ECAC Projected Standings 2021-2022

[lugnut92]

After a 19 month hiatus, we're back with another year of specious predictions in this season's ECAC KRACH predictions thread. As always, this early in the season, KRACH needs some help to be real and finite for every team. Instead of the hypothetical tie, I'm trying out a different little mathematical trick using last year's results (for those teams that played last year). It shouldn't make too much of a difference, and these are just for fun anyway.

For this year, I am also changing how I handle games decided in OT to match how they're handled in pairwise. That is, OT wins will only count as 0.55 wins, and conversely OT losses will count as 0.45 wins. I don't really love those specific numbers, but with the move to 3x3 OT, I cannot really rate wins in extra time as equivalent to wins in regulation. All games that end in shootouts will still be considered ties, as before.

It's also worth noting that instead of each game having three possible outcomes this year, each game has 6 possible outcomes, which massively inflates the number of possibilities. The points table will also be 50% larger this year with the move to three point games. Oh boy.

Anyway, obviously at this point the Ivies are all the same, because even looking at last year doesn't provide any information for them. What can you do.

[lugnut92]

Simulated Final Standings (Monte Carlo simulation of 10^102.7 possibilities; n=1,000,000):

1. Quinnipiac
2. SLU
3. Colgate
4. Clarkson
   –––––
5. RPI
6. Brown
7. Yale
8. Cornell
   —————
9. Harvard
10. Princeton
11. Dartmouth
12. Union

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.

Rank and Points breakdown:

   |  KRACH |     1     2     3     4     5     6     7     8     9    10    11    12 |Avg Rk |AvgPts
-----------------------------------------------------------------------------------------------------
Qu |  869.6 |  67.5  22.8   8.3   1.3   0.1   0.0   0.0   0.0     x     x     x     x |  1.44 | 46.43
SL |  422.5 |  17.5  37.7  32.5  10.1   1.8   0.3   0.1   0.0   0.0   0.0     x     x |  2.42 | 41.80
Cg |  380.8 |  13.7  32.7  37.5  12.9   2.6   0.5   0.1   0.0   0.0   0.0   0.0     x |  2.60 | 41.02
Ck |  178.0 |   1.2   5.8  16.6  45.9  18.4   6.7   2.9   1.4   0.6   0.3   0.1   0.0 |  4.20 | 34.47
RP |  105.9 |   0.1   0.8   3.9  17.4  32.9  18.1  11.0   7.0   4.4   2.7   1.4   0.4 |  5.75 | 29.33
Br |   54.2 |   0.0   0.0   0.2   2.1   7.3  12.2  14.0  14.7  14.9  14.5  13.2   6.9 |  8.41 | 22.47
Ya |   54.2 |   0.0   0.0   0.2   2.1   7.3  12.2  14.0  14.7  14.9  14.5  13.1   6.9 |  8.41 | 22.47
Cr |   54.2 |   0.0   0.0   0.2   2.0   7.3  12.2  14.1  14.6  14.9  14.6  13.1   6.9 |  8.41 | 22.47
Ha |   54.2 |   0.0   0.0   0.2   2.1   7.3  12.3  14.1  14.7  14.9  14.5  13.1   6.9 |  8.41 | 22.47
Pr |   54.2 |   0.0   0.0   0.2   2.0   7.3  12.3  14.0  14.8  14.8  14.5  13.1   6.9 |  8.41 | 22.47
Da |   54.2 |   0.0   0.0   0.2   2.0   7.3  12.3  14.0  14.8  14.9  14.4  13.2   6.9 |  8.41 | 22.46
Un |   23.7 |     x     x   0.0   0.0   0.3   0.9   1.8   3.3   5.7  10.0  19.7  58.3 | 11.14 | 14.83

   |  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    45    46    47    48    49    50    51    52    53    54    55    56    57    58    59    60    61    62    63    64    65    66 |AvgPts
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Qu |  869.6 |     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   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.1   0.2   0.3   0.6   0.9   1.6   2.3   3.4   4.8   6.3   7.9   9.4  10.4  10.9  10.5   9.5   7.8   5.7   3.8   2.1   1.0   0.3     x     x     x     x     x     x     x     x     x     x     x | 46.43
SL |  422.5 |     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   0.0   0.1   0.2   0.3   0.5   0.8   1.2   1.8   2.5   3.5   4.7   5.9   7.1   8.2   9.0   9.3   9.2   8.6   7.6   6.2   4.8   3.5   2.3   1.4   0.7   0.4   0.1   0.0   0.0     x     x     x     x     x     x     x     x     x     x     x | 41.80
Cg |  380.8 |     x     x     x     x     x     x     x     x     x     x     x     x     x     x     x     x     x   0.0   0.0     x   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.1   0.1   0.3   0.4   0.7   1.1   1.7   2.5   3.3   4.5   5.7   6.8   7.9   8.7   9.2   9.1   8.6   7.8   6.5   5.1   3.8   2.6   1.6   0.9   0.5   0.2   0.1   0.0   0.0     x     x     x     x     x     x     x     x     x     x     x | 41.02
Ck |  178.0 |     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   0.1   0.2   0.3   0.5   0.8   1.2   1.7   2.5   3.3   4.2   5.2   6.2   7.1   7.8   8.3   8.3   8.0   7.4   6.6   5.5   4.5   3.4   2.5   1.7   1.1   0.7   0.4   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 | 34.47
RP |  105.9 |     x     x     x     x     x   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.1   0.1   0.2   0.4   0.6   1.0   1.4   2.0   2.7   3.6   4.5   5.4   6.3   7.1   7.6   7.9   7.9   7.6   7.0   6.2   5.3   4.3   3.3   2.5   1.8   1.2   0.8   0.5   0.3   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 | 29.33
Br |   54.2 |     x   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.1   0.2   0.3   0.5   0.9   1.3   1.9   2.7   3.6   4.5   5.5   6.4   7.1   7.6   7.9   7.8   7.5   6.9   6.1   5.2   4.3   3.4   2.6   1.9   1.3   0.9   0.6   0.4   0.2   0.1   0.1   0.0   0.0   0.0   0.0   0.0   0.0   0.0     x     x   0.0     x     x     x     x     x     x     x     x     x     x     x     x     x     x     x     x     x     x | 22.47
Ya |   54.2 |     x   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.1   0.2   0.3   0.5   0.9   1.3   1.9   2.7   3.6   4.5   5.5   6.4   7.1   7.6   7.9   7.8   7.5   6.9   6.1   5.2   4.3   3.4   2.6   1.9   1.3   0.9   0.6   0.4   0.2   0.1   0.1   0.0   0.0   0.0   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 | 22.47
Cr |   54.2 |     x     x   0.0   0.0   0.0   0.0   0.0   0.0   0.1   0.2   0.3   0.5   0.9   1.4   1.9   2.7   3.5   4.5   5.5   6.4   7.1   7.7   7.9   7.8   7.5   6.9   6.1   5.2   4.3   3.4   2.6   1.9   1.3   0.9   0.6   0.4   0.2   0.1   0.1   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0     x   0.0     x     x     x     x     x     x     x     x     x     x     x     x     x     x     x     x     x     x | 22.47
Ha |   54.2 |     x     x   0.0   0.0   0.0   0.0   0.0   0.0   0.1   0.2   0.3   0.5   0.9   1.3   2.0   2.7   3.6   4.5   5.4   6.4   7.1   7.6   7.9   7.9   7.6   6.9   6.1   5.2   4.3   3.4   2.6   1.9   1.3   0.9   0.6   0.4   0.2   0.1   0.1   0.0   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 | 22.47
Pr |   54.2 |     x   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.1   0.2   0.3   0.5   0.9   1.3   1.9   2.7   3.5   4.5   5.5   6.4   7.1   7.7   7.9   7.8   7.5   7.0   6.1   5.2   4.3   3.4   2.6   1.9   1.3   0.9   0.6   0.4   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     x     x     x     x     x     x     x     x     x     x     x     x     x | 22.47
Da |   54.2 |   0.0     x   0.0   0.0   0.0   0.0   0.0   0.0   0.1   0.2   0.3   0.5   0.9   1.3   2.0   2.7   3.6   4.5   5.4   6.3   7.1   7.6   7.9   7.9   7.5   6.9   6.1   5.2   4.3   3.4   2.6   1.9   1.3   0.9   0.6   0.4   0.2   0.1   0.1   0.0   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 | 22.46
Un |   23.7 |   0.0   0.0   0.1   0.2   0.4   0.7   1.3   2.1   3.1   4.2   5.4   6.6   7.5   8.3   8.6   8.6   8.1   7.4   6.5   5.4   4.4   3.4   2.5   1.8   1.2   0.8   0.5   0.3   0.2   0.1   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     x     x     x     x     x     x     x | 14.83
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.
Blank outcomes are impossible

Playoffs:

   |    Qu    SL    Cg    Ck    RP    Br    Ya    Cr    Ha    Pr    Da    Un |   BYE
------------------------------------------------------------------------------------
Qu |     x     x     x     x   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.1 |  99.9
SL |     x     x     x   0.0   0.0   0.2   0.2   0.2   0.2   0.2   0.2   1.1 |  97.8
Cg |     x     x     x   0.0   0.0   0.3   0.3   0.3   0.3   0.3   0.3   1.6 |  96.8
Ck |     x   0.0   0.0     x   0.2   2.8   2.8   2.8   2.8   2.8   2.8  12.4 |  69.5
RP |     x   0.0   0.0   0.1     x   7.4   7.5   7.5   7.5   7.5   7.5  24.0 |  22.2
Br |     x   0.0   0.0   0.2   1.4     x   7.5   7.5   7.5   7.5   7.5   9.1 |   2.3
Ya |     x   0.0   0.0   0.2   1.4   7.6     x   7.5   7.5   7.5   7.5   9.1 |   2.3
Cr |     x   0.0   0.0   0.2   1.4   7.5   7.6     x   7.5   7.5   7.5   9.1 |   2.3
Ha |     x   0.0   0.0   0.2   1.4   7.6   7.5   7.5     x   7.5   7.5   9.1 |   2.3
Pr |     x   0.0   0.0   0.2   1.4   7.5   7.6   7.6   7.5     x   7.6   9.1 |   2.3
Da |     x   0.0   0.0   0.2   1.4   7.5   7.5   7.6   7.5   7.5     x   9.1 |   2.3
Un |     x   0.0   0.0   0.0   0.2   1.0   1.0   1.0   1.0   1.0   1.0     x |   0.0
Hosts on the left, visitors across the top.
0.0 means the outcome occurred, but fewer than 500 times.
x means the outcome never occurred.

[Ralph Baer]

Could you explain why there are six possible outcomes for each game? Since you stated that you would consider games ending in a shootout as ties, it looks to me that there are only five. (W, L, OT-W, OT-L, and T

[DrDemento]

Really glad to have this thread back posted. Even though the math is a touch mind boggling for me, I am amazed that even at my advancing age I sort of understand it all! Thanks Lug!!!!!!!

[sezenack]

Could you explain why there are six possible outcomes for each game? Since you stated that you would consider games ending in a shootout as ties, it looks to me that there are only five. (W, L, OT-W, OT-L, and T

He considers shootouts as ties in the KRACH formula, but the ECAC is using shootouts for standings points still

[lugnut92]

He considers shootouts as ties in the KRACH formula, but the ECAC is using shootouts for standings points still

This is correct. Shootout wins are not considered wins in the 2nd tiebreaker, and must be considered and counted separately. It should be noted that I am using constant OT and SO rates for all games, just as I used a single tie rate constant in previous seasons.

[lugnut92]

Some more games happened! But not ECAC games!

Simulated Final Standings (Monte Carlo simulation of 10^102.7 possibilities; n=1,000,000):

1. Quinnipiac
2. RPI
3. Colgate
4. Clarkson
   –––––
5. Dartmouth
6. Cornell
7. Harvard
8. Brown
   —————
9. Princeton
10. Yale
11. SLU
12. Union

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.

Rank and Points breakdown:

   |  KRACH |     1     2     3     4     5     6     7     8     9    10    11    12 |Avg Rk |AvgPts
-----------------------------------------------------------------------------------------------------
Qu |  303.7 |  74.6  19.5   4.5   1.1   0.2   0.1   0.0   0.0   0.0   0.0     x     x |  1.33 | 45.20
RP |  153.3 |  18.8  46.7  20.6   8.6   3.2   1.3   0.5   0.2   0.1   0.0   0.0   0.0 |  2.38 | 39.94
Cg |   91.1 |   3.7  16.8  30.1  22.5  12.0   6.8   3.9   2.2   1.2   0.6   0.2   0.0 |  3.82 | 34.89
Ck |   81.4 |   2.4  12.3  25.2  24.8  14.5   8.7   5.4   3.3   1.9   1.0   0.4   0.1 |  4.23 | 33.71
Da |   39.5 |   0.1   0.8   3.2   7.1  11.4  13.3  14.0  14.1  13.5  11.7   7.6   3.2 |  7.47 | 25.73
Cr |   39.5 |   0.1   0.8   3.3   7.0  11.4  13.3  14.1  14.1  13.4  11.8   7.5   3.2 |  7.48 | 25.72
Ha |   39.5 |   0.1   0.8   3.3   7.1  11.4  13.3  14.0  14.1  13.4  11.8   7.6   3.2 |  7.48 | 25.72
Br |   39.5 |   0.1   0.8   3.2   7.0  11.3  13.3  14.1  14.1  13.5  11.8   7.6   3.2 |  7.48 | 25.71
Pr |   39.5 |   0.1   0.8   3.2   7.1  11.5  13.4  14.0  14.1  13.5  11.8   7.6   3.2 |  7.48 | 25.71
Ya |   39.5 |   0.1   0.8   3.2   7.0  11.4  13.3  14.1  14.1  13.5  11.8   7.6   3.2 |  7.48 | 25.71
SL |   20.2 |   0.0   0.0   0.1   0.5   1.3   2.5   4.1   6.5  10.3  16.7  29.6  28.3 | 10.30 | 18.60
Un |   15.3 |   0.0   0.0   0.0   0.1   0.4   0.9   1.7   3.2   5.8  11.1  24.4  52.5 | 11.06 | 16.05    

   |  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    45    46    47    48    49    50    51    52    53    54    55    56    57    58    59    60    61    62    63    64    65    66 |AvgPts
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Qu |  303.7 |     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     x   0.0   0.0   0.0   0.0   0.0   0.0   0.1   0.1   0.2   0.3   0.5   0.8   1.4   2.0   2.9   4.0   5.2   6.6   7.9   9.0   9.7  10.0   9.7   8.6   7.3   5.6   3.8   2.4   1.3   0.5   0.2     x     x     x     x     x     x     x     x     x     x     x |  45.2
RP |  153.3 |     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   0.0   0.0   0.0   0.0   0.1   0.1   0.2   0.4   0.6   1.0   1.4   2.0   2.7   3.6   4.6   5.6   6.7   7.6   8.2   8.5   8.4   8.1   7.3   6.3   5.1   4.0   2.9   1.9   1.2   0.7   0.4   0.2   0.1   0.0   0.0     x     x     x     x     x     x     x     x     x     x     x | 39.94
Cg |   91.1 |     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   0.0   0.1   0.1   0.2   0.3   0.5   0.8   1.2   1.7   2.3   3.1   3.9   4.8   5.7   6.6   7.2   7.7   8.0   7.9   7.4   6.7   5.9   5.0   4.0   3.0   2.2   1.5   1.0   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     x     x | 34.89
Ck |   81.4 |     x     x     x     x     x     x     x     x   0.0     x   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.1   0.1   0.2   0.4   0.6   0.9   1.3   1.8   2.5   3.2   4.1   5.0   5.9   6.7   7.3   7.7   7.8   7.7   7.2   6.6   5.7   4.8   3.8   2.9   2.1   1.5   1.0   0.6   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     x     x     x     x     x | 33.71
Da |   39.5 |     x     x     x   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.1   0.1   0.2   0.4   0.6   0.9   1.4   1.9   2.6   3.4   4.2   5.1   6.0   6.7   7.3   7.5   7.6   7.4   6.9   6.2   5.4   4.6   3.7   2.9   2.2   1.6   1.1   0.7   0.5   0.3   0.2   0.1   0.1   0.0   0.0   0.0   0.0   0.0   0.0   0.0     x   0.0     x     x     x     x     x     x     x     x     x     x     x     x     x     x     x | 25.73
Cr |   39.5 |     x     x     x   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.1   0.1   0.2   0.4   0.6   0.9   1.4   1.9   2.6   3.4   4.2   5.1   6.0   6.6   7.2   7.6   7.6   7.4   6.9   6.3   5.4   4.6   3.7   2.9   2.2   1.6   1.1   0.7   0.5   0.3   0.2   0.1   0.1   0.0   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 | 25.72
Ha |   39.5 |     x     x     x   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.1   0.1   0.2   0.4   0.6   0.9   1.3   1.9   2.6   3.4   4.3   5.1   6.0   6.7   7.2   7.5   7.6   7.4   6.9   6.2   5.4   4.6   3.7   2.9   2.2   1.6   1.1   0.8   0.5   0.3   0.2   0.1   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 | 25.72
Br |   39.5 |     x     x     x   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.1   0.1   0.2   0.4   0.6   0.9   1.4   2.0   2.6   3.4   4.3   5.1   6.0   6.7   7.2   7.5   7.6   7.4   6.9   6.2   5.4   4.5   3.7   2.9   2.2   1.6   1.1   0.8   0.5   0.3   0.2   0.1   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 | 25.71
Pr |   39.5 |     x     x     x   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.1   0.1   0.2   0.4   0.6   0.9   1.4   1.9   2.6   3.4   4.3   5.1   6.0   6.7   7.2   7.5   7.6   7.3   6.9   6.3   5.4   4.6   3.7   2.9   2.2   1.6   1.1   0.7   0.5   0.3   0.2   0.1   0.1   0.0   0.0   0.0   0.0   0.0   0.0     x     x   0.0     x     x     x     x     x     x     x     x     x     x     x     x     x     x     x | 25.71
Ya |   39.5 |     x     x     x   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.1   0.1   0.2   0.4   0.6   0.9   1.4   1.9   2.6   3.4   4.3   5.2   6.0   6.7   7.2   7.6   7.6   7.4   6.9   6.2   5.5   4.6   3.7   2.9   2.2   1.6   1.1   0.8   0.5   0.3   0.2   0.1   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 | 25.71
SL |   20.2 |   0.0   0.0   0.0   0.0   0.0   0.1   0.2   0.4   0.7   1.2   1.8   2.6   3.5   4.5   5.5   6.4   7.2   7.8   8.0   7.9   7.5   6.9   6.1   5.2   4.3   3.4   2.6   1.9   1.4   0.9   0.6   0.4   0.3   0.2   0.1   0.0   0.0   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     x |  18.6
Un |   15.3 |   0.0   0.0   0.0   0.1   0.2   0.4   0.8   1.3   2.1   2.9   4.0   5.1   6.2   7.2   7.9   8.3   8.4   8.0   7.4   6.6   5.6   4.6   3.7   2.8   2.1   1.5   1.0   0.7   0.4   0.3   0.2   0.1   0.1   0.0   0.0   0.0   0.0   0.0   0.0   0.0     x     x   0.0     x     x     x     x     x     x     x     x     x     x     x     x     x     x     x     x     x     x     x     x     x     x     x     x | 16.05
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.
Blank outcomes are impossible

Playoffs:

   |    Qu    RP    Cg    Ck    Da    Cr    Ha    Br    Pr    Ya    SL    Un |   BYE
------------------------------------------------------------------------------------
Qu |           x   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.1   0.1 |  99.7
RP |     x         0.0   0.0   0.3   0.3   0.3   0.3   0.3   0.3   1.4   2.1 |  94.7
Cg |   0.0   0.0         0.1   1.6   1.6   1.6   1.6   1.7   1.6   6.4   8.5 |  73.1
Ck |   0.0   0.0   0.1         2.2   2.2   2.2   2.2   2.2   2.2   8.0  10.5 |  64.8
Da |   0.0   0.0   0.3   0.5         5.8   5.8   5.8   5.8   5.8  11.3  11.8 |  11.2
Cr |     x   0.0   0.3   0.5   5.8         5.8   5.8   5.8   5.8  11.4  11.8 |  11.1
Ha |   0.0   0.0   0.3   0.5   5.8   5.8         5.8   5.7   5.8  11.4  11.7 |  11.2
Br |   0.0   0.0   0.3   0.5   5.8   5.8   5.8         5.9   5.8  11.4  11.7 |  11.1
Pr |   0.0   0.0   0.3   0.5   5.8   5.8   5.8   5.8         5.8  11.4  11.8 |  11.1
Ya |   0.0   0.0   0.3   0.5   5.8   5.8   5.8   5.8   5.8        11.3  11.7 |  11.1
SL |     x   0.0   0.1   0.2   2.0   2.0   2.0   2.0   2.0   2.0         2.0 |   0.7
Un |     x   0.0   0.1   0.1   0.9   0.8   0.8   0.9   0.8   0.8   0.9       |   0.1

Hosts on the left, visitors across the top.

      KRACH |   1st    QF    SF     F
-------------------------------------
Qu |  303.7 | 100.0  96.5  78.9  57.2
RP |  153.3 |  99.7  87.5  57.0  24.1
Cg |   91.1 |  96.3  69.4  26.7   8.7
Ck |   81.4 |  94.3  62.9  21.8   6.7
Da |   39.5 |  61.2  13.7   2.6   0.5
Cr |   39.5 |  61.3  13.7   2.6   0.5
Ha |   39.5 |  61.3  13.7   2.6   0.5
Br |   39.5 |  61.3  13.6   2.6   0.5
Pr |   39.5 |  61.3  13.7   2.6   0.5
Ya |   39.5 |  61.3  13.7   2.6   0.5
SL |   20.2 |  25.2   1.2   0.1   0.0
Un |   15.3 |  16.8   0.4   0.0   0.0
0.0 means the outcome occurred, but fewer than 500 times.
x means the outcome never occurred.

[lugnut92]

Last post before the league slate starts, and unfortunately the Ivies remain too cowardly to participate in sporting events.

Simulated Final Standings (Monte Carlo simulation of 10^102.7 possibilities; n=1,000,000):

1. Quinnipiac
2. Colgate
3. Clarkson
4. RPI
   –––––
5. SLU
6. Cornell
7. Brown
8. Yale
   —————
9. Harvard
10. Dartmouth
11. Princeton
12. Union

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.

Rank and Points breakdown:

   |  KRACH |     1     2     3     4     5     6     7     8     9    10    11    12 |Avg Rk |AvgPts
-----------------------------------------------------------------------------------------------------
Qu |  648.1 |  86.0  11.2   2.3   0.4   0.0   0.0   0.0     x     x     x     x     x |  1.17 | 47.47
Cg |  195.0 |   8.1  43.0  27.8  15.2   4.1   1.1   0.4   0.1   0.0   0.0   0.0   0.0 |  2.70 | 39.44
Ck |  146.4 |   3.3  23.9  31.6  26.5   9.2   3.2   1.3   0.6   0.2   0.1   0.0   0.0 |  3.35 | 36.88
RP |  134.5 |   2.4  19.5  29.3  30.1  11.3   4.2   1.8   0.8   0.4   0.2   0.1   0.0 |  3.56 | 36.07
SL |   64.8 |   0.1   1.7   5.5  13.4  27.4  18.1  12.1   8.3   5.8   3.9   2.4   1.2 |  6.04 | 28.54
Cr |   37.4 |   0.0   0.1   0.6   2.3   7.7  11.5  13.1  13.6  13.7  13.6  12.9  10.9 |  8.51 | 22.61
Br |   37.4 |   0.0   0.1   0.6   2.3   7.6  11.5  13.0  13.7  13.8  13.6  12.8  11.0 |  8.52 | 22.60
Ya |   37.4 |   0.0   0.1   0.6   2.3   7.7  11.6  13.1  13.6  13.7  13.5  12.9  11.0 |  8.51 | 22.60
Ha |   37.4 |   0.0   0.1   0.6   2.3   7.6  11.6  13.0  13.7  13.7  13.5  12.9  11.0 |  8.51 | 22.60
Da |   37.4 |   0.0   0.1   0.6   2.3   7.7  11.6  13.1  13.6  13.7  13.6  12.9  10.9 |  8.51 | 22.60
Pr |   37.4 |   0.0   0.1   0.6   2.3   7.6  11.5  13.1  13.6  13.8  13.5  12.9  11.0 |  8.51 | 22.60
Un |   25.4 |     x   0.0   0.1   0.4   2.0   4.0   6.1   8.4  11.1  14.6  20.3  33.0 | 10.11 | 18.66    

   |  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    45    46    47    48    49    50    51    52    53    54    55    56    57    58    59    60    61    62    63    64    65    66 |AvgPts
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Qu |  648.1 |     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   0.0   0.0   0.0   0.0   0.1   0.1   0.3   0.5   0.8   1.4   2.1   3.2   4.5   6.2   7.9   9.6  10.8  11.4  11.2  10.0   8.1   5.9   3.5   1.8   0.6     x     x     x     x     x     x     x     x     x     x     x | 47.47
Cg |  195.0 |     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   0.0   0.1   0.1   0.2   0.3   0.5   0.7   1.1   1.6   2.2   3.1   4.1   5.2   6.2   7.3   8.0   8.6   8.7   8.5   7.8   6.9   5.7   4.5   3.3   2.2   1.4   0.9   0.5   0.2   0.1   0.0   0.0   0.0     x     x     x     x     x     x     x     x     x     x     x | 39.44
Ck |  146.4 |     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   0.0   0.0   0.1   0.1   0.2   0.3   0.4   0.7   1.0   1.5   2.1   2.9   3.8   4.7   5.7   6.7   7.5   8.1   8.4   8.3   7.8   7.1   6.1   5.0   3.9   2.9   2.0   1.3   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     x     x     x | 36.88
RP |  134.5 |     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   0.0   0.0   0.0   0.1   0.2   0.3   0.4   0.7   1.0   1.4   2.0   2.8   3.6   4.6   5.6   6.5   7.3   7.8   8.2   8.2   7.8   7.2   6.3   5.2   4.1   3.1   2.2   1.5   0.9   0.5   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 | 36.07
SL |   64.8 |     x     x     x     x   0.0     x   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.1   0.1   0.3   0.4   0.6   1.0   1.4   2.0   2.6   3.4   4.3   5.2   6.1   6.9   7.4   7.7   7.7   7.5   7.0   6.3   5.4   4.5   3.6   2.8   2.0   1.4   1.0   0.6   0.4   0.2   0.1   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 | 28.54
Cr |   37.4 |     x     x   0.0   0.0   0.0   0.0   0.0   0.1   0.1   0.2   0.3   0.6   0.9   1.3   1.9   2.7   3.5   4.4   5.3   6.2   6.9   7.4   7.7   7.7   7.4   6.9   6.2   5.3   4.4   3.6   2.7   2.0   1.5   1.0   0.7   0.4   0.3   0.2   0.1   0.0   0.0   0.0   0.0   0.0   0.0   0.0     x   0.0     x     x     x     x     x     x     x     x     x     x     x     x     x     x     x     x     x     x     x | 22.61
Br |   37.4 |     x     x   0.0   0.0   0.0   0.0   0.0   0.0   0.1   0.2   0.3   0.6   0.9   1.3   1.9   2.6   3.5   4.4   5.4   6.2   6.9   7.4   7.7   7.7   7.5   6.8   6.1   5.3   4.4   3.5   2.8   2.0   1.5   1.0   0.7   0.4   0.3   0.1   0.1   0.0   0.0   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 | 22.60
Ya |   37.4 |     x   0.0   0.0   0.0   0.0   0.0   0.0   0.1   0.1   0.2   0.3   0.6   0.9   1.3   1.9   2.7   3.5   4.4   5.4   6.2   6.9   7.4   7.7   7.7   7.4   6.9   6.1   5.3   4.4   3.5   2.8   2.1   1.5   1.0   0.7   0.4   0.3   0.2   0.1   0.0   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 | 22.60
Ha |   37.4 |     x   0.0   0.0   0.0   0.0   0.0   0.0   0.1   0.1   0.2   0.3   0.6   0.9   1.3   2.0   2.6   3.5   4.4   5.3   6.2   6.9   7.5   7.7   7.7   7.4   6.9   6.2   5.3   4.4   3.5   2.7   2.0   1.5   1.0   0.7   0.4   0.3   0.2   0.1   0.0   0.0   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 | 22.60
Da |   37.4 |     x     x   0.0   0.0   0.0   0.0   0.0   0.0   0.1   0.2   0.3   0.5   0.9   1.4   1.9   2.7   3.5   4.4   5.3   6.2   6.9   7.5   7.7   7.7   7.4   6.9   6.2   5.3   4.4   3.6   2.7   2.0   1.4   1.0   0.7   0.4   0.3   0.2   0.1   0.0   0.0   0.0   0.0   0.0   0.0   0.0     x   0.0     x     x     x     x     x     x     x     x     x     x     x     x     x     x     x     x     x     x     x | 22.60
Pr |   37.4 |     x     x     x   0.0   0.0   0.0   0.0   0.1   0.1   0.2   0.3   0.6   0.9   1.3   1.9   2.7   3.5   4.4   5.4   6.2   6.9   7.5   7.7   7.7   7.4   6.9   6.2   5.4   4.4   3.5   2.7   2.0   1.4   1.0   0.7   0.4   0.3   0.2   0.1   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0     x     x   0.0     x     x     x     x     x     x     x     x     x     x     x     x     x     x     x     x     x | 22.60
Un |   25.4 |   0.0   0.0   0.0   0.0   0.0   0.1   0.2   0.4   0.7   1.2   1.8   2.5   3.4   4.5   5.4   6.4   7.1   7.7   8.0   7.9   7.6   7.0   6.2   5.3   4.4   3.5   2.7   2.0   1.4   1.0   0.6   0.4   0.3   0.1   0.1   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0     x   0.0     x     x     x     x     x     x     x     x     x     x     x     x     x     x     x     x     x     x     x     x     x     x | 18.66
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.
Blank outcomes are impossible

Playoffs:

   |    Qu    Cg    Ck    RP    SL    Cr    Br    Ya    Ha    Da    Pr    Un |   BYE
------------------------------------------------------------------------------------
Qu |           x     x     x   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0 | 100.0
Cg |     x         0.0   0.0   0.1   0.7   0.7   0.7   0.7   0.7   0.7   1.7 |  94.2
Ck |     x   0.0         0.0   0.2   1.7   1.7   1.7   1.7   1.7   1.7   4.0 |  85.3
RP |     x   0.0   0.0         0.3   2.2   2.1   2.2   2.1   2.1   2.1   5.0 |  81.3
SL |     x   0.0   0.0   0.1         8.4   8.5   8.4   8.4   8.4   8.4  15.4 |  20.6
Cr |     x   0.0   0.1   0.1   2.0         6.9   7.0   7.0   7.0   7.0   8.9 |   3.0
Br |     x   0.0   0.0   0.1   1.9   6.9         7.0   7.0   7.0   7.0   8.8 |   3.0
Ya |     x   0.0   0.1   0.1   2.0   7.0   7.0         7.0   7.0   7.0   8.8 |   3.0
Ha |     x   0.0   0.1   0.1   1.9   7.0   7.0   7.0         7.0   7.0   8.8 |   3.0
Da |     x   0.0   0.0   0.1   2.0   7.0   7.0   7.0   7.0         7.0   8.8 |   3.0
Pr |     x   0.0   0.1   0.1   2.0   7.0   7.0   6.9   7.0   7.0         8.8 |   3.0
Un |     x   0.0   0.0   0.1   1.1   3.2   3.2   3.2   3.2   3.2   3.2       |   0.5

Hosts on the left, visitors across the top.

      KRACH |   1st    QF    SF     F
-------------------------------------
Qu |  648.1 | 100.0  99.1  84.4  67.6
Cg |  195.0 |  99.6  89.5  49.0  15.3
Ck |  146.4 |  98.6  81.6  32.1   8.8
RP |  134.5 |  98.0  78.3  27.9   7.3
SL |   64.8 |  77.5  22.0   3.9   0.7
Cr |   37.4 |  49.3   4.7   0.5   0.1
Br |   37.4 |  49.3   4.7   0.5   0.1
Ya |   37.4 |  49.4   4.7   0.5   0.1
Ha |   37.4 |  49.4   4.7   0.5   0.1
Da |   37.4 |  49.3   4.7   0.5   0.1
Pr |   37.4 |  49.4   4.7   0.4   0.1
Un |   25.4 |  30.1   1.1   0.1   0.0
0.0 means the outcome occurred, but fewer than 500 times.
x means the outcome never occurred.

[lugnut92]

Hey the ECAC season started! And fittingly, the most important thing that happened to affect the rankings was Colgate losing in OT to Western Michigan. We love October KRACH, don't we folks. Also a fun note, there was a bug in my sim where road teams that won in regulation would only earn two points. Whoops! In this very early prediction, we have an obvious top 5 that will all contend for the byes, three teams that seem destined for first round home ice, and four losers waiting to find out where they'll have to travel for the playoffs. Surely nothing will change about these tiers in the next 128 games...

Simulated Final Standings (Monte Carlo simulation of 10^99.6 possibilities; n=1,000,000):

1. Colgate
2. Clarkson
3. Quinnipiac
4. RPI
   –––––
5. Harvard
6. Brown
7. SLU
8. Cornell
   —————
9. Union
10. Yale
11. Dartmouth
12. 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.

Rank and Points breakdown:

   |  KRACH |     1     2     3     4     5     6     7     8     9    10    11    12 |Avg Rk |AvgPts
-----------------------------------------------------------------------------------------------------
Cg |  254.9 |  26.9  22.4  18.7  15.1  10.6   4.6   1.4   0.3   0.0   0.0     x     x |  2.81 | 46.89
Ck |  245.7 |  24.6  21.7  19.0  15.8  11.6   5.1   1.7   0.4   0.0   0.0   0.0     x |  2.92 | 46.51
Qu |  222.6 |  19.2  19.8  19.2  17.8  14.1   6.9   2.4   0.6   0.0   0.0   0.0     x |  3.21 | 45.51
RP |  199.7 |  17.7  19.2  19.6  18.4  14.9   7.1   2.5   0.6   0.0   0.0   0.0     x |  3.28 | 45.31
Ha |  173.6 |  10.4  14.0  17.0  19.7  20.8  11.8   4.8   1.4   0.1   0.0   0.0     x |  3.89 | 43.26
Br |   91.1 |   0.9   2.2   4.3   8.1  15.4  30.6  23.4  12.9   1.8   0.4   0.1   0.0 |  5.99 | 36.02
SL |   67.9 |   0.2   0.5   1.3   2.9   7.0  17.9  31.0  29.9   6.7   2.0   0.6   0.2 |  7.04 | 31.84
Cr |   63.0 |   0.1   0.3   0.9   2.2   5.6  15.3  28.9  34.6   8.2   2.6   0.9   0.2 |  7.25 | 30.97
Un |   22.1 |     x     x   0.0   0.0   0.0   0.3   1.5   6.6  26.1  25.3  22.1  18.2 | 10.13 | 18.53
Ya |   20.1 |     x   0.0   0.0   0.0   0.0   0.2   1.1   5.3  22.8  24.9  24.0  21.7 | 10.30 | 17.88
Da |   17.5 |     x   0.0     x   0.0   0.0   0.1   0.7   3.8  17.8  22.8  26.1  28.7 | 10.55 | 16.80
Pr |   16.1 |     x     x     x   0.0   0.0   0.1   0.7   3.4  16.5  22.0  26.3  31.0 | 10.63 | 16.50    

   |  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    45    46    47    48    49    50    51    52    53    54    55    56    57    58    59    60    61    62    63    64    65    66 |AvgPts
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Cg |  254.9 |     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   0.0   0.0   0.0   0.0   0.0   0.1   0.1   0.2   0.3   0.5   0.7   1.0   1.4   1.9   2.5   3.1   3.9   4.7   5.5   6.2   6.8   7.2   7.4   7.4   7.0   6.5   5.8   5.0   4.1   3.3   2.5   1.8   1.2   0.8   0.5   0.3   0.1   0.1   0.0   0.0   0.0   0.0 | 46.89
Ck |  245.7 |     x     x     x     x     x     x     x     x     x     x     x     x     x     x     x     x   0.0     x     x   0.0     x   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.1   0.1   0.2   0.2   0.4   0.6   0.8   1.1   1.6   2.1   2.7   3.5   4.2   5.0   5.7   6.4   7.0   7.3   7.3   7.2   6.8   6.3   5.5   4.7   3.8   3.0   2.2   1.6   1.1   0.7   0.4   0.2   0.1   0.1   0.0   0.0   0.0   0.0 | 46.51
Qu |  222.6 |     x     x     x     x     x     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   0.0   0.0   0.0   0.1   0.1   0.2   0.3   0.4   0.6   0.8   1.2   1.6   2.2   2.8   3.5   4.2   5.0   5.8   6.4   6.9   7.2   7.3   7.1   6.8   6.2   5.5   4.6   3.8   3.0   2.2   1.6   1.1   0.7   0.5   0.3   0.1   0.1   0.0   0.0   0.0   0.0   0.0 | 45.51
RP |  199.7 |                                         x     x     x     x     x     x     x     x     x     x     x     x   0.0     x     x   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.1   0.1   0.2   0.4   0.6   0.8   1.2   1.7   2.2   2.9   3.6   4.4   5.3   6.0   6.6   7.2   7.4   7.4   7.2   6.7   6.0   5.3   4.4   3.5   2.8   2.0   1.5   1.0   0.6   0.4   0.2   0.1   0.1   0.0   0.0   0.0   0.0   0.0 | 45.31
Ha |  173.6 |                       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   0.0   0.0   0.0   0.1   0.1   0.2   0.3   0.4   0.6   0.9   1.3   1.8   2.4   3.0   3.7   4.5   5.3   5.9   6.5   7.0   7.2   7.2   7.0   6.5   5.8   5.2   4.4   3.5   2.8   2.1   1.5   1.1   0.7   0.4   0.3   0.1   0.1   0.0   0.0   0.0   0.0   0.0   0.0     x | 43.26
Br |   91.1 |                       x     x     x     x     x     x     x   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.1   0.1   0.2   0.3   0.5   0.7   1.0   1.5   2.0   2.6   3.3   4.0   4.8   5.5   6.1   6.6   7.0   7.1   7.0   6.6   6.2   5.5   4.8   4.0   3.3   2.6   2.0   1.5   1.1   0.7   0.5   0.3   0.2   0.1   0.1   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0     x     x     x     x     x | 36.02
SL |   67.9 |     x     x     x     x     x     x   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.1   0.1   0.2   0.4   0.5   0.8   1.1   1.6   2.1   2.8   3.4   4.2   4.9   5.6   6.2   6.6   6.9   7.0   6.8   6.5   6.0   5.3   4.7   3.9   3.2   2.5   1.9   1.4   1.1   0.7   0.5   0.3   0.2   0.1   0.1   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0     x     x     x     x     x     x     x     x | 31.84
Cr |   63.0 |     x     x     x     x     x     x   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.1   0.1   0.2   0.3   0.5   0.8   1.1   1.5   2.1   2.7   3.4   4.1   4.8   5.6   6.1   6.6   6.9   7.0   6.9   6.5   6.0   5.4   4.7   4.0   3.2   2.6   2.0   1.5   1.1   0.8   0.5   0.3   0.2   0.1   0.1   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0     x     x     x     x     x     x     x     x | 30.97
Un |   22.1 |   0.0   0.0   0.0   0.0   0.1   0.2   0.3   0.5   0.9   1.4   2.0   2.8   3.6   4.6   5.5   6.4   7.1   7.6   7.8   7.7   7.3   6.7   6.0   5.1   4.3   3.4   2.6   2.0   1.4   1.0   0.7   0.4   0.3   0.2   0.1   0.1   0.0   0.0   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                                     | 18.53
Ya |   20.1 |   0.0   0.0   0.0   0.0   0.1   0.2   0.4   0.7   1.1   1.7   2.5   3.3   4.3   5.3   6.2   6.9   7.5   7.8   7.8   7.5   7.0   6.2   5.4   4.5   3.6   2.9   2.2   1.6   1.1   0.8   0.5   0.3   0.2   0.1   0.1   0.0   0.0   0.0   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                   | 17.88
Da |   17.5 |   0.0   0.0   0.0   0.1   0.2   0.4   0.7   1.1   1.7   2.5   3.4   4.4   5.4   6.3   7.1   7.6   7.9   7.9   7.5   6.9   6.2   5.3   4.4   3.5   2.8   2.1   1.5   1.1   0.7   0.5   0.3   0.2   0.1   0.1   0.0   0.0   0.0   0.0   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     x     x     x     x     x     x                   | 16.80
Pr |   16.1 |   0.0   0.0   0.0   0.1   0.3   0.4   0.8   1.3   2.0   2.8   3.7   4.7   5.7   6.6   7.3   7.8   7.9   7.8   7.3   6.7   5.9   5.0   4.1   3.3   2.5   1.9   1.4   1.0   0.7   0.4   0.3   0.2   0.1   0.1   0.0   0.0   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     x     x | 16.50
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.
Blank outcomes are impossible

[lugnut92]

Too many characters for one post!

Playoffs:

   |    Cg    Ck    Qu    RP    Ha    Br    SL    Cr    Un    Ya    Da    Pr |   BYE
------------------------------------------------------------------------------------
Cg |           x   0.0     x   0.0   0.0   0.1   0.1   3.4   3.9   4.6   4.9 |  83.1
Ck |     x         0.0     x   0.0   0.0   0.1   0.1   3.8   4.3   5.1   5.4 |  81.2
Qu |   0.0     x         0.0   0.0   0.0   0.1   0.2   4.9   5.5   6.5   6.8 |  76.0
RP |   0.0   0.0     x         0.0   0.0   0.1   0.2   5.3   5.7   6.7   7.1 |  74.9
Ha |     x   0.0   0.0   0.0         0.0   0.2   0.3   8.0   8.9  10.5  10.9 |  61.1
Br |   0.0   0.0   0.0   0.0   0.0         1.0   1.4  19.4  19.7  20.4  20.5 |  15.4
SL |   0.0   0.0   0.0   0.0   0.0   0.4         2.5  22.1  21.6  20.0  19.3 |   4.8
Cr |   0.0   0.0   0.0   0.0   0.0   0.4   2.1        22.3  21.5  19.4  18.8 |   3.5
Un |   0.0   0.0   0.0   0.0   0.0   0.6   2.0   2.6         1.2   1.0   0.9 |   0.0
Ya |   0.0   0.0   0.0   0.0   0.0   0.3   1.7   2.1   1.1         0.7   0.7 |   0.0
Da |   0.0   0.0   0.0   0.0   0.0   0.3   1.1   1.4   0.7   0.6         0.5 |   0.0
Pr |   0.0   0.0   0.0   0.0   0.0   0.3   1.0   1.2   0.6   0.5   0.4       |   0.0

Hosts on the left, visitors across the top.

      KRACH |   1st    QF    SF     F
-------------------------------------
Cg |  254.9 |  99.8  78.5  45.6  25.3
Ck |  245.7 |  99.7  76.8  43.6  23.7
Qu |  222.6 |  99.6  72.0  38.5  19.7
RP |  199.7 |  99.4  68.0  33.9  16.2
Ha |  173.6 |  98.9  57.6  26.2  11.6
Br |   91.1 |  92.4  21.8   6.5   2.0
SL |   67.9 |  85.5  13.1   3.1   0.8
Cr |   63.0 |  83.4  11.4   2.6   0.6
Un |   22.1 |  13.8   0.3   0.0   0.0
Ya |   20.1 |  11.5   0.2   0.0   0.0
Da |   17.5 |   8.7   0.1   0.0   0.0
Pr |   16.1 |   7.4   0.1   0.0   0.0
0.0 means the outcome occurred, but fewer than 500 times.
x means the outcome never occurred.

[lugnut92]

It was the first full twelve-game slate in 20 months, and we loved to see it. Also, those tiers changed. Whoops!

Simulated Final Standings (Monte Carlo simulation of 10^90.3 possibilities; n=1,000,000):

1. Harvard
2. Quinnipiac
3. RPI
4. SLU
   –––––
5. Clarkson
6. Colgate
7. Cornell
8. Princeton
   —————
9. Dartmouth
10. Union
11. Brown
12. Yale

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.

Rank and Points breakdown:

   |  KRACH |     1     2     3     4     5     6     7     8     9    10    11    12 |Avg Rk |AvgPts
-----------------------------------------------------------------------------------------------------
Ha |  632.2 |  81.6  15.6   2.4   0.3   0.0   0.0   0.0   0.0     x     x     x     x |  1.22 | 55.59
Qu |  292.9 |  14.9  53.9  20.5   6.9   2.5   0.9   0.3   0.1   0.0   0.0     x     x |  2.33 | 48.47
RP |  185.1 |   3.0  21.2  40.8  19.1   9.1   4.2   1.8   0.6   0.2   0.0   0.0     x |  3.34 | 43.62
SL |   97.8 |   0.3   4.0  13.6  23.0  20.6  16.3  11.3   6.7   3.1   0.9   0.1   0.0 |  5.13 | 37.44
Ck |  121.8 |   0.1   2.2   8.7  18.8  20.9  18.7  14.6   9.3   4.8   1.6   0.3   0.0 |  5.61 | 35.82
Cg |  110.4 |   0.1   1.6   6.9  14.3  18.4  19.5  17.3  12.1   6.8   2.6   0.6   0.0 |  6.01 | 34.51
Cr |   79.3 |   0.0   1.2   5.6  12.2  16.8  19.3  18.8  13.9   8.0   3.3   0.8   0.0 |  6.24 | 33.83
Pr |   48.9 |   0.0   0.2   1.1   3.4   6.7  10.9  16.6  22.4  21.9  12.9   3.9   0.1 |  7.81 | 29.03
Da |   47.1 |   0.0   0.1   0.5   1.8   4.1   7.8  13.5  21.3  26.0  17.6   7.1   0.2 |  8.32 | 27.42
Un |   31.9 |     x   0.0   0.0   0.2   0.7   1.9   4.7  10.3  20.3  36.6  23.9   1.5 |  9.60 | 22.81
Br |   23.6 |     x   0.0   0.0   0.0   0.1   0.4   1.2   3.3   9.0  23.9  57.5   4.5 | 10.45 | 18.90
Ya |    6.9 |     x     x     x     x     x     x   0.0   0.0   0.1   0.6   5.6  93.7 | 11.93 |  8.55

   |  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    45    46    47    48    49    50    51    52    53    54    55    56    57    58    59    60    61    62    63    64    65    66 |AvgPts
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Ha |  632.2 |                                                           x     x     x     x     x     x     x     x     x     x     x     x     x     x     x     x     x     x     x     x     x     x     x     x   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.1   0.1   0.2   0.3   0.5   0.8   1.3   1.9   2.7   3.6   4.8   6.0   7.2   8.3   9.1   9.6   9.4   8.8   7.7   6.2   4.7   3.2   1.9   1.0   0.5   0.1 | 55.59
Qu |  292.9 |                                         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   0.0   0.0   0.0   0.1   0.1   0.2   0.3   0.5   0.7   1.0   1.4   2.0   2.6   3.4   4.2   5.1   5.9   6.7   7.3   7.6   7.7   7.7   7.2   6.5   5.6   4.7   3.7   2.8   2.0   1.3   0.8   0.5   0.3   0.1   0.1   0.0   0.0   0.0 | 48.47
RP |  185.1 |                                                           x     x     x     x     x     x     x     x     x     x   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.1   0.1   0.2   0.4   0.6   0.9   1.3   1.8   2.5   3.2   4.1   5.1   6.0   6.8   7.5   7.8   8.0   7.8   7.3   6.6   5.7   4.6   3.7   2.8   1.9   1.3   0.9   0.5   0.3   0.2   0.1   0.0   0.0   0.0   0.0   0.0                   | 43.62
SL |   97.8 |                                   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   0.1   0.2   0.4   0.6   0.8   1.2   1.7   2.2   2.9   3.6   4.4   5.2   5.9   6.6   7.0   7.2   7.2   7.0   6.6   6.0   5.2   4.4   3.6   2.9   2.2   1.6   1.1   0.8   0.5   0.3   0.2   0.1   0.1   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0     x     x     x       | 37.44
Ck |  121.8 |           x     x     x     x     x     x     x     x     x     x   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.1   0.1   0.2   0.3   0.5   0.7   1.0   1.5   2.0   2.6   3.3   4.1   4.9   5.6   6.3   6.8   7.2   7.3   7.2   6.9   6.3   5.6   4.7   4.0   3.1   2.4   1.8   1.3   0.8   0.6   0.4   0.2   0.1   0.1   0.0   0.0   0.0   0.0   0.0   0.0     x     x     x                               | 35.82
Cg |  110.4 |     x     x     x     x     x     x     x     x   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.1   0.1   0.2   0.4   0.6   0.8   1.2   1.6   2.2   2.8   3.6   4.3   5.1   5.9   6.5   6.9   7.2   7.2   7.0   6.6   6.0   5.3   4.5   3.7   2.9   2.2   1.7   1.2   0.8   0.5   0.3   0.2   0.1   0.1   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0     x     x                               | 34.51
Cr |   79.3 |                       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   0.3   0.5   0.8   1.1   1.5   2.0   2.7   3.4   4.2   4.9   5.7   6.3   6.8   7.1   7.2   7.0   6.7   6.1   5.4   4.7   3.9   3.2   2.5   1.9   1.4   0.9   0.6   0.4   0.3   0.2   0.1   0.1   0.0   0.0   0.0   0.0   0.0   0.0   0.0     x     x     x     x     x                   | 33.83
Pr |   48.9 |                                         x   0.0   0.0   0.0   0.0   0.0   0.0   0.1   0.1   0.2   0.4   0.6   0.9   1.3   1.9   2.6   3.3   4.1   5.0   5.7   6.4   6.9   7.2   7.3   7.1   6.7   6.2   5.5   4.7   3.9   3.2   2.5   1.9   1.4   1.0   0.7   0.5   0.3   0.2   0.1   0.1   0.0   0.0   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 | 29.03
Da |   47.1 |                       x   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.1   0.2   0.3   0.4   0.7   1.1   1.6   2.2   2.9   3.7   4.6   5.4   6.2   6.9   7.2   7.5   7.4   7.1   6.6   5.9   5.1   4.3   3.4   2.7   2.0   1.5   1.0   0.7   0.5   0.3   0.2   0.1   0.1   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0     x     x     x     x     x     x                                     | 27.42
Un |   31.9 |                     0.0   0.0   0.0   0.0   0.0   0.1   0.1   0.2   0.4   0.7   1.1   1.7   2.4   3.3   4.2   5.2   6.2   7.0   7.6   7.9   7.9   7.7   7.1   6.3   5.5   4.5   3.6   2.8   2.1   1.5   1.1   0.7   0.5   0.3   0.2   0.1   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0     x   0.0     x     x     x     x     x     x     x     x     x                                                       | 22.81
Br |   23.6 |                     0.0   0.0   0.0   0.1   0.3   0.5   0.9   1.5   2.3   3.2   4.3   5.3   6.3   7.2   7.8   8.2   8.1   7.7   7.1   6.3   5.4   4.5   3.5   2.8   2.0   1.5   1.0   0.7   0.5   0.3   0.2   0.1   0.1   0.0   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                                     | 18.90
Ya |    6.9 |   0.3   1.1   2.3   4.0   6.1   8.0   9.4  10.4  10.6  10.0   9.0   7.7   6.2   4.7   3.4   2.4   1.6   1.1   0.7   0.4   0.2   0.1   0.1   0.0   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     x     x     x     x     x                                                       |  8.55
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.
Blank outcomes are impossible

Playoffs:

   |    Ha    Qu    RP    SL    Ck    Cg    Cr    Pr    Da    Un    Br    Ya |   BYE
------------------------------------------------------------------------------------
Ha |           x     x     x     x   0.0   0.0   0.0   0.0   0.0   0.0   0.0 |  99.9
Qu |     x         0.0   0.0   0.0   0.0   0.0   0.1   0.2   0.4   0.8   2.4 |  96.2
RP |     x   0.0         0.0   0.1   0.1   0.1   0.5   0.8   2.1   3.3   8.7 |  84.1
SL |     x   0.0   0.0         0.4   0.7   0.9   3.7   5.3   9.9  13.7  20.4 |  40.9
Ck |     x   0.0   0.0   0.4         0.9   1.2   5.0   6.9  12.3  16.1  20.8 |  29.8
Cg |     x   0.0   0.0   0.5   0.8         1.5   6.1   8.4  14.2  17.4  18.4 |  22.8
Cr |     x   0.0   0.0   0.5   0.8   1.3         6.7   9.7  15.1  17.8  17.0 |  19.1
Pr |     x   0.0   0.0   1.0   1.6   2.4   3.0        13.6  14.9  13.0   7.0 |   4.6
Da |     x   0.0   0.1   1.1   1.8   2.8   3.0  11.0        12.5  10.1   4.4 |   2.3
Un |     x   0.0   0.0   0.5   0.9   1.4   1.8   4.5   4.8         2.8   0.8 |   0.2
Br |     x   0.0   0.0   0.2   0.3   0.4   0.6   1.1   1.3   1.0         0.1 |   0.0
Ya |     x     x     x   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0       |     0

Hosts on the left, visitors across the top.

      KRACH |   1st    QF    SF     F
-------------------------------------
Ha |  632.2 | 100.0  97.3  81.3  60.2
Qu |  292.9 |  99.9  87.1  57.2  22.7
RP |  185.1 |  99.5  73.2  29.7   9.4
SL |   97.8 |  92.3  36.6   8.3   1.9
Ck |  121.8 |  92.4  40.6  10.4   2.8
Cg |  110.4 |  89.5  33.2   7.8   2.0
Cr |   79.3 |  82.8  21.5   4.0   0.8
Pr |   48.9 |  55.0   5.6   0.7   0.1
Da |   47.1 |  47.8   3.9   0.5   0.1
Un |   31.9 |  24.6   0.7   0.1   0.0
Br |   23.6 |  14.7   0.2   0.0   0.0
Ya |    6.9 |   1.6   0.0     x     x
0.0 means the outcome occurred, but fewer than 500 times.
x means the outcome never occurred.

[40-Year Big Red Fan]

Where do you get your KRACH ratings? Quite different from CHN: https://www.collegehockeynews.com/ratings/krach/

[lugnut92]

Where do you get your KRACH ratings? Quite different from CHN: https://www.collegehockeynews.com/ratings/krach/

I make them myself, and there are two notable differences. First is how we rectify the issue of undefeated/winless teams. CHN does it the "traditional" way, where they pretend that every team has a tie against a hypothetical average team. What I do is include the results from last season as an ever-diminishing proportion of each team's rating. Of course, that method doesn't do anything for RPI, Union, and the Ivies, so they still have the hypothetical tie, but they are the only teams with said tie. Second, I am using the .55/.45 win split for 3x3 overtime wins and losses, while I believe CHN is considering them full wins/losses. I believe that 3x3 results are largely disconnected from team strength, but they give us some information, so I'm using the split that is also used in calculating RPI.

In the end, none of this really matters, and the exact model I use my little predictions won't matter too much by the time the models are actually at all useful.

[sezenack]

I make them myself, and there are two notable differences. First is how we rectify the issue of undefeated/winless teams. CHN does it the "traditional" way, where they pretend that every team has a tie against a hypothetical average team. What I do is include the results from last season as an ever-diminishing proportion of each team's rating. Of course, that method doesn't do anything for RPI, Union, and the Ivies, so they still have the hypothetical tie, but they are the only teams with said tie. Second, I am using the .55/.45 win split for 3x3 overtime wins and losses, while I believe CHN is considering them full wins/losses. I believe that 3x3 results are largely disconnected from team strength, but they give us some information, so I'm using the split that is also used in calculating RPI.

In the end, none of this really matters, and the exact model I use my little predictions won't matter too much by the time the models are actually at all useful.

CHN is using the .55/.45 split from what I can tell because the winning % in the chart matches the Pwr winning %

[DrDemento]

I was told there would be no math.