Re: ECAC Byes and Home-Ice - A Mathematical Journey 2012-13
Current Mease Rankings (THETA):
And, here are the results, organized by expected final standings...
Mease Simulation (35,000 trials):
"XXXX" indicates that the finish is mathematically possible, but did not occur in any of the 35,000 trails. "----" indicates that it is not possible. "0.0" means that it occurred 17 times or less.
First-Round Match-ups:
The home team is listed on the left and the away team is listed on top. These matchups adds up the number of occurrences of the 5v12, 6v11, 7v10, and 8v9 matchups and lists it all in one block.
HOST (the far right column) indicates how often a team finished in Spots 5-8. ROAD (bottom row) indicates how often a team finished in Spots 9-12. The difference of 100 and the sum of HOST and ROAD indicates how often a team earned a bye and finished in the Top 4.
Current Mease Rankings (THETA):
Code:
------------------------- | Team | Theta | ------------------------- | Quinnipiac | 0.939 | | Yale | 0.459 | | Princeton | -0.023 | | Rensselaer | 0.202 | | Dartmouth | 0.284 | | St. Lawrence | 0.037 | | Union | 0.153 | | Brown | 0.056 | | Clarkson | -0.279 | | Colgate | 0.130 | | Cornell | -0.175 | | Harvard | -0.389 | ------------------------- PHI = 0.200059
Mease Simulation (35,000 trials):
Code:
------------------------------------------------------------------------------------------------------------ | | 1st | 2nd | 3rd | 4th | 5th | 6th | 7th | 8th | 9th | 10th | 11th | 12th | ExpPl | ------------------------------------------------------------------------------------------------------------ | Quinnipiac |100.0 | XXXX | ---- | ---- | ---- | ---- | ---- | ---- | ---- | ---- | ---- | ---- | 1.00 | | Yale | XXXX | 58.3 | 19.8 | 10.5 | 6.1 | 3.2 | 1.3 | 0.5 | 0.1 | 0.0 | XXXX | ---- | 2.83 | | Dartmouth | ---- | 11.5 | 24.8 | 21.2 | 16.1 | 11.7 | 7.2 | 4.4 | 2.1 | 0.9 | 0.1 | XXXX | 4.47 | | Rensselaer | ---- | 14.9 | 19.2 | 18.3 | 15.9 | 12.9 | 9.0 | 5.6 | 2.8 | 1.2 | 0.2 | XXXX | 4.64 | | Princeton | ---- | 6.6 | 13.9 | 15.5 | 16.5 | 16.0 | 13.3 | 9.5 | 6.3 | 2.4 | 0.0 | XXXX | 5.45 | | Union | ---- | 6.3 | 11.4 | 15.6 | 16.9 | 16.0 | 13.0 | 9.7 | 6.5 | 3.9 | 0.6 | XXXX | 5.63 | | St. Lawrence | ---- | 1.5 | 6.7 | 9.8 | 13.0 | 16.4 | 18.6 | 16.4 | 11.3 | 5.8 | 0.6 | 0.0 | 6.53 | | Brown | ---- | 0.5 | 2.5 | 5.2 | 8.4 | 11.6 | 16.0 | 19.8 | 19.1 | 13.6 | 3.2 | 0.0 | 7.55 | | Colgate | ---- | 0.2 | 0.9 | 1.9 | 3.7 | 6.1 | 11.2 | 17.6 | 24.0 | 26.1 | 7.7 | 0.5 | 8.54 | | Clarkson | ---- | 0.1 | 0.8 | 2.0 | 3.4 | 5.9 | 9.8 | 15.1 | 23.3 | 33.2 | 6.2 | 0.1 | 8.64 | | Cornell | ---- | XXXX | XXXX | 0.0 | 0.1 | 0.1 | 0.5 | 1.4 | 4.2 | 11.8 | 65.6 | 16.3 | 10.89 | | Harvard | ---- | ---- | ---- | ---- | XXXX | XXXX | XXXX | 0.0 | 0.2 | 1.1 | 15.7 | 83.0 | 11.82 | ------------------------------------------------------------------------------------------------------------
First-Round Match-ups:
Code:
------------------------------------------------------------------------------------------ |TEAM| YA | DA | RP | PN | UC | SL | BN | CG | CK | CR | HA | HOST | ------------------------------------------------------------------------------------------ | YA | XX | 0.1 | 0.0 | 0.0 | 0.0 | 0.2 | 0.4 | 0.6 | 0.9 | 3.4 | 5.5 | 11.2 | | DA | 0.0 | XX | 0.3 | 0.3 | 0.9 | 0.6 | 3.0 | 3.7 | 4.2 | 11.4 | 15.0 | 39.4 | | RP | 0.0 | 0.2 | XX | 0.5 | 0.6 | 1.3 | 2.4 | 5.3 | 5.4 | 12.4 | 15.3 | 43.4 | | PN | 0.0 | 0.2 | 0.5 | XX | 1.0 | 1.7 | 3.3 | 8.9 | 8.0 | 14.7 | 17.0 | 55.3 | | UC | 0.0 | 0.2 | 0.6 | 1.4 | XX | 1.7 | 4.1 | 7.7 | 8.0 | 15.4 | 16.5 | 55.6 | | SL | 0.0 | 0.5 | 0.4 | 1.1 | 1.6 | XX | 7.1 | 12.1 | 11.8 | 16.0 | 13.7 | 64.3 | | BN | 0.0 | 0.4 | 0.9 | 1.8 | 2.2 | 3.0 | XX | 12.7 | 14.0 | 11.8 | 8.9 | 55.8 | | CG | 0.1 | 0.9 | 0.7 | 1.0 | 1.9 | 2.7 | 10.8 | XX | 10.1 | 6.5 | 4.1 | 38.6 | | CK | 0.0 | 0.6 | 0.7 | 2.6 | 2.6 | 6.1 | 4.5 | 6.9 | XX | 6.4 | 3.9 | 34.3 | | CR | 0.0 | 0.1 | 0.0 | 0.0 | 0.2 | 0.4 | 0.4 | 0.5 | 0.4 | XX | 0.1 | 2.1 | | HA | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | XX | 0.0 | ------------------------------------------------------------------------------------------ |ROAD| 0.2 | 3.1 | 4.2 | 8.7 | 11.1 | 17.7 | 36.0 | 58.4 | 62.9 | 97.9 |100.0 | | ------------------------------------------------------------------------------------------
HOST (the far right column) indicates how often a team finished in Spots 5-8. ROAD (bottom row) indicates how often a team finished in Spots 9-12. The difference of 100 and the sum of HOST and ROAD indicates how often a team earned a bye and finished in the Top 4.
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