1 10.5 9.2 7.5 5.6 3.8 2.4 1.4 0.7 0.4 0.2 0.1 0.0 0.0 0.0 0.0 x x x | 25.72
Cr | 270.1 | x x x x x x x 0.0 0.0 0.0 0.0 0.0 0.0 0.1 0.2 0.3 0.6 1.1 1.9 3.0 4.5 6.1 7.8 9.3 10.3 10.7 10.4 9.3 7.8 6.0 4.3 2.8 1.7 1.0 0.5 0.2 0.1 0.0 0.0 0.0 0.0 0.0 x x x | 24.91
Pr | 132.6 | x x x 0.0 0.0 0.0 0.0 0.0 0.1 0.2 0.4 0.8 1.4 2.3 3.6 5.1 6.8 8.4 9.7 10.4 10.5 9.8 8.6 7.0 5.3 3.8 2.5 1.5 0.9 0.5 0.2 0.1 0.0 0.0 0.0 0.0 0.0 x x x x x x x x | 19.58
RP | 93.0 | x x x x 0.0 0.0 0.0 0.0 0.1 0.2 0.4 0.9 1.8 3.1 4.8 6.7 8.7 10.2 11.3 11.3 10.5 9.0 7.2 5.3 3.6 2.3 1.3 0.7 0.4 0.2 0.1 0.0 0.0 0.0 0.0 0.0 x x 0.0 x x x x x x | 18.70
Cg | 60.5 | 0.0 0.0 0.0 0.1 0.2 0.4 1.0 1.8 3.1 4.7 6.6 8.4 9.9 10.8 10.9 10.3 8.9 7.3 5.5 3.9 2.6 1.6 0.9 0.5 0.2 0.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 x x x x x x x x x x x x | 13.84
Un | 71.7 | 0.0 0.0 0.0 0.1 0.2 0.5 1.2 2.2 3.7 5.6 7.7 9.6 11.1 11.6 11.2 10.0 8.2 6.2 4.5 2.9 1.7 1.0 0.5 0.2 0.1 0.0 0.0 0.0 0.0 0.0 x 0.0 0.0 x x x x x x x x x x x x | 13.27
Da | 36.3 | 0.0 0.1 0.5 1.1 2.4 4.2 6.5 8.8 10.8 11.9 12.1 11.1 9.5 7.4 5.3 3.6 2.2 1.3 0.7 0.3 0.2 0.1 0.0 0.0 0.0 0.0 0.0 x x x x x x x x x x x x x x x x x x | 9.90
Br | 29.3 | 0.1 0.2 0.7 1.7 3.4 5.5 8.0 10.1 11.6 12.2 11.6 10.1 8.2 6.1 4.3 2.7 1.6 0.9 0.5 0.2 0.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 x x x x x x x x x x x x x x x x x | 9.33

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.

lugnut92
11-08-2015, 08:53 PM
12 games this weekend! Isn't that just the best? Quinnipiac needs to go ahead and lose though. Okay? Thanks.

Simulated Final Standings (1,000,000 simulations of 10^55.35 possibilities):

Quinnipiac
Yale
Harvard
Cornell

RPI
SLU
Clarkson
Colgate

Union
Dartmouth
Princeton
Brown


Reminder: KRACH doesn't do ties. KRACH doesn't do prediction, it does retrodiction. KRACH cares not about your momentum, injuries, home-ice, etc. KRACH thinks you're exactly as good as your record. This early in the season, it is necessary to have the aforementioned hypothetical tie to keep all of the ratings finite and non-zero.

Rank and Points breakdown:

| KRACH | 1 2 3 4 5 6 7 8 9 10 11 12 |Avg Rk |AvgPts
-----------------------------------------------------------------------------------------------------
Qu | 5704.2 | 98.1 1.8 0.1 0.0 0.0 x x x x x x x | 1.02 | 40.10
Ya | 585.7 | 1.2 46.0 28.7 13.8 6.2 2.8 1.0 0.2 0.0 0.0 0.0 x | 2.91 | 30.90
Ha | 453.9 | 0.6 33.3 32.6 18.0 9.0 4.4 1.7 0.3 0.0 0.0 0.0 x | 3.23 | 30.01
Cr | 334.5 | 0.1 11.4 18.7 26.1 19.2 13.5 8.1 2.3 0.5 0.1 0.0 x | 4.41 | 27.03
RP | 170.6 | 0.0 3.2 8.1 16.7 24.1 23.9 17.4 5.1 1.2 0.2 0.0 0.0 | 5.38 | 24.62
SL | 241.3 | 0.0 2.5 6.4 13.2 20.1 23.9 22.8 8.0 2.4 0.6 0.1 0.0 | 5.73 | 23.95
Ck | 257.2 | 0.0 1.8 5.2 11.4 18.5 23.2 24.9 10.2 3.6 0.9 0.2 0.0 | 5.97 | 23.38
Cg | 83.2 | 0.0 0.0 0.1 0.6 1.8 4.5 11.3 29.6 28.8 16.6 6.3 0.4 | 8.54 | 16.98
Un | 93.7 | x 0.0 0.0 0.2 0.9 2.9 9.4 29.8 30.6 18.0 7.6 0.5 | 8.73 | 16.52
Da | 58.3 | x x 0.0 0.0 0.2 0.6 2.4 10.0 20.6 34.9 28.8 2.5 | 9.83 | 13.35
Pr | 49.5 | x 0.0 0.0 0.0 0.0 0.2 0.9 4.5 12.0 27.2 47.3 8.0 | 10.39 | 11.64
Br | 13.3 | x x x x 0.0 0.0 0.0 0.0 0.2 1.5 9.6 88.7 | 11.87 | 5.52

| KRACH | 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 |AvgPts
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Qu | 5704.2 | x x x x x x x x x x x x x x x x x x x x x x x x x x x x 0.0 0.0 0.0 0.0 0.1 0.2 0.6 1.4 3.0 5.8 10.0 14.7 18.4 19.0 15.4 8.7 2.7 | 40.10
Ya | 585.7 | x x x x x x x x x x x x 0.0 x 0.0 0.0 0.0 0.0 0.0 0.0 0.1 0.2 0.4 0.8 1.4 2.5 3.9 5.7 7.8 9.7 11.3 12.1 11.8 10.4 8.4 6.0 3.8 2.1 1.0 0.4 0.1 0.0 0.0 0.0 x | 30.90
Ha | 453.9 | x x x x x x x x x x x x x x 0.0 0.0 0.0 0.0 0.0 0.1 0.2 0.4 0.7 1.4 2.4 3.8 5.6 7.7 9.6 11.2 12.0 11.7 10.4 8.5 6.1 4.1 2.3 1.2 0.5 0.2 0.0 0.0 0.0 x x | 30.01
Cr | 334.5 | x x x x x x x x x x 0.0 0.0 0.0 0.0 0.0 0.1 0.1 0.3 0.5 1.0 1.7 2.8 4.2 5.8 7.5 9.2 10.5 11.0 10.7 9.7 8.2 6.3 4.5 2.8 1.7 0.9 0.4 0.2 0.1 0.0 0.0 0.0 x x x | 27.03
RP | 170.6 | x x x x x x x x x 0.0 0.0 0.0 0.0 0.0 0.1 0.2 0.4 0.9 1.7 3.0 4.6 6.7 8.7 10.7 11.6 11.8 10.9 9.3 7.2 5.1 3.3 1.9 1.1 0.5 0.2 0.1 0.0 0.0 0.0 0.0 x x x x x | 24.62
SL | 241.3 | x x x x x x x 0.0 0.0 0.0 0.0 0.0 0.0 0.1 0.2 0.5 1.0 1.7 2.8 4.2 6.0 7.8 9.5 10.7 11.1 10.7 9.6 7.9 6.0 4.2 2.7 1.6 0.8 0.4 0.2 0.1 0.0 0.0 0.0 0.0 x x x x x | 23.95
Ck | 257.2 | x x x x x x x 0.0 0.0 0.0 0.0 0.0 0.1 0.2 0.4 0.7 1.3 2.3 3.6 5.2 7.0 8.9 10.2 11.1 11.0 10.2 8.7 6.8 4.9 3.3 2.0 1.1 0.6 0.2 0.1 0.0 0.0 0.0 0.0 0.0 x x x x x | 23.38
Cg | 83.2 | x x 0.0 0.0 0.0 0.0 0.1 0.2 0.4 0.9 1.6 2.8 4.4 6.2 8.2 9.8 10.9 11.1 10.6 9.2 7.6 5.8 4.1 2.7 1.7 1.0 0.5 0.2 0.1 0.1 0.0 0.0 0.0 0.0 0.0 0.0 x x x x x x x x x | 16.98
Un | 93.7 | x x x 0.0 0.0 0.0 0.0 0.1 0.4 0.9 1.8 3.0 4.9 7.0 9.2 10.9 12.0 11.8 10.7 8.9 6.9 4.8 3.1 1.8 1.0 0.5 0.2 0.1 0.0 0.0 0.0 0.0 0.0 x x x x x x x x x x x x | 16.52
Da | 58.3 | x x 0.0 0.0 0.1 0.4 0.9 1.9 3.4 5.3 7.6 9.8 11.3 11.9 11.6 10.2 8.4 6.3 4.4 2.8 1.7 0.9 0.5 0.2 0.1 0.0 0.0 0.0 0.0 0.0 x x x x x x x x x x x x x x x | 13.35
Pr | 49.5 | 0.0 0.0 0.1 0.3 0.7 1.5 2.9 4.7 7.1 9.2 11.1 11.9 11.8 10.6 9.0 6.9 4.9 3.2 2.0 1.1 0.6 0.3 0.1 0.1 0.0 0.0 0.0 0.0 0.0 0.0 x x x x x x x x x x x x x x x | 11.64
Br | 13.3 | 0.9 3.2 7.1 11.2 14.4 15.5 14.4 11.8 8.7 5.7 3.4 1.9 0.9 0.4 0.2 0.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 x x x x x x x x x x x x x x x x x x x x x x | 5.52

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.

lugnut92
11-16-2015, 05:01 PM
Sooooomedaaaaay Quinnipiac will lose a game. Soooooomedaaaaay they won't break everything...

Simulated Final Standings (1,000,000 simulations of 10^50.10 possibilities):

Quinnipiac
Cornell
Harvard
Yale

RPI
SLU
Clarkson
Dartmouth

Colgate
Brown
Union
Princeton


Reminder: KRACH doesn't do ties. KRACH doesn't do prediction, it does retrodiction. KRACH cares not about your momentum, injuries, home-ice, etc. KRACH doesn't care if you got completely hosed by a broken video review system. KRACH thinks you're exactly as good as your record. This early in the season, it is necessary to have the aforementioned hypothetical tie to keep all of the ratings finite and non-zero

Rank and Points breakdown:

| KRACH | 1 2 3 4 5 6 7 8 9 10 11 12 |Avg Rk |AvgPts
-----------------------------------------------------------------------------------------------------
Qu | 7774.6 | 99.5 0.5 0.0 0.0 x x x x x x x x | 1.01 | 40.86
Cr | 521.7 | 0.3 42.5 30.1 15.1 7.7 3.5 0.8 0.1 0.0 0.0 0.0 x | 3.01 | 30.68
Ha | 487.6 | 0.2 41.0 32.3 15.3 7.4 3.1 0.6 0.0 0.0 0.0 0.0 x | 3.01 | 30.57
Ya | 313.5 | 0.0 7.4 15.8 25.9 24.0 18.7 6.5 1.3 0.3 0.0 0.0 0.0 | 4.57 | 26.44
RP | 185.6 | 0.0 4.2 11.0 21.9 27.7 23.3 9.2 2.3 0.4 0.1 0.0 0.0 | 4.94 | 25.47
SL | 258.5 | 0.0 4.1 10.0 18.7 24.5 28.1 10.6 3.0 0.7 0.2 0.0 0.0 | 5.11 | 25.21
Ck | 180.0 | x 0.2 0.8 2.6 6.4 15.0 38.3 21.3 9.6 4.2 1.6 0.2 | 7.21 | 19.95
Da | 99.2 | x 0.0 0.1 0.5 1.8 5.8 20.4 33.7 20.6 11.2 5.3 0.6 | 8.22 | 17.17
Cg | 65.3 | x 0.0 0.0 0.1 0.4 1.4 6.6 16.3 24.8 24.3 21.3 4.8 | 9.46 | 14.14
Br | 55.7 | x 0.0 0.0 0.0 0.2 0.8 4.5 12.9 24.6 27.9 22.5 6.7 | 9.68 | 13.59
Un | 64.5 | x 0.0 0.0 0.0 0.0 0.2 2.4 8.6 17.4 26.7 33.6 11.1 | 10.13 | 12.45
Pr | 29.5 | x x x x 0.0 0.0 0.1 0.4 1.7 5.5 15.6 76.7 | 11.66 | 7.46

| KRACH | 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 |AvgPts
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Qu | 7774.6 | x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x 0.0 0.0 0.0 0.0 0.1 0.4 1.1 2.7 5.9 11.0 17.2 21.7 21.0 13.9 4.9 | 40.86
Cr | 521.7 | x x x x x x x x x x x x x 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.1 0.2 0.5 0.9 1.7 2.8 4.3 6.1 8.2 10.1 11.5 11.9 11.5 9.9 7.9 5.5 3.5 1.8 0.9 0.3 0.1 0.0 0.0 x x | 30.68
Ha | 487.6 | x x x x x x x x x x x x x x x 0.0 0.0 0.0 0.0 0.0 0.1 0.2 0.4 0.8 1.5 2.6 4.3 6.4 8.7 10.8 12.1 12.8 11.8 10.1 7.4 5.1 2.8 1.5 0.5 0.2 0.0 0.0 x x x | 30.57
Ya | 313.5 | x x x x x x x x x x 0.0 x 0.0 0.0 0.0 0.0 0.1 0.2 0.5 1.1 1.9 3.2 4.9 6.9 8.9 10.6 11.7 11.8 10.9 9.3 7.0 4.9 3.0 1.7 0.8 0.3 0.1 0.0 0.0 0.0 0.0 0.0 x x x | 26.44
RP | 185.6 | x x x x x x x x x x x x 0.0 0.0 0.0 0.0 0.2 0.4 0.9 1.6 3.0 4.7 7.0 9.2 11.2 12.1 12.2 11.0 9.2 6.8 4.7 2.9 1.6 0.8 0.3 0.1 0.0 0.0 0.0 0.0 x x x x x | 25.47
SL | 258.5 | x x x x x x x x x 0.0 0.0 0.0 0.0 0.0 0.1 0.2 0.4 0.7 1.4 2.4 3.7 5.4 7.4 9.1 10.6 11.3 11.2 10.2 8.5 6.5 4.6 2.9 1.7 0.9 0.4 0.2 0.1 0.0 0.0 0.0 x x x x x | 25.21
Ck | 180.0 | x x x 0.0 0.0 0.0 0.0 0.0 0.0 0.1 0.2 0.5 0.9 1.7 2.8 4.3 6.0 8.0 9.6 10.8 11.2 10.8 9.5 7.9 5.9 4.2 2.6 1.5 0.8 0.4 0.2 0.1 0.0 0.0 0.0 0.0 x x x x x x x x x | 19.95
Da | 99.2 | x x x x 0.0 0.0 0.0 0.1 0.2 0.5 1.2 2.2 3.8 5.6 7.9 9.7 11.3 11.7 11.4 10.0 8.3 6.1 4.3 2.7 1.6 0.8 0.4 0.2 0.1 0.0 0.0 0.0 0.0 x x x x x x x x x x x x | 17.17
Cg | 65.3 | x x 0.0 0.0 0.1 0.2 0.6 1.3 2.4 4.0 6.0 8.0 9.8 11.0 11.4 10.9 9.6 7.9 6.1 4.3 2.8 1.7 0.9 0.5 0.2 0.1 0.0 0.0 0.0 0.0 0.0 0.0 x x x x x x x x x x x x x | 14.14
Br | 55.7 | x x x 0.0 0.1 0.2 0.6 1.5 2.8 4.8 7.0 9.4 11.2 12.2 11.9 10.8 8.9 6.8 4.8 3.1 1.8 1.0 0.5 0.2 0.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 x x x x x x x x x x x x x | 13.59
Un | 64.5 | x x 0.0 0.0 0.2 0.6 1.4 2.7 4.9 7.2 9.8 11.7 12.8 12.4 11.1 8.8 6.5 4.3 2.6 1.5 0.7 0.3 0.1 0.1 0.0 0.0 0.0 0.0 x x x x x x x x x x x x x x x x x | 12.45
Pr | 29.5 | 0.3 0.9 2.4 4.7 7.7 10.5 12.6 13.4 12.7 10.9 8.6 6.1 4.0 2.4 1.4 0.7 0.3 0.1 0.1 0.0 0.0 0.0 0.0 x x x x x x x x x x x x x x x x x x x x x x | 7.46


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.

antioch1098
11-17-2015, 10:42 AM
This is a great analysis! However, I do hope that the QU winning streak continues. :)

lugnut92
11-17-2015, 11:32 AM
This is a great analysis! However, I do hope that the QU winning streak continues. :)

We'll compromise. They can tie a game.

MarkEagleUSA
11-17-2015, 11:45 AM
We'll compromise. They can tie a game.Only if it's non-con... ;

lugnut92
11-22-2015, 01:23 PM
Well, Quinnipiac did their part to make KRACH work by tying a couple games this weekend, but Colorado College is still terrible and we still need the hypothetical tie.

Simulated Final Standings (1,000,000 simulations of 10^46.28 possibilities):

Quinnipiac
Harvard
Cornell
Yale

SLU
RPI
Clarkson
Dartmouth

Brown
Union
Colgate
Princeton


Reminder: KRACH doesn't do ties. KRACH doesn't do prediction, it does retrodiction. KRACH cares not about your momentum, injuries, home-ice, etc. KRACH thinks you're exactly as good as your record. This early in the season, it is necessary to have the aforementioned hypothetical tie to keep all of the ratings finite and non-zero.

Rank and Points breakdown:

| KRACH | 1 2 3 4 5 6 7 8 9 10 11 12 |Avg Rk |AvgPts
-----------------------------------------------------------------------------------------------------
Qu | 1770.5 | 88.9 8.8 1.7 0.4 0.1 0.0 0.0 x x x x x | 1.14 | 37.19
Ha | 481.9 | 4.6 33.7 25.5 17.9 11.5 6.2 0.5 0.0 0.0 0.0 x x | 3.19 | 30.51
Cr | 457.4 | 3.5 28.2 25.4 19.8 13.8 8.2 0.9 0.1 0.0 0.0 x x | 3.41 | 29.93
Ya | 402.0 | 1.7 13.5 21.0 24.1 21.8 15.7 1.9 0.2 0.0 0.0 0.0 0.0 | 4.07 | 28.32
SL | 325.9 | 1.0 10.6 16.0 20.5 24.6 23.4 3.3 0.5 0.1 0.0 0.0 0.0 | 4.44 | 27.50
RP | 209.9 | 0.4 5.0 10.1 16.5 25.4 34.0 6.9 1.4 0.2 0.0 0.0 0.0 | 4.99 | 25.95
Ck | 155.1 | 0.0 0.0 0.1 0.4 1.5 6.3 37.0 27.7 13.8 7.5 4.0 1.8 | 7.91 | 17.88
Da | 111.3 | x 0.0 0.1 0.3 1.2 5.4 33.7 30.5 15.2 8.0 4.1 1.6 | 8.00 | 17.44
Br | 56.2 | x x 0.0 0.0 0.0 0.3 4.0 10.7 19.9 23.1 22.6 19.4 | 10.07 | 12.71
Un | 74.9 | x x 0.0 0.0 0.0 0.2 5.0 11.7 19.1 21.2 21.8 21.0 | 10.06 | 12.66
Cg | 60.2 | x x 0.0 0.0 0.0 0.4 4.8 11.2 18.9 21.8 22.9 20.0 | 10.06 | 12.63
Pr | 58.0 | x x x 0.0 0.0 0.1 1.9 5.9 12.8 18.5 24.6 36.2 | 10.66 | 11.27

| KRACH | 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 |AvgPts
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Qu | 1770.5 | x x x x x x x x x x x x x x x x x x x x x x 0.0 0.0 0.0 0.0 0.1 0.2 0.4 0.9 2.0 3.7 6.3 9.7 13.2 15.8 16.4 14.2 10.2 5.2 1.9 | 37.19
Ha | 481.9 | x x x x x x x x x x x x x 0.0 0.0 0.0 0.0 0.0 0.1 0.2 0.5 0.9 1.7 2.9 4.5 6.6 8.7 10.8 11.9 12.3 11.4 9.7 7.3 5.1 2.9 1.6 0.7 0.3 0.1 0.0 x | 30.51
Cr | 457.4 | x x x x x x x x x x x 0.0 x 0.0 0.0 0.0 0.0 0.1 0.2 0.4 0.7 1.4 2.4 3.9 5.7 7.9 9.8 11.4 12.0 11.8 10.2 8.4 5.9 3.9 2.2 1.1 0.4 0.2 0.0 0.0 x | 29.93
Ya | 402.0 | x x x x x x x x x x 0.0 0.0 0.0 0.0 0.0 0.0 0.1 0.2 0.5 1.0 1.8 3.1 4.9 7.0 9.3 11.2 12.3 12.2 11.3 9.1 6.8 4.4 2.6 1.3 0.6 0.2 0.1 0.0 0.0 x x | 28.32
SL | 325.9 | x x x x x x x x x x 0.0 0.0 0.0 0.0 0.0 0.1 0.3 0.6 1.1 2.0 3.2 4.9 6.8 8.7 10.3 11.5 11.5 10.8 9.1 7.2 5.1 3.3 1.9 1.0 0.4 0.2 0.1 0.0 0.0 0.0 x | 27.50
RP | 209.9 | x x x x x x x x x x 0.0 0.0 0.0 0.0 0.1 0.3 0.7 1.4 2.5 4.0 6.0 8.1 10.1 11.3 12.0 11.3 10.0 7.9 5.8 3.8 2.4 1.3 0.6 0.3 0.1 0.0 0.0 0.0 0.0 0.0 x | 25.95
Ck | 155.1 | x 0.0 0.0 0.0 0.0 0.1 0.2 0.4 0.9 1.6 2.8 4.3 6.3 8.2 9.9 11.0 11.4 10.7 9.5 7.6 5.7 3.9 2.5 1.4 0.8 0.4 0.2 0.1 0.0 0.0 0.0 0.0 0.0 x x x x x x x x | 17.88
Da | 111.3 | x x 0.0 0.0 0.0 0.1 0.2 0.5 1.1 2.0 3.4 5.1 7.3 9.1 10.8 11.6 11.5 10.3 8.7 6.7 4.8 3.1 1.9 1.0 0.5 0.2 0.1 0.0 0.0 0.0 0.0 0.0 x x x x x x x x x | 17.44
Br | 56.2 | x x 0.1 0.3 1.0 2.2 4.3 6.7 9.6 11.6 12.8 12.7 11.4 9.3 7.0 4.8 3.0 1.7 0.9 0.4 0.2 0.1 0.0 0.0 0.0 0.0 x 0.0 0.0 x x x x x x x x x x x x | 12.71
Un | 74.9 | 0.0 0.1 0.2 0.6 1.4 2.6 4.6 6.7 9.3 11.0 12.3 12.2 11.2 9.2 7.1 4.9 3.1 1.8 1.0 0.5 0.2 0.1 0.0 0.0 0.0 0.0 x x x x x x x x x x x x x x x | 12.66
Cg | 60.2 | x 0.0 0.2 0.6 1.3 2.8 4.7 7.2 9.3 11.3 12.2 12.1 10.9 9.0 6.8 4.8 3.1 1.8 1.0 0.5 0.3 0.1 0.0 0.0 0.0 0.0 0.0 0.0 x x x x x x x x x x x x x | 12.63
Pr | 58.0 | 0.1 0.2 0.7 1.6 3.2 5.3 7.9 10.2 12.2 12.7 12.1 10.4 8.3 6.0 4.0 2.5 1.4 0.7 0.3 0.1 0.1 0.0 0.0 0.0 0.0 0.0 x x x x x x x x x x x x x x x | 11.27


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.

joecct
11-22-2015, 07:58 PM
Clarkson @ 7 assumes that CCT will actually score some goals.

LynahFan
11-22-2015, 08:07 PM
Well, Quinnipiac did their part to make KRACH work by tying a couple games this weekend, but Colorado College is still terrible and we still need the hypothetical tie.I'm not a statistician, but I believe their recommendation is to always use the "hypothetical" tie, even if the results are well-formed. I don't know all the reasons why, but that stuck in my brain somehow.

FlagDUDE08
11-23-2015, 04:55 AM
I'm not a statistician, but I believe their recommendation is to always use the "hypothetical" tie, even if the results are well-formed. I don't know all the reasons why, but that stuck in my brain somehow.

The hypothetical tie typically goes away when every team involved has played each other team at least once.

Red Cloud
11-23-2015, 09:30 AM
The hypothetical tie typically goes away when every team involved has played each other team at least once.

False. Try again.

lugnut92
11-23-2015, 11:33 AM
The hypothetical tie typically goes away when every team involved has played each other team at least once.

It's when you can say every team is better than any other team by a transitive chain (e.g., UA_ is better than BC because UA_ > RPI > BC). They can be quite a bit more complicated, but that's what you need. We're waiting on Colorado College to win a game. I don't actually know if the other 59 teams are all in one comparable group. Someone on ELynah usually keeps track of that, but I haven't looked at it this season.

Ralph Baer
11-23-2015, 11:42 AM
It's when you can say every team is better than any other team by a transitive chain (e.g., UA_ is better than BC because UA_ > RPI > BC). They can be quite a bit more complicated, but that's what you need. We're waiting on Colorado College to win a game. I don't actually know if the other 59 teams are all in one comparable group. Someone on ELynah usually keeps track of that, but I haven't looked at it this season.

He hasn't done that in at least two years.

FlagDUDE08
11-23-2015, 11:43 AM
It's when you can say every team is better than any other team by a transitive chain (e.g., UA_ is better than BC because UA_ > RPI > BC). They can be quite a bit more complicated, but that's what you need. We're waiting on Colorado College to win a game. I don't actually know if the other 59 teams are all in one comparable group. Someone on ELynah usually keeps track of that, but I haven't looked at it this season.

Fair enough; I thought you got rid of it when everyone played each other last year. Perhaps they were coincidental. I did see, on the Quinnipiac thread, how AIC is better than BC.

Red Cloud
11-23-2015, 11:59 AM
We're waiting on Colorado College to win a game.

More accurately, not lose a game.

lugnut92
11-23-2015, 12:02 PM
He hasn't done that in at least two years.

Oh. Well okay. I don't have an ELynah account, so I don't actually go over there unless linked in.


More accurately, not lose a game.

A tie is half a win :p

LynahFan
11-23-2015, 01:44 PM
Here's Ken's own explanation: link. (http://www.mscs.dal.ca/~butler/krachexp.htm)

Note that he recommends keeping the fictitious tie, even after it is not numerically necessary.

lugnut92
11-23-2015, 03:38 PM
Note that he recommends keeping the fictitious tie, even after it is not numerically necessary.

He says that he keeps them to maintain comparisons from week to week. I suppose I could do that, I just don't like to.

FlagDUDE08
11-28-2015, 10:23 PM
Colorado College finally won a game.