ECAC Byes and Home-Ice - A Mathematical Journey 2012-13 - USCHO.com Fan Forum

hockeyplayer1015 replied

03-02-2013, 01:52 AM
Originally posted by goblue78 View Post

Burgie: What happens in the case of a 4-way 24 point tie for places 3-6? Plus, there are also 4 possible three-way ties at 24. Which teams get the two byes?

All I know is that SLU would lose those tiebreakers. We lose on points vs top 4 to Dartmouth and Union, and it wouldn't even get that far with Yale since they beat us both games this year.

We need to win and get help from no less than 2 teams.
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goblue78 replied

03-01-2013, 11:04 PM
Re: ECAC Byes and Home-Ice - A Mathematical Journey 2012-13

Burgie: What happens in the case of a 4-way 24 point tie for places 3-6? Plus, there are also 4 possible three-way ties at 24. Which teams get the two byes?

Last edited by goblue78; 03-01-2013, 11:12 PM.
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burgie12 replied

03-01-2013, 10:28 PM
Re: ECAC Byes and Home-Ice - A Mathematical Journey 2012-13

Current Standings:
Quinnipiac 35-37 [1]
Rensselaer 25-27 [2]
--- Bye Lock - 24+
Yale 23-25 [3-6]
Dartmouth 22-24 [3-6]
Union 22-24 [3-6]
St. Lawrence 22-24 [3-6]
--- Bye Eligible - 22+
--- Home Lock - 21
Cornell 19-21 [7-10]
Clarkson 19-21 [7-10]
Brown 18-20 [7-10]
Princeton 18-20 [7-10]
--- Home Eligible - 19+
Colgate 15-17 [11-12]
Harvard 14-16 [11-12]

Dartmouth (2-1-1) wins the three-way tiebreaker with St. Lawrence (2-2-0) and Union (1-2-1).

Union wins the tiebreaker against St. Lawrence on Points vs Top 4 (3-3-2 vs 2-5-0).

Cornell wins the tiebreaker against Clarkson on Points vs Top 4 (2-4-1 vs 2-6-0).

Brown swept Princeton and holds 9th because of it.

Miscellaneous Links:
TBRW's ECAC Page (the ECAC predictors are hosted elsewhere, but the DIY PWR calculator is still on slack)
Sioux Sports' What-If Calculator (which doesn't use tiebreakers)
ECAC Tiebreakers page (which you will come to know and love)

Remaining League Schedules:

Code:

---------------------------- | | ||S3/02| ---------------------------- | Quinnipiac | QN || @DA | | Rensselaer | RP || SL | | Yale | YA || CR | | Dartmouth | DA || QN | | Union | UC || CK | | St. Lawrence | SL || @RP | | Cornell | CR || @YA | | Clarkson | CK || @UC | | Brown | BN || CG | | Princeton | PN || @HA | | Colgate | CG || @BN | | Harvard | HA || PN | ----------------------------

Destinies Controlled:
Quinnipiac and Rensselaer have guaranteed themselves first and second place finishes.

Yale controls their destiny for third.

Dartmouth, if they beat Quinnipiac Saturday night, cannot finish lower than 4th place.

Union, with a win against Clarkson, cannot finish below 5th place.

St. Lawrence cannot control their destiny above 6th place. They need help to advance.

Neither Clarkson nor Cornell control their destiny for 7th place. Either team would require the proper Top 4 teams to win the tiebreaker against the other team. They do still control their destiny for 8th place and home-ice, though.

A Brown win ensures them at least 9th place.

Princeton needs help to move up past 10th.

A win by Colgate over Brown ensures that they cannot finish in the basement, but they can't move up past 11th.

Harvard can finish in 11th, but would need help to not finish in the basement for the first time in program history.
Leave a comment:

burgie12 replied

02-28-2013, 10:02 AM

Re: ECAC Byes and Home-Ice - A Mathematical Journey 2012-13

Current Mease Rankings (THETA): (by current standings)

Code:

-------------------------
|     Team     |  Theta |
-------------------------
| Quinnipiac   |  0.860 |
| Rensselaer   |  0.254 |
| St. Lawrence |  0.143 |
| Yale         |  0.314 |
| Dartmouth    |  0.225 |
| Union        |  0.158 |
| Clarkson     | -0.224 |
| Brown        |  0.050 |
| Princeton    | -0.189 |
| Cornell      |  0.007 |
| Colgate      |  0.050 |
| Harvard      | -0.286 |
-------------------------

PHI = 0.195337

And, here are the results, organized by expected final standings...
Mease Simulation (65,000 trials):

Code:

------------------------------------------------------------------------------------------------------------
|              |  1st |  2nd |  3rd |  4th |  5th |  6th |  7th |  8th |  9th | 10th | 11th | 12th | ExpPl |
------------------------------------------------------------------------------------------------------------
| Quinnipiac   |100.0 | ---- | ---- | ---- | ---- | ---- | ---- | ---- | ---- | ---- | ---- | ---- |  1.00 |
| Rensselaer   | ---- | 71.4 | 17.0 |  8.0 |  2.6 |  1.1 | ---- | ---- | ---- | ---- | ---- | ---- |  2.45 |
| St. Lawrence | ---- | 19.5 | 22.0 | 22.4 | 16.5 | 17.4 |  2.1 | ---- | ---- | ---- | ---- | ---- |  3.97 |
| Yale         | ---- |  3.9 | 34.2 | 30.0 | 16.1 | 12.8 |  2.5 |  0.5 |  0.0 | ---- | ---- | ---- |  4.09 |
| Dartmouth    | ---- |  2.9 | 13.5 | 22.6 | 35.3 | 14.0 |  6.8 |  3.8 |  1.1 | ---- | ---- | ---- |  4.85 |
| Union        | ---- |  2.4 | 12.7 | 14.5 | 20.6 | 28.5 | 12.1 |  7.8 |  1.2 |  0.1 | ---- | ---- |  5.34 |
| Clarkson     | ---- | ---- |  0.5 |  2.4 |  6.8 | 12.6 | 20.9 | 36.6 | 15.2 |  4.5 |  0.5 | ---- |  7.47 |
| Brown        | ---- | ---- | ---- |  0.1 |  1.3 |  7.2 | 36.2 | 25.3 | 13.5 | 10.8 |  5.7 | ---- |  7.97 |
| Princeton    | ---- | ---- | ---- | ---- |  0.2 |  4.4 |  6.1 | 10.7 | 44.3 | 28.6 |  5.7 | ---- |  9.03 |
| Cornell      | ---- | ---- | ---- |  0.1 |  0.6 |  1.9 | 12.8 | 13.4 | 19.1 | 44.5 |  7.6 | ---- |  9.12 |
| Colgate      | ---- | ---- | ---- | ---- | ---- | ---- |  0.4 |  1.9 |  5.7 | 11.5 | 78.9 |  1.6 | 10.71 |
| Harvard      | ---- | ---- | ---- | ---- | ---- | ---- | ---- | ---- | ---- | ---- |  1.6 | 98.4 | 11.98 |
------------------------------------------------------------------------------------------------------------

"XXXX" indicates that the finish is mathematically possible, but did not occur in any of the 45,000 trails. "----" indicates that it is not possible. "0.0" means that it occurred 32 times or less.

I'm not sure how it happened, but the tiebreakers glitched a couple times and Yale ended up in 9th three times. They can't finish in 9th. I don't know how/why it happened.

First-Round Match-ups:

Code:

---------------------------------------------------------------------
|TEAM|  DA  |  UC  |  CK  |  BN  |  PN  |  CR  |  CG  |  HA  | HOST |
---------------------------------------------------------------------
| RP |  0.0 |  0.0 |  0.0 |  0.0 |  0.0 |  0.1 |  1.0 |  2.6 |  3.7 |
| SL |  0.0 |  0.0 |  0.0 |  0.9 |  1.6 |  2.2 | 14.7 | 16.6 | 36.1 |
| YA |  0.0 |  0.0 |  0.4 |  1.8 |  3.7 |  1.7 |  8.4 | 16.0 | 31.9 |
| DA |  XX  |  0.6 |  1.9 |  3.2 |  1.1 |  5.4 | 12.9 | 34.9 | 59.9 |
| UC |  0.0 |  XX  |  0.1 |  4.9 |  8.9 |  8.7 | 25.6 | 20.9 | 69.0 |
| CK |  0.0 |  0.0 |  XX  |  7.6 | 33.0 | 15.6 | 13.9 |  6.8 | 76.9 |
| BN |  0.0 |  0.1 |  7.7 |  XX  | 21.6 | 28.1 | 11.0 |  1.5 | 70.0 |
| PN |  0.7 |  0.1 |  3.6 |  2.7 |  XX  |  9.2 |  4.8 |  0.2 | 21.4 |
| CR |  0.3 |  0.5 |  5.1 |  8.3 |  8.5 |  XX  |  5.3 |  0.7 | 28.7 |
| CG |  0.0 |  0.0 |  1.3 |  0.6 |  0.2 |  0.2 |  XX  |  0.0 |  2.3 |
---------------------------------------------------------------------
|ROAD|  1.1 |  1.3 | 20.2 | 29.9 | 78.6 | 71.2 | 97.7 |100.0 |      |
---------------------------------------------------------------------

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.

Point / Place Distribution Tables:
Brown:

Code:

|Pl\Pts|  18  |  19  |  20  |  21  |  22  |      |
|  4th |    0 |    0 |    0 |    0 |   39 |   39 |
|  5th |    0 |    0 |    0 |  116 |  725 |  841 |
|  6th |    0 |    0 |    0 |  879 | 3779 | 4658 |
|  7th |    0 | 1168 | 9260 | 6050 | 7071 |23549 |
|  8th |    0 | 2843 |11659 | 1448 |  500 |16450 |
|  9th | 2174 | 2879 | 3647 |   49 |    0 | 8749 |
| 10th | 5456 | 1263 |  305 |    0 |    0 | 7024 |
| 11th | 3540 |  150 |    0 |    0 |    0 | 3690 |
|      |11170 | 8303 |24871 | 8542 |12114 |      |

Clarkson:

Code:

|Pl\Pts|  19  |  20  |  21  |  22  |  23  |      |
|  3rd |    0 |    0 |    0 |   27 |  318 |  345 |
|  4th |    0 |    0 |   24 |  300 | 1234 | 1558 |
|  5th |    0 |    0 |  567 | 1444 | 2384 | 4395 |
|  6th |    0 |    0 | 5102 | 2483 |  633 | 8218 |
|  7th |  802 | 1761 |10396 |  652 |    0 |13611 |
|  8th |10884 | 7116 | 5689 |   84 |    0 |23773 |
|  9th | 8000 | 1855 |    0 |    0 |    0 | 9855 |
| 10th | 2795 |  119 |    0 |    0 |    0 | 2914 |
| 11th |  331 |    0 |    0 |    0 |    0 |  331 |
|      |22812 |10851 |21778 | 4990 | 4569 |      |

Colgate:

Code:

|Pl\Pts|  15  |  16  |  17  |  18  |  19  |      |
|  7th |    0 |    0 |    0 |    0 |  241 |  241 |
|  8th |    0 |    0 |    0 |    0 | 1263 | 1263 |
|  9th |    0 |    0 |    0 |  737 | 2962 | 3699 |
| 10th |    0 |    0 |    0 | 3588 | 3893 | 7481 |
| 11th |13837 | 9219 |24718 | 3032 |  495 |51301 |
| 12th |  677 |  338 |    0 |    0 |    0 | 1015 |
|      |14514 | 9557 |24718 | 7357 | 8854 |      |

Cornell:

Code:

|Pl\Pts|  17  |  18  |  19  |  20  |  21  |      |
|  4th |    0 |    0 |    0 |    0 |   36 |   36 |
|  5th |    0 |    0 |    0 |    0 |  407 |  407 |
|  6th |    0 |    0 |    0 |    0 | 1204 | 1204 |
|  7th |    0 |    0 |  628 | 2403 | 5317 | 8348 |
|  8th |    0 |    0 | 4651 | 3033 | 1034 | 8718 |
|  9th |    0 | 1903 | 9127 | 1289 |   98 |12417 |
| 10th |11755 | 6723 |10161 |  294 |    0 |28933 |
| 11th | 3853 |  982 |  102 |    0 |    0 | 4937 |
|      |15608 | 9608 |24669 | 7019 | 8096 |      |

Dartmouth:

Code:

|Pl\Pts|  21  |  22  |  23  |  24  |  25  |      |
|  2nd |    0 |    0 |    0 |  214 | 1660 | 1874 |
|  3rd |    0 |   30 | 1478 | 3002 | 4263 | 8773 |
|  4th |   27 |  996 | 9134 | 2743 | 1788 |14688 |
|  5th |  643 | 4692 |16701 |  727 |  195 |22958 |
|  6th | 3477 | 2519 | 3129 |    0 |    0 | 9125 |
|  7th | 4344 |   45 |    0 |    0 |    0 | 4389 |
|  8th | 2492 |    0 |    0 |    0 |    0 | 2492 |
|  9th |  701 |    0 |    0 |    0 |    0 |  701 |
|      |11684 | 8282 |30442 | 6686 | 7906 |      |

Harvard:

Code:

|Pl\Pts|  12  |  13  |  14  |  15  |  16  |      |
| 11th |    0 |    0 |    0 |  193 |  822 | 1015 |
| 12th |25033 |10774 |24026 | 2698 | 1454 |63985 |
|      |25033 |10774 |24026 | 2891 | 2276 |      |

Princeton:

Code:

|Pl\Pts|  17  |  18  |  19  |  20  |  21  |      |
|  5th |    0 |    0 |    0 |    0 |  114 |  114 |
|  6th |    0 |    0 |    0 |    0 | 2884 | 2884 |
|  7th |    0 |    0 |  258 |  588 | 3145 | 3991 |
|  8th |    0 |    0 | 2483 | 2738 | 1715 | 6936 |
|  9th | 2708 | 3347 |19043 | 3290 |  379 |28767 |
| 10th | 9275 | 5153 | 3908 |  246 |    0 |18582 |
| 11th | 2830 |  836 |   60 |    0 |    0 | 3726 |
|      |14813 | 9336 |25752 | 6862 | 8237 |      |

Quinnipiac:

Code:

|Pl\Pts|  35  |  36  |  37  |  38  |  39  |      |
|  1st | 1219 | 1787 |15612 |10364 |36018 |65000 |
|      | 1219 | 1787 |15612 |10364 |36018 |      |

Rensselaer:

Code:

|Pl\Pts|  23  |  24  |  25  |  26  |  27  |      |
|  2nd |    0 |  759 |16799 |10420 |18417 |46395 |
|  3rd | 1410 | 2891 | 6731 |    0 |    0 |11032 |
|  4th | 2749 | 1916 |  516 |    0 |    0 | 5181 |
|  5th | 1367 |  303 |    0 |    0 |    0 | 1670 |
|  6th |  722 |    0 |    0 |    0 |    0 |  722 |
|      | 6248 | 5869 |24046 |10420 |18417 |      |

St. Lawrence:

Code:

|Pl\Pts|  22  |  23  |  24  |  25  |  26  |      |
|  2nd |    0 |    0 |  840 | 1615 |10198 |12653 |
|  3rd |    0 |  306 | 9793 | 4227 |    0 |14326 |
|  4th |  167 | 2207 |10320 | 1892 |    0 |14586 |
|  5th | 2717 | 4440 | 3401 |  195 |    0 |10753 |
|  6th | 8661 | 2132 |  502 |    0 |    0 |11295 |
|  7th | 1387 |    0 |    0 |    0 |    0 | 1387 |
|      |12932 | 9085 |24856 | 7929 |10198 |      |

Union:

Code:

|Pl\Pts|  20  |  21  |  22  |  23  |  24  |      |
|  2nd |    0 |    0 |    0 |    0 | 1559 | 1559 |
|  3rd |    0 |    0 |   77 |  740 | 7470 | 8287 |
|  4th |    0 |    7 | 1370 | 2387 | 5640 | 9404 |
|  5th |    0 |  119 | 7781 | 4131 | 1386 |13417 |
|  6th |    0 | 1703 |14197 | 2649 |    0 |18549 |
|  7th | 3092 | 3414 | 1339 |    0 |    0 | 7845 |
|  8th | 3830 | 1234 |    0 |    0 |    0 | 5064 |
|  9th |  673 |  136 |    0 |    0 |    0 |  809 |
| 10th |   66 |    0 |    0 |    0 |    0 |   66 |
|      | 7661 | 6613 |24764 | 9907 |16055 |      |

Yale:

Code:

|Pl\Pts|  21  |  22  |  23  |  24  |  25  |      |
|  2nd |    0 |    0 |    0 |  204 | 2315 | 2519 |
|  3rd |    0 |   23 | 2674 | 4959 |14581 |22237 |
|  4th |   48 |  641 |12387 | 4652 | 1780 |19508 |
|  5th |  745 | 2358 | 6625 |  717 |    0 |10445 |
|  6th | 3792 | 2958 | 1595 |    0 |    0 | 8345 |
|  7th | 1475 |  164 |    0 |    0 |    0 | 1639 |
|  8th |  304 |    0 |    0 |    0 |    0 |  304 |
|  9th |    3 |    0 |    0 |    0 |    0 |    3 |
|      | 6367 | 6144 |23281 |10532 |18676 |      |

Leave a comment:

burgie12 replied

02-27-2013, 11:07 AM
Re: ECAC Byes and Home-Ice - A Mathematical Journey 2012-13

Current Standings (but not really):
Quinnipiac 35-39 [1]
--- Bye Lock - 25+
Rensselaer 23-27 [2-6]
St. Lawrence 22-26 [2-7]
Yale 21-25 [2-8]
--- Home Lock - 21+
Dartmouth 21-25 [2-9]
Union 20-24 [2-10]
Clarkson 19-23 [3-11]
Brown 18-22 [4-11]
Cornell 17-21 [4-11]*
--- Bye Eligible - 21+
Princeton 17-21 [5-11]*
Colgate 15-19 [7-12]
--- Home Eligible - 19
Harvard 10-16 [11-12]

Yale and Dartmouth split the season series. Yale leads the tiebreaker on ECAC wins. (If the tiebreaker stays as just a two-way tie, Yale will win if it's decided by ECAC wins and will lose otherwise.)

Princeton swept Cornell and is in 9th place because of it, but is not bye eligible, while Cornell is, so they had to be swapped in the table above.

Miscellaneous Links:
TBRW's ECAC Page (the ECAC predictors are hosted elsewhere, but the DIY PWR calculator is still on slack)
Sioux Sports' What-If Calculator (which doesn't use tiebreakers)
ECAC Tiebreakers page (which you will come to know and love)

Remaining League Schedules:

Code:

---------------------------------- | | ||F3/01|S3/02| ---------------------------------- | Quinnipiac | QN || @HA | @DA | | Rensselaer | RP || CK | SL | | St. Lawrence | SL || @UC | @RP | | Yale | YA || CG | CR | | Dartmouth | DA || PN | QN | | Union | UC || SL | CK | | Clarkson | CK || @RP | @UC | | Brown | BN || CR | CG | | Princeton | PN || @DA | @HA | | Cornell | CR || @BN | @YA | | Colgate | CG || @YA | @BN | | Harvard | HA || QN | PN | ----------------------------------

Destinies Controlled:
Quinnipiac has guaranteed themselves a first-place finish.

Rensselaer, currently alone in second place, controls their destiny for second.

St. Lawrence has to face the Engineers (the team ahead of them), so they also control their own destiny for second.

Yale's ceiling of 25 points can be passed by either RPI or SLU, but not both, forcing the other to still be tied with the Bulldogs. RPI's sweep of Yale makes that an easy choice to keep Yale down. Alternatively, it could be a three- or four-way tie involving Dartmouth and/or SLU, but I still can't find a way for Yale to finish below 4th place if they win out.

A three-way tie between Dartmouth, RPI, and Yale at 25 points (with SLU at 26), results in the Engineers winning the head-to-head criteria based on their sweep of the Bulldogs and Yale winning the two-way tiebreaker based on ECAC wins (12-9-1 vs 11-8-3). So, Dartmouth could win out and still have to host a playoff series next weekend by finishing in the #5 seed.

Union's loss to Cornell on Saturday hurt them pretty bad. If they sweep this weekend, then it is still possible for SLU to tie them (beating RPI in their only remaining game), RPI to finish ahead of the Dutchmen (beating Clarkson in their only remaining game), and SLU to win the tiebreaker. But, SLU only wins that tiebreaker if Dartmouth is a Top 4 team and Yale isn't. So, the options to leave Union in 5th are to have both Dartmouth and Yale pass the Dutchmen or have SLU finish tied and have only the Big Green pass by.

If Clarkson reaches their ceiling of 23 points, then they cannot be caught by Union, but every other team in front of them would still be able to simultaneously catch / pass the Knights. Therefore, Clarkson doesn't control their destiny anywhere above 6th place.

Brown does not face anyone in front of them during the last weekend of the regular season. So, the only difficulty lies in getting both Clarkson and Union past the Bears. Since Union won the season series, it's easiest to let Clarkson win out and have Union win their game against SLU on Friday to have them finish in a tie with Brown. Union wins the tiebreaker and proves that Brown doesn't control their own destiny above 8th.

If Princeton wins out, they can only be caught by one of Brown or Cornell, but not both simultaneously. Since Princeton swept Cornell, it's better to allow Brown to finish at / above 21 points and keep the Tigers sequestered to 9th place.

If Cornell wins out, they guarantee finishing ahead of Brown, but can't shake Princeton and would lose that tiebreaker. So, Cornell also controls their own destiny to 9th place.

Colgate can win out and still finish in 11th place. Winning out would guarantee them a sweep of Brown, but Brown would have had the chance on Friday against Cornell to put some distance between themselves and the Raiders so that they couldn't be caught on Saturday. Then, it falls to Cornell to beat Yale on Saturday to also end up at 19 points. Then, as long as Clarkson earns at least a point in the Capital District, then it's just a two-way tie between the travel partners and Colgate lost the season series and ends up in 11th.

Harvard can't control their way out of 12th place, unfortunately.
Leave a comment:
burgie12 replied

02-26-2013, 09:12 PM
Re: ECAC Byes and Home-Ice - A Mathematical Journey 2012-13

Is anyone else having some serious formatting issues?

For example, the "Legend" cuts off very early for me. And then there are some blocks where it will try and show the "How" section, but that will delete the whole "winning" section, which destroys the whole purpose of posting these tiebreakers.

Edit: Since the tiebreakers are illegible for me on USCHO, I'm just going to provide a direct link to the text document where I have all of the tiebreakers laid out with their explanations. Next year, I'll do it in an Excel spreadsheet or something and fancy it up a bit. I promise I'm not giving you a virus.

Anyways, the MEASE Simulation is running on one of my computers, so I'll be able to post some simulation results tomorrow.

Controlled destinies and such should be up by the end of the night, but if they're not, they'll be up early tomorrow.

Happy reading, burgie12

Last edited by burgie12; 02-27-2013, 08:39 AM. Reason: link instead of tables
Leave a comment:
LTsatch replied

02-24-2013, 05:36 PM
Re: ECAC Byes and Home-Ice - A Mathematical Journey 2012-13

Originally posted by burgie12 View Post

slapschotts posted an excellent ranging summary on his we blog (web log? web blog? w eblog?) last night / this morning, meaning that I may omit some of the explanations when I post my summary later.

I will try and delve deeper into the controlling of destinies, paths to a bye / home-ice, a simulation or five, and may even put up one of my famous / infamous tiebreaker posts.

I hope everyone's been enjoying the posts so far. I'll try to keep everyone entertained.

Please do! The ECAC is a mess this year.
Leave a comment:
burgie12 replied

02-24-2013, 07:35 AM
Re: ECAC Byes and Home-Ice - A Mathematical Journey 2012-13

Originally posted by yaledoc View Post

Burgie 12;

This post, and the one immediately before it, are things of beauty.......and I mean that sincerely. If I read your signature correctly, you have NOT been to The Whale; if and when you get there (glancing at the standings, it looks HIGHLY unlikely THIS year), and it is a weekend that I am there, drinks at Mory's are on me. All the best, Doc.

I appreciate the kudos, doc.

Glancing at my broken femur, I find it even less likely that I'll be making my way out to Connecticut from Buffalo during the remainder of this season.

I enjoy these posts / threads, that's why I keep doing it.

Hopefully, we'll be able to meet up at the Whale sometime. Best of luck to the Elis.
Leave a comment:
burgie12 replied

02-24-2013, 07:31 AM
Re: ECAC Byes and Home-Ice - A Mathematical Journey 2012-13

slapschotts posted an excellent ranging summary on his we blog (web log? web blog? w eblog?) last night / this morning, meaning that I may omit some of the explanations when I post my summary later.

I will try and delve deeper into the controlling of destinies, paths to a bye / home-ice, a simulation or five, and may even put up one of my famous / infamous tiebreaker posts.

I hope everyone's been enjoying the posts so far. I'll try to keep everyone entertained.
Leave a comment:
yaledoc replied

02-23-2013, 02:06 PM
Re: ECAC Byes and Home-Ice - A Mathematical Journey 2012-13

Burgie 12;

This post, and the one immediately before it, are things of beauty.......and I mean that sincerely. If I read your signature correctly, you have NOT been to The Whale; if and when you get there (glancing at the standings, it looks HIGHLY unlikely THIS year), and it is a weekend that I am there, drinks at Mory's are on me. All the best, Doc.

Originally posted by burgie12 View Post

Destinies Controlled:
Quinnipiac has guaranteed themselves a first-place finish.

St. Lawrence, currently alone in second place, controls their destiny for second.

Rensselaer has to face the Saints (the team ahead of them), so they also control their own destiny for second.

Union, if they beat St. Lawrence, can either finish tied with St. Lawrence (with the tiebreaker going down to Record vs Top X) or behind Rensselaer. Either way, Union does not control their destiny above third.

Yale's ceiling of 25 points can be beaten by two of Rensselaer / St. Lawrence / Union and tied by the other. If RPI ends up tied with Yale, then the Elis lose the tiebreaker (since they got swept by the Engineers) and can't guarantee themselves a finish above 5th.

Dartmouth, despite the fact that they face SLU tonight and SLU has to face the Capital District next weekend, also doesn't control above the #5 seed. If SLU beats both RPI and Union, they end up at 26. If RPI beats Colgate and Clarkson, they end up at 25. The Dartmouth / RPI tiebreaker would go to Record vs Top X, which the Big Green would win 6 points to 5. But, we can also let Yale sweep without having an effect on any already "completed" games. That would let the Engineers win the three-way tiebreaker and Yale / Dartmouth would be broken by ECAC wins (Yale has 12 while Dartmouth has 11). So, there you go, DC doesn't control above 5th.

Clarkson's sweep of their remaining games would push them up to 25 points, leaving Union with a ceiling of 24 points and RPI with a ceiling of 25. If RPI beats SLU, then the Saints' new ceiling is 26, but since Union can't catch the Knights anymore anyways, we can let St. Lawrence win that matchup anyways. That doesn't let Dartmouth catch the men of Potsdam anymore, but doesn't affect Yale's ceiling. So, it's a three-way tie between Clarkson, RPI, and Yale. Rensselaer wins the head-to-head tiebreaker with a 3-1-0 record. Yale wins the tiebreaker against Clarkson on ECAC wins. So, the Knights can win out and still not control their fate above the #5 seed.

If Brown wins out, then the only teams that can't catch the Bears are Colgate, Cornell, and Harvard. It can be arranged to be a five-way tie between Brown, Dartmouth, Princeton, Rensselaer, and Yale for 5th. RPI would win the head-to-head tiebreaker. With the Engineers out of the way, everyone else went 0.500 in the head-to-head games. Yale's 11-10-1 record gives them the tiebreaker win on ECAC wins. Brown, Dartmouth, and Princeton also split against each other (2-2-0 each), dropping Brown from the tiebreaker because they have a 9-8-5 record while the other two have 10-9-3 records. Therefore, Brown could win out, but lose that tiebreaker and finish 9th.

Since we just established that the Brown / Princeton / Dartmouth tiebreaker breaks against Brown, it's also worth noting that it breaks in Princeton's favor. Since there's no point in letting Dartmouth get up to 23 points (since that would just add the Tiger's sweep into their head-to-head comparisons), that lets us push each of the North Country / Capital District teams above 23, not just some of them. It's now a three-way tie between Brown, Princeton, and Yale for 6th place at 23 points. Brown's sweep of Princeton now comes in handy, giving them the head-to-head comparison. Yale and Princeton split (each team won at home), so Yale's lack of ties wins them the tiebreakers. Princeton is not guaranteed a spot above 8th, even if they win out.

Just like heading into yesterday, only one of Brown or Colgate can catch Cornell. Since Brown split with Cornell while Cornell won the season series against Colgate, we let the Bears win their head-to-head against the Raiders. Then, to stop the tiebreaker from going to ECAC wins (which Cornell would win), we keep Princeton back at 21 points, too. Brown wins the three-way (3-1-0) and then Princeton's sweep of the Big Red keeps Cornell back in 10th place.

Again, it's only one of Brown or Cornell that can catch Colgate. With Cornell having won the season series during the home-and-home in November, it's a pretty easy choice. The Big Red can pretty easily keep the Raiders sequestered to 10th or worse, even if they win out. If that looks familiar, it should.

Harvard can't control their way out of 12th place, unfortunately.

For those of you looking for a simulation, I was happy I could stay up to the conclusion of the ECAC games; there's no way I was going to stay up after the west-coast games to change the Mease rankings to run the simulation. There will be simulations run for / during the week to give some potential finishes after the last twelve games.
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burgie12 replied

02-23-2013, 06:48 AM
Re: ECAC Byes and Home-Ice - A Mathematical Journey 2012-13

Destinies Controlled:
Quinnipiac has guaranteed themselves a first-place finish.

St. Lawrence, currently alone in second place, controls their destiny for second.

Rensselaer has to face the Saints (the team ahead of them), so they also control their own destiny for second.

Union, if they beat St. Lawrence, can either finish tied with St. Lawrence (with the tiebreaker going down to Record vs Top X) or behind Rensselaer. Either way, Union does not control their destiny above third.

Yale's ceiling of 25 points can be beaten by two of Rensselaer / St. Lawrence / Union and tied by the other. If RPI ends up tied with Yale, then the Elis lose the tiebreaker (since they got swept by the Engineers) and can't guarantee themselves a finish above 5th.

Dartmouth, despite the fact that they face SLU tonight and SLU has to face the Capital District next weekend, also doesn't control above the #5 seed. If SLU beats both RPI and Union, they end up at 26. If RPI beats Colgate and Clarkson, they end up at 25. The Dartmouth / RPI tiebreaker would go to Record vs Top X, which the Big Green would win 6 points to 5. But, we can also let Yale sweep without having an effect on any already "completed" games. That would let the Engineers win the three-way tiebreaker and Yale / Dartmouth would be broken by ECAC wins (Yale has 12 while Dartmouth has 11). So, there you go, DC doesn't control above 5th.

Clarkson's sweep of their remaining games would push them up to 25 points, leaving Union with a ceiling of 24 points and RPI with a ceiling of 25. If RPI beats SLU, then the Saints' new ceiling is 26, but since Union can't catch the Knights anymore anyways, we can let St. Lawrence win that matchup anyways. That doesn't let Dartmouth catch the men of Potsdam anymore, but doesn't affect Yale's ceiling. So, it's a three-way tie between Clarkson, RPI, and Yale. Rensselaer wins the head-to-head tiebreaker with a 3-1-0 record. Yale wins the tiebreaker against Clarkson on ECAC wins. So, the Knights can win out and still not control their fate above the #5 seed.

If Brown wins out, then the only teams that can't catch the Bears are Colgate, Cornell, and Harvard. It can be arranged to be a five-way tie between Brown, Dartmouth, Princeton, Rensselaer, and Yale for 5th. RPI would win the head-to-head tiebreaker. With the Engineers out of the way, everyone else went 0.500 in the head-to-head games. Yale's 11-10-1 record gives them the tiebreaker win on ECAC wins. Brown, Dartmouth, and Princeton also split against each other (2-2-0 each), dropping Brown from the tiebreaker because they have a 9-8-5 record while the other two have 10-9-3 records. Therefore, Brown could win out, but lose that tiebreaker and finish 9th.

Since we just established that the Brown / Princeton / Dartmouth tiebreaker breaks against Brown, it's also worth noting that it breaks in Princeton's favor. Since there's no point in letting Dartmouth get up to 23 points (since that would just add the Tiger's sweep into their head-to-head comparisons), that lets us push each of the North Country / Capital District teams above 23, not just some of them. It's now a three-way tie between Brown, Princeton, and Yale for 6th place at 23 points. Brown's sweep of Princeton now comes in handy, giving them the head-to-head comparison. Yale and Princeton split (each team won at home), so Yale's lack of ties wins them the tiebreakers. Princeton is not guaranteed a spot above 8th, even if they win out.

Just like heading into yesterday, only one of Brown or Colgate can catch Cornell. Since Brown split with Cornell while Cornell won the season series against Colgate, we let the Bears win their head-to-head against the Raiders. Then, to stop the tiebreaker from going to ECAC wins (which Cornell would win), we keep Princeton back at 21 points, too. Brown wins the three-way (3-1-0) and then Princeton's sweep of the Big Red keeps Cornell back in 10th place.

Again, it's only one of Brown or Cornell that can catch Colgate. With Cornell having won the season series during the home-and-home in November, it's a pretty easy choice. The Big Red can pretty easily keep the Raiders sequestered to 10th or worse, even if they win out. If that looks familiar, it should.

Harvard can't control their way out of 12th place, unfortunately.

For those of you looking for a simulation, I was happy I could stay up to the conclusion of the ECAC games; there's no way I was going to stay up after the west-coast games to change the Mease rankings to run the simulation. There will be simulations run for / during the week to give some potential finishes after the last twelve games.

Last edited by burgie12; 02-23-2013, 06:54 AM.
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burgie12 replied

02-23-2013, 06:47 AM
Re: ECAC Byes and Home-Ice - A Mathematical Journey 2012-13

Current Standings (by Points ):
Quinnipiac 34-40 [1]
--- Bye Lock - 25+
--- Home Lock - 23+
St. Lawrence 22-28 [2-9]
Rensselaer 21-27 [2-9]
Union 20-26 [2-11]
Yale 19-25 [1-11]
Dartmouth 19-25 [2-11]
Clarkson 19-25 [2-11]
Brown 17-23 [2-11]
Princeton 17-23 [2-11]
Cornell 15-21 [4-12]
Colgate 15-21 [4-12]
--- Bye Eligible - 21+
--- Home Eligible - 17+
Harvard 10-16 [10-12]

Yale wins the three-way tiebreaker based on ECAC wins. Each of the Bulldogs, Big Green, and Knights have split their respective season series. Yale's 9-9-1 record gives them 5th over Dartmouth's and Clarkson's 8-8-3 records.

Dartmouth and Clarkson have to go down to Record vs Top 8 to determine 6th place. They split the season series, have identical records, and identical 2-3-1 records against teams in the Top 4. Dartmouth has a 6-5-1 record against Top 8 teams while Clarkson has a 3-7-2 record.

Brown completed their sweep of Princeton last night and hold 8th place because of it.

Miscellaneous Links:
TBRW's ECAC Page (still... currently down)
Sioux Sports' What-If Calculator (which doesn't use tiebreakers)
ECAC Tiebreakers page (which you will come to know and love)

Remaining League Schedules:

Code:

---------------------------------------- | | ||S2/23|F3/01|S3/02| ---------------------------------------- | Quinnipiac | QN || BN | @HA | @DA | | St. Lawrence | SL || DA | @UC | @RP | | Rensselaer | RP || @CG | CK | SL | | Union | UC || @CR | SL | CK | | Yale | YA || @PN | CG | CR | | Dartmouth | DA || @SL | PN | QN | | Clarkson | CK || HA | @RP | @UC | | Brown | BN || @QN | CR | CG | | Princeton | PN || YA | @DA | @HA | | Cornell | CR || UC | @BN | @YA | | Colgate | CG || RP | @YA | @BN | | Harvard | HA || @CK | QN | PN | ----------------------------------------

Individual Team Limits:
Teams Losing Out (Floors)
Quinnipiac has clinched 1st place.

St. Lawrence cannot be caught by Cornell, Colgate, or Harvard. Anyone else can catch and pass the Saints, even simultaneously.

There aren't enough points left to push everybody past Rensselaer, so we have to leave at least one of Cornell and Colgate behind the Engineers. If we leave the Big Red back, we can make a four-way tie for 7th with Brown, Colgate, and Princeton where RPI would eventually finish in third, leaving them in 9th.

Union can be passed by everyone down to a three-way tie between Cornell, Colgate, and themselves. The Big Red already beat Colgate and would have swept the Dutchmen, so they'd finish 9th. The tiebreaker for 10th would go down to Record vs Top X. If the teams are adjusted properly (for example, not RPI or Princeton), then the Dutchmen will lose the tiebreaker and finish in 11th.

Each of Yale, Dartmouth, Clarkson, Brown, and Princeton (the remaining teams with more points than Harvard's maximum) can be passed by everybody else to finish by themselves in 11th.

Cornell, Colgate, and Harvard can each finish by themselves in 12th.

Teams Winning Out (Ceilings)
Harvard can catch the Central New York pair and nobody else, so their ceiling is pretty easy to figure out. If you need it spelled out for you, it's 10th.

Due to the North Country and Capital District pairs having to face off next weekend, two teams (in addition to Quinnipiac) need to finish ahead of Cornell or Colgate, meaning that they each have a ceiling of 4th place. There would have to be a three-way tie, but it's pretty easy to find teams where the Raiders and Big Red can win (for example: Union, Yale).

Princeton's ceiling of 23 points could leave them in a three-way tie for 2nd with two of the North Country / Capital District teams, with just the Bobcats ahead of them. If the games fall correctly, then Princeton, SLU and RPI each end up with a 1-1-2 head-to-head record and Princeton's 10-9-3 record would beat the hypothetical 9-8-5 records of the Engineers and Saints.

Brown is in the same situation (obviously, since they have the same number of points). If we leave Princeton at 23 to allow Brown's sweep to boost their head-to-head score and make the two North Country / Capital District teams at 23 points Clarkson and St. Lawrence (instead of RPI and SLU), then Brown and Clarkson win the four-way tie having won 8 points in the six head-to-head games. Brown won the season series against Clarkson (they won in Potsdam and tied in Providence), so the Bears can also win the tiebreaker to finish in 2nd.

Each of the teams in between 2nd and 7th (inclusive) can finish by themselves in 2nd.

Thresholds:
Bye Lock - If Yale wins out, it doesn't hurt the potential of any of the Top 4 teams. With SLU having to face both RPI and Union, we'll let each team win their game tonight and then let Clarkson lose both of their games next weekend. That leaves SLU and Union at 24 points each and RPI at 25. There is some set of game results between these three teams so that one team remains tied with Yale while the other two finish at 26 points. So, it's 25 plus tiebreakers to guarantee yourselves a tie resulting in a weekend off.

Bye Eligible - If we let SLU and RPI win out, then Union (20 points) and Clarkson (19 points) still need to face each other, meaning that 21 points (plus tiebreakers) would be the minimum for 4th place. Hey, look at that, that's the same thing that was decided in the Cornell / Colgate winning out scenarios.

Home Lock - With Colgate, Cornell, and Harvard, losing out, we can let everyone coalesce around 23 points. Yes, each of Brown, Princeton, Dartmouth, and Yale can simultaneously finish at 23 points. And, then, it's really pretty easy to let the North Country / Capital District teams finish with at least 23. So, it's 23 plus tiebreakers to earn another pair of home-ice games after the season is over.

Home Eligible - If Brown and Princeton lose out, then Cornell and Colgate each earn a win over the Bears and sit at 17 points. If they also lose out, then it's a 4-way tie for 8th place (Princeton wins the first tiebreaker at 4-2-0, Brown loses the three-way tiebreaker, and Cornell wins the head-to-head tiebreaker against Colgate so it would break PN/CR/CG/BN) with the Crimson stuck in 12th. So, it takes 17 points plus the proper tiebreakers to be eligible for two more home games.
Last edited by burgie12; 02-23-2013, 06:50 AM.
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QUAlum2004 replied

02-22-2013, 10:20 PM
Re: ECAC Byes and Home-Ice - A Mathematical Journey 2012-13

Unbelievable that Clarkson is a point out of a bye in the 1st round round and they are 9-15-7 on the season.
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burgie12 replied

02-21-2013, 10:17 PM

Re: ECAC Byes and Home-Ice - A Mathematical Journey 2012-13

Princeton:

Code:

|Pl\Pts|  17  |  18  |  19  |  20  |  21  |  22  |  23  |  24  |  25  |      |
|  2nd |    0 |    0 |    0 |    0 |    0 |    0 |    2 |    4 |   54 |   60 |
|  3rd |    0 |    0 |    0 |    0 |    0 |    0 |   40 |  104 |  234 |  378 |
|  4th |    0 |    0 |    0 |    0 |    0 |   17 |  455 |  429 |  276 | 1177 |
|  5th |    0 |    0 |    0 |    0 |   66 |  437 | 1669 |  461 |   66 | 2699 |
|  6th |    0 |    0 |    0 |   55 | 1184 | 2095 | 1959 |  135 |    6 | 5434 |
|  7th |    0 |   35 |  818 | 2642 | 6115 | 2449 |  543 |    4 |    0 |12606 |
|  8th |   67 |  575 | 3847 | 3697 | 3243 |  283 |   14 |    0 |    0 |11726 |
|  9th | 1430 | 2049 | 4247 | 1097 |  307 |    2 |    0 |    0 |    0 | 9132 |
| 10th |  882 |  460 |  274 |   13 |    2 |    0 |    0 |    0 |    0 | 1631 |
| 11th |  135 |   17 |    2 |    0 |    0 |    0 |    0 |    0 |    0 |  154 |
| 12th |    3 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    3 |
|      | 2517 | 3136 | 9188 | 7504 |10917 | 5283 | 4682 | 1137 |  636 |      |

Quinnipiac:

Code:

|Pl\Pts|  32  |  33  |  34  |  35  |  36  |  37  |  38  |  39  |  40  |      |
|  1st |   19 |   71 |  616 | 1159 | 4626 | 5434 |13228 | 7671 |12176 |45000 |
|      |   19 |   71 |  616 | 1159 | 4626 | 5434 |13228 | 7671 |12176 |      |

Rensselaer:

Code:

|Pl\Pts|  21  |  22  |  23  |  24  |  25  |  26  |  27  |  28  |  29  |      |
|  2nd |    0 |    0 |    2 |   84 | 1611 | 3306 | 8504 | 4063 | 4123 |21693 |
|  3rd |    0 |    2 |  135 |  901 | 4692 | 3503 | 2321 |  389 |    0 |11943 |
|  4th |    0 |   31 |  823 | 1793 | 2710 |  782 |   84 |    0 |    0 | 6223 |
|  5th |   10 |  185 | 1344 | 1198 |  503 |   35 |    0 |    0 |    0 | 3275 |
|  6th |  108 |  351 |  738 |  178 |   25 |    1 |    0 |    0 |    0 | 1401 |
|  7th |  131 |  148 |   85 |    3 |    0 |    0 |    0 |    0 |    0 |  367 |
|  8th |   78 |   14 |    1 |    0 |    0 |    0 |    0 |    0 |    0 |   93 |
|  9th |    5 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    5 |
| 10th |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|      |  332 |  731 | 3128 | 4157 | 9541 | 7627 |10909 | 4452 | 4123 |      |

St. Lawrence:

Code:

|Pl\Pts|  20  |  21  |  22  |  23  |  24  |  25  |  26  |  27  |  28  |      |
|  2nd |    0 |    0 |    0 |    0 |  110 |  551 | 3130 | 1585 | 1488 | 6864 |
|  3rd |    0 |    0 |    1 |   86 | 1634 | 2534 | 3382 |  535 |    0 | 8172 |
|  4th |    0 |    0 |  105 |  832 | 4540 | 2620 |  601 |   15 |    0 | 8713 |
|  5th |    1 |   39 | 1177 | 2725 | 4032 |  880 |   74 |    1 |    0 | 8929 |
|  6th |  195 |  842 | 4236 | 2683 | 1056 |   60 |    2 |    0 |    0 | 9074 |
|  7th |  557 |  761 | 1095 |  181 |    2 |    0 |    0 |    0 |    0 | 2596 |
|  8th |  377 |  172 |   51 |    2 |    0 |    0 |    0 |    0 |    0 |  602 |
|  9th |   44 |    4 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |   48 |
| 10th |    2 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    2 |
| 11th |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|      | 1176 | 1818 | 6665 | 6509 |11374 | 6645 | 7189 | 2136 | 1488 |      |

Union:

Code:

|Pl\Pts|  20  |  21  |  22  |  23  |  24  |  25  |  26  |  27  |  28  |      |
|  2nd |    0 |    0 |    0 |    1 |  144 | 1044 | 4167 | 3308 | 3417 |12081 |
|  3rd |    0 |    0 |    4 |  122 | 1678 | 3448 | 5331 | 1000 |  343 |11926 |
|  4th |    0 |    0 |   92 |  824 | 4102 | 2467 | 1142 |   31 |    0 | 8658 |
|  5th |    1 |   21 |  772 | 1946 | 2975 |  561 |   81 |    0 |    0 | 6357 |
|  6th |   30 |  234 | 1918 | 1295 |  780 |   44 |    2 |    0 |    0 | 4303 |
|  7th |  169 |  410 |  636 |  106 |    5 |    0 |    0 |    0 |    0 | 1326 |
|  8th |  158 |  106 |   46 |    6 |    0 |    0 |    0 |    0 |    0 |  316 |
|  9th |   26 |    6 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |   32 |
| 10th |    1 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    1 |
| 11th |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|      |  385 |  777 | 3468 | 4300 | 9684 | 7564 |10723 | 4339 | 3760 |      |

Yale:

Code:

|Pl\Pts|  19  |  20  |  21  |  22  |  23  |  24  |  25  |  26  |  27  |      |
|  2nd |    0 |    0 |    0 |    0 |    0 |   37 |  404 |  470 |  858 | 1769 |
|  3rd |    0 |    0 |    0 |    2 |  126 |  783 | 2950 | 1360 |  960 | 6181 |
|  4th |    0 |    0 |    5 |  119 | 2138 | 3458 | 4801 |  742 |  150 |11413 |
|  5th |    0 |    1 |  302 | 1601 | 6041 | 2852 | 1292 |   58 |    0 |12147 |
|  6th |    0 |  120 | 2088 | 2976 | 3036 |  428 |   45 |    0 |    0 | 8693 |
|  7th |  102 |  492 | 1967 |  667 |  137 |    1 |    0 |    0 |    0 | 3366 |
|  8th |  296 |  393 |  374 |   30 |    3 |    0 |    0 |    0 |    0 | 1096 |
|  9th |  213 |   58 |   21 |    0 |    0 |    0 |    0 |    0 |    0 |  292 |
| 10th |   42 |    1 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |   43 |
| 11th |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|      |  653 | 1065 | 4757 | 5395 |11481 | 7559 | 9492 | 2630 | 1968 |      |

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ECAC Byes and Home-Ice - A Mathematical Journey 2012-13

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