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

  1. #21
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    Re: ECAC Byes and Home-Ice - A Mathematical Journey 2012-13

    Quote Originally Posted by DrDemento View Post
    If you follow most of the postings on any of the RPI threads you will discover that we have an incredibly intelligent group of posters who have entirely too much time on their hands.
    Engineers with time on their hands....yikes....

    Here's how I'm looking at it...since I follow Union, I look at the First Round Matchups numbers. Basically, there's a 55.6% chance that they'll finish in a spot that gives them a home playoff series and an 11.1% chance that they'll be on the road. Since that totals 66.7, then the remaining 33.3% is the chance they'll finish in the top 4. So, odds are that Union would be either home in the first round or on a bye.

    What I usually like to see is their range - what places they can finish in. As of right now, that's anywhere from 2nd to 11th...which is usually the case this time of year in this league. Because the standings are packed so tightly, it usually is best to wait until after an evening of games to see the possibilities.
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  2. #22
    The Merchant of Truth
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    Re: ECAC Byes and Home-Ice - A Mathematical Journey 2012-13

    Hey burgie12, I do hope you get well soon. In the meantime, just to keep everyone abreast of the chart, I'll give this a quick update. I'm not going to do all of the fancy math that burgie12 does, but I can at least handle this part.

    Current Standings (by Points %):
    Quinnipiac 32-40 [1]
    --- Bye Lock - 27+
    --- Home Lock - 24
    Rensselaer 21-29 [2-10]
    St. Lawrence 20-28 [2-11]
    Union 20-28 [2-11]
    Yale 19-27 [2-11]
    Dartmouth 19-27 [2-11]
    Clarkson 17-25 [2-12]
    Princeton 17-25 [2-12]
    Brown 15-23 [2-12]
    Cornell 13-21 [3-12]
    Colgate 13-21 [4-12]
    --- Bye Eligible - 20+
    Harvard 10-18 [7-12]
    --- Home Eligible - 17

    St. Lawrence beat Union on 9 February, so they currently have the advantage in the tiebreaker. The two teams will meet again on the final weekend to firm up this tiebreaker.

    Yale and Dartmouth split their series, but because Yale has more ECAC wins, they get the nod there.

    Clarkson swept the series with Princeton, so they get the nod.

    Cornell won the series over Colgate by a point total of 3-1, so Cornell gets the nod.

    Miscellaneous Links:
    TBRW's ECAC Page (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:
    ----------------------------------------------
    |              |    ||F2/22|S2/23|F3/01|S3/02|
    ----------------------------------------------
    | Quinnipiac   | QN ||  YA |  BN | @HA | @DA |
    | Yale         | YA || @QN | @PN |  CG |  CR |
    | Union        | UC || @CG | @CR |  SL |  CK |
    | Dartmouth    | DA || @CK | @SL |  PN |  QN |
    | St. Lawrence | SL ||  HA |  DA | @UC | @RP |
    | Princeton    | PN ||  BN |  YA | @DA | @HA |
    | Rensselaer   | RP || @CR | @CG |  CK |  SL |
    | Colgate      | CG ||  UC |  RP | @YA | @BN |
    | Clarkson     | CK ||  DA |  HA | @RP | @UC |
    | Brown        | BN || @PN | @QN |  CR |  CG |
    | Cornell      | CR ||  RP |  UC | @BN | @YA |
    | Harvard      | HA || @SL | @CK |  QN |  PN |
    ----------------------------------------------
    Individual Team Limits:
    Teams Losing Out (Floors)
    Quinnipiac cannot be caught; they have clinched the regular season championship.

    Rensselaer cannot be caught by Harvard, so they cannot reach 12th. With games remaining, they can't get down to 11th. To try for 10th, the one way I found is with a 5-way tie between Princeton, Union, RPI, Cornell, and Brown for 6th.

    St. Lawrence canot be caught by Harvard, so they can't go into 12th. They can go into 11th, with a five-way tie for 7th alongside Colgate, Cornell, Clarkson, and Yale.

    Union cannot be caught by Harvard, so they can't go into 12th. They can go into 11th, with a three-way tie for 9th alongside Colgate and Cornell.

    Yale and Dartmouth cannot be caught by Harvard, so they can't finish in 12th. Both may finish in sole possession of 11th.

    Any of the remaining six teams can finish in 12th place by themselves.

    Teams Winning Out (Ceilings)
    Quinnipiac cannot be caught; they have clinched the regular season championship.

    If Harvard wins out, they'll reach 18 points. The easiest way I have found for Harvard to attain 7th is if Brown beats Princeton, and then Brown is swept by Cornell and Colgate, while any games by Clarkson thru Colgate involving top 6 teams results in losses.

    Colgate cannot reach second. Even if they win out and RPI loses out, RPI still has a game against SLU, and that would pull SLU ahead of these teams. In order to get into a possible 3rd for Colgate, there has to be a 5-way tie with Clarkson, Union, SLU, and Dartmouth. However, Clarkson beats them on points between all teams affected, so 3rd is out. In fact, with that 5-way tie, Colgate would end up 6th or 7th (not going to bother figuring it out). Now to try to get them into 4th, let's have Colgate, RPI, and QPac win out, and because of the tiebreaks, SLU win out. With this, I was able to get Colgate to 4th, but also involving a five-way tie 5th between Union, Dartmouth, Clarkson, Princeton, and Yale.

    Cornell cannot reach second either, by virtue of the same reasons as Colgate. For 3rd, we get the same 5-way tie as before, only replace Colgate with Cornell. With this one, Cornell and Clarkson end up breaking from the pack in the first tie-break, they'd have the same ECAC wins, but Cornell would win the points vs. top 4 tiebreak, 4-2, so Cornell indeed can finish 3rd.

    The remaining teams can all finish by themselves in 2nd place.

    Thresholds:
    Bye Lock - Because Union, RPI, and SLU still need to play each other, 4th place cannot reach the potential of 28. I was able to get them to 27, though, and given that's the potential of 5th, 27 + tiebreak (Yale) becomes the lock.

    Bye Eligible - 20 is the bare minimum based upon the 4th place team's total; I was able to get a 4th place 5-way tie at 20.

    Home Lock - With Colgate, Cornell, Harvard, and Quinnipiac losing out, the lowest potential that is available for the remaining teams is 23 points (Brown), so we are going to make 24 points the home lock.

    Home Eligible - The base is, of course, 17, because that is where 8th place currently is. I'm able to get 17 with Clarkson alone, and Princeton with a tiebreak, so we'll label it as 17 alone at this time.
    Last edited by FlagDUDE08; 02-17-2013 at 02:22 PM.
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    Quote Originally Posted by Kepler View Post
    Just assume I'm being an idiot
    Quote Originally Posted by Foxton View Post
    Hey, you're actually correct.
    Quote Originally Posted by Rover View Post
    I'm not happy about it either, but Flag is correct (cue the Twilight Zone music!).
    Quote Originally Posted by French Rage View Post
    Ahh crap I agree exactly with what FlagDude said.
    Quote Originally Posted by jericho on rpitv's chat
    I never thought I would say this, but you are right.

  3. #23
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    Re: ECAC Byes and Home-Ice - A Mathematical Journey 2012-13

    Quote Originally Posted by DrDemento View Post
    If you follow most of the postings on any of the RPI threads you will discover that we have an incredibly intelligent group of posters who have entirely too much time on their hands.
    Really? I never noticed...
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  4. #24
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    Re: ECAC Byes and Home-Ice - A Mathematical Journey 2012-13

    Does anyone know if TBRW's ECAC page will return?

  5. #25
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    Re: ECAC Byes and Home-Ice - A Mathematical Journey 2012-13

    Quote Originally Posted by aweise View Post
    Does anyone know if TBRW's ECAC page will return?
    You'd probably get a better answer on eLynah, given it's a Cornell fan that runs it. However, considering the URL is a straight IP address and the user isn't using DNS renaming, I suspect the address changed, possibly from a server upgrade.
    It was an honor to present your colors, RPI. Let's Go 'TUTE!
    May 14th, 2011, 11:00 PM ET: 2147483647

    USCHO Poser of the Year Championships: 2011, 2012, 2013

    Quote Originally Posted by Kepler View Post
    Just assume I'm being an idiot
    Quote Originally Posted by Foxton View Post
    Hey, you're actually correct.
    Quote Originally Posted by Rover View Post
    I'm not happy about it either, but Flag is correct (cue the Twilight Zone music!).
    Quote Originally Posted by French Rage View Post
    Ahh crap I agree exactly with what FlagDude said.
    Quote Originally Posted by jericho on rpitv's chat
    I never thought I would say this, but you are right.

  6. #26
    Let's Go 'Tute! Ralph Baer's Avatar
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    Re: ECAC Byes and Home-Ice - A Mathematical Journey 2012-13

    Quote Originally Posted by FlagDUDE08 View Post
    You'd probably get a better answer on eLynah, given it's a Cornell fan that runs it. However, considering the URL is a straight IP address and the user isn't using DNS renaming, I suspect the address changed, possibly from a server upgrade.

    According to a post on this thread (scroll down to the recent posts)
    John and I are in negotiations.

  7. #27
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    Re: ECAC Byes and Home-Ice - A Mathematical Journey 2012-13

    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) and the Dutchmen (the team tied with them), so they also control their own destiny for second.

    Union cannot catch Qpac and could become unlucky enough to finish behind RPI, even if they won out, but they would free themselves of being tied with the Saints. So, they control the path towards the #3 seed.

    Yale does not play a team ahead of them in the standings throughout the rest of the season, but with the standings so tight and SLU still having to visit the Capital District, they can move themselves past St. Lawrence. However, they can't clear themselves of Dartmouth. And, that means that they only control their destiny to 5th. "But, burgie12! They win the tiebreaker against Dartmouth! Since they pass SLU, that means they get 4th, right?" Ah, but they don't win a three-way tiebreaker if we bring Union into the picture. Dartmouth wins the head-to-head tiebreaker with 5 of 8 possible points earned. The Union / Yale tiebreaker is also settled on the basis of head-to-head play with the Dutchmen having gone 1-0-1 against the Elis. If the cards fall wrong, then Yale is still stuck in the #5 seed.

    Dartmouth does play a team in front of them (St. Lawrence), which wouldn't leave the Saints with enough points to pass back the Big Green. But, RPI, Union, and Yale can still finish ahead of or tied with DC. So, they don't control anywhere ahead of 5th.

    Clarkson has a tough road to hoe with both Capital District and the Harvard / Dartmouth pair to face. That's three teams ahead of them in the standings. With every season series in their reach now at least a split, a lack of an abundance of ties, and now points against Top 4 teams, they're not going to lose any / many tiebreakers. For example, only one of Dartmouth or Princeton can now reach Clarkson's total, but it does us no good to let either of them get up to 25 points, as they'll just lose on either head-to-head (Princeton) or Record vs Top 4 (Dartmouth) criteria. Now, two of the remaining three teams (RPI, SLU, and UC) can pass the Knights while the third is stuck either tied and losing the tiebreaker or behind CCT. So, Clarkson also controls their destiny for the #5 spot.

    Princeton, however, won't have the same "good fortune" as Clarkson of facing off against the teams around them. They can still lose a large number of tiebreakers against the teams with whom they'll be battling for these spots. Luckily for the Tigers, there aren't enough points remaining to get everyone in contention (aka not Brown, Cornell, Colgate, or Harvard) up to 25, so we have to start leaving teams behind. First off is Clarkson, with the aforementioned three games against teams ahead of them in the standings. Now, RPI and Union can lose their games against St. Lawrence. That leaves just Dartmouth at Appleton this upcoming Saturday on the league schedule. Unfortunately, all that happens if we let the Big Green win that game is that we let Princeton's sweep of them come into play and start to move them up the tiebreaker ranks. So, Princeton still controls their destiny to 6th place.

    Brown, despite the fact that they're just two points behind Princeton, beat the Tigers at the beginning of the month, and still need to play Prier's players, don't control their own destiny to finish ahead of Princeton. If there is a three-way tie between Brown, Princeton, and Dartmouth for 7th place at 23 points, then Princeton would have to complete their sweep of the Big Green, forcing each team in the tie to have a 2-2-0 record (2-0-0 against one team and 0-2-0 against the other). Princeton and Dartmouth would then win the three-way tiebreaker based on ECAC wins (10-9-3 records vs Brown's 9-8-5 record), leaving the Bears stuck in 9th place. They do not control their destiny above the #9 seed.

    Only one of Brown or Colgate can catch Cornell. If it's Colgate, it becomes almost immediately impossible to find a beneficial third team so that it doesn't still end up as Cornell v Colgate in the two-way tiebreaker. So, we'll make it Brown, against whom the Big Red have hypothetically split. Now, we bring Princeton into the mix and can still keep everyone else at least 22 points and ahead of Cornell. Brown wins the head-to-head with a 3-1-0 record and then Princeton has already swept Cornell, so they'd keep them stuck down in 10th. There's no guarantee that Cornell finishes above 10th place, even if they win out.

    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.

    Harvard can only crest 18 points and despite the fact that Brown has to face each of Colgate, Cornell, and Princeton, they're each ahead enough in the standings that all four of them easily stay in front of the Crimson. At this point, Donato's charges can't destiny their way out of the basement.

    Current Mease Rankings (THETA): (by current standings)
    Code:
    -------------------------
    |     Team     |  Theta |
    -------------------------
    | Quinnipiac   |  0.867 |
    | Rensselaer   |  0.279 |
    | St. Lawrence |  0.143 |
    | Union        |  0.250 |
    | Yale         |  0.316 |
    | Dartmouth    |  0.241 |
    | Clarkson     | -0.256 |
    | Princeton    | -0.124 |
    | Brown        | -0.034 |
    | Cornell      | -0.121 |
    | Colgate      |  0.024 |
    | Harvard      | -0.304 |
    -------------------------
    
    PHI = 0.196654
    This is a simulation. It is only a simulation. It uses a retrodictive ranking system. There are more than 280 x 10^9 possibilities and there were only 45 x 10^3 simulations with no guarantee of uniqueness.

    Here are the results, organized by expected final standings...
    Mease Simulation (45,000 trials):
    Code:
    ------------------------------------------------------------------------------------------------------------
    |              |  1st |  2nd |  3rd |  4th |  5th |  6th |  7th |  8th |  9th | 10th | 11th | 12th | ExpPl |
    ------------------------------------------------------------------------------------------------------------
    | Quinnipiac   |100.0 | ---- | ---- | ---- | ---- | ---- | ---- | ---- | ---- | ---- | ---- | ---- |  1.00 |
    | Rensselaer   | ---- | 48.2 | 26.5 | 13.8 |  7.3 |  3.1 |  0.8 |  0.2 |  0.0 | XXXX | ---- | ---- |  2.94 |
    | Union        | ---- | 26.8 | 26.5 | 19.2 | 14.1 |  9.6 |  2.9 |  0.7 |  0.1 |  0.0 | XXXX | ---- |  3.65 |
    | St. Lawrence | ---- | 15.3 | 18.2 | 19.4 | 19.8 | 20.2 |  5.8 |  1.3 |  0.1 |  0.0 | XXXX | ---- |  4.35 |
    | Yale         | ---- |  3.9 | 13.7 | 25.4 | 27.0 | 19.3 |  7.5 |  2.4 |  0.6 |  0.1 | XXXX | ---- |  4.80 |
    | Dartmouth    | ---- |  5.4 | 13.5 | 17.8 | 21.2 | 23.5 | 12.3 |  5.2 |  1.1 |  0.1 | XXXX | ---- |  5.07 |
    | Princeton    | ---- |  0.1 |  0.8 |  2.6 |  6.0 | 12.1 | 28.0 | 26.1 | 20.3 |  3.6 |  0.3 |  0.0 |  7.43 |
    | Clarkson     | ---- |  0.2 |  0.8 |  1.8 |  4.2 |  9.6 | 22.9 | 30.2 | 21.3 |  7.6 |  1.5 |  0.0 |  7.74 |
    | Brown        | ---- | XXXX |  0.0 |  0.0 |  0.4 |  2.2 | 16.9 | 22.8 | 25.6 | 18.6 | 12.6 |  1.0 |  8.82 |
    | Colgate      | ---- | ---- | ---- |  0.0 |  0.0 |  0.3 |  2.0 |  7.0 | 16.5 | 31.5 | 35.5 |  7.2 | 10.12 |
    | Cornell      | ---- | ---- | XXXX | XXXX |  0.0 |  0.2 |  0.9 |  4.1 | 14.0 | 34.7 | 36.4 |  9.8 | 10.30 |
    | Harvard      | ---- | ---- | ---- | ---- | ---- | ---- |  0.0 |  0.1 |  0.3 |  3.8 | 13.8 | 82.0 | 11.77 |
    ------------------------------------------------------------------------------------------------------------
    "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 22 times or less.
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  8. #28
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    Re: ECAC Byes and Home-Ice - A Mathematical Journey 2012-13

    First-Round Match-ups:
    Code:
    ------------------------------------------------------------------------------------------
    |TEAM|  RP  |  UC  |  SL  |  YA  |  DA  |  PN  |  CK  |  BN  |  CG  |  CR  |  HA  | HOST |
    ------------------------------------------------------------------------------------------
    | RP |  XX  |  0.0 |  0.0 |  0.0 |  0.0 |  0.1 |  0.1 |  0.9 |  1.9 |  1.9 |  6.6 | 11.4 |
    | UC |  0.0 |  XX  |  0.0 |  0.0 |  0.0 |  0.3 |  0.2 |  2.5 |  5.4 |  5.9 | 13.0 | 27.3 |
    | SL |  0.0 |  0.0 |  XX  |  0.0 |  0.0 |  0.4 |  0.6 |  4.0 | 10.6 | 11.6 | 19.8 | 47.1 |
    | YA |  0.0 |  0.0 |  0.0 |  XX  |  0.0 |  0.5 |  1.8 |  5.2 | 11.9 | 12.8 | 24.0 | 56.2 |
    | DA |  0.0 |  0.0 |  0.0 |  0.0 |  XX  |  0.4 |  1.3 |  8.0 | 15.2 | 16.0 | 21.1 | 62.1 |
    | PN |  0.0 |  0.0 |  0.0 |  0.1 |  0.5 |  XX  |  8.4 | 16.8 | 19.1 | 19.3 |  7.8 | 72.1 |
    | CK |  0.0 |  0.0 |  0.1 |  0.1 |  0.2 | 11.8 |  XX  | 15.3 | 16.5 | 17.0 |  5.7 | 66.8 |
    | BN |  0.0 |  0.0 |  0.0 |  0.1 |  0.2 |  9.1 | 12.8 |  XX  |  8.7 |  9.4 |  1.9 | 42.2 |
    | CG |  0.0 |  0.0 |  0.0 |  0.2 |  0.1 |  1.1 |  3.3 |  3.7 |  XX  |  0.8 |  0.1 |  9.4 |
    | CR |  0.0 |  0.0 |  0.0 |  0.0 |  0.1 |  0.5 |  1.8 |  1.3 |  1.3 |  XX  |  0.1 |  5.2 |
    | HA |  0.0 |  0.0 |  0.0 |  0.0 |  0.0 |  0.0 |  0.0 |  0.0 |  0.0 |  0.0 |  XX  |  0.1 |
    ------------------------------------------------------------------------------------------
    |ROAD|  0.0 |  0.1 |  0.1 |  0.7 |  1.2 | 24.3 | 30.4 | 57.8 | 90.6 | 94.8 | 99.9 |      |
    ------------------------------------------------------------------------------------------
    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: (assuming that FlagDUDE did his math correctly, which I am fairly confident is a proper assumption)

    Brown:
    Code:
    |Pl\Pts|  15  |  16  |  17  |  18  |  19  |  20  |  21  |  22  |  23  |      |
    |  2nd |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
    |  3rd |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    1 |    1 |
    |  4th |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    1 |   11 |   12 |
    |  5th |    0 |    0 |    0 |    0 |    0 |    0 |   26 |   29 |  109 |  164 |
    |  6th |    0 |    0 |    0 |    0 |   11 |   39 |  448 |  257 |  219 |  974 |
    |  7th |    0 |    0 |    8 |   85 | 1570 | 2063 | 3155 |  560 |  151 | 7592 |
    |  8th |    0 |    0 |  307 | 1316 | 4816 | 2536 | 1190 |   82 |    2 |10249 |
    |  9th |    0 |  151 | 2358 | 3862 | 4244 |  804 |  120 |    0 |    0 |11539 |
    | 10th |    0 | 1037 | 4613 | 1903 |  772 |   26 |    0 |    0 |    0 | 8351 |
    | 11th | 1936 | 1602 | 1901 |  204 |   19 |    0 |    0 |    0 |    0 | 5662 |
    | 12th |  339 |  101 |   16 |    0 |    0 |    0 |    0 |    0 |    0 |  456 |
    |      | 2275 | 2891 | 9203 | 7370 |11432 | 5468 | 4939 |  929 |  493 |      |
    Clarkson:
    Code:
    |Pl\Pts|  17  |  18  |  19  |  20  |  21  |  22  |  23  |  24  |  25  |      |
    |  2nd |    0 |    0 |    0 |    0 |    0 |    0 |    2 |   19 |   67 |   88 |
    |  3rd |    0 |    0 |    0 |    0 |    0 |    3 |   81 |  150 |  112 |  346 |
    |  4th |    0 |    0 |    0 |    0 |    2 |   64 |  444 |  223 |   56 |  789 |
    |  5th |    0 |    0 |    0 |    2 |  137 |  544 | 1031 |  157 |   19 | 1890 |
    |  6th |    0 |    0 |    2 |  183 | 1566 | 1590 |  945 |   38 |    1 | 4325 |
    |  7th |    0 |   48 | 1110 | 2559 | 4957 | 1351 |  266 |    0 |    0 |10291 |
    |  8th |  219 | 1053 | 5591 | 4096 | 2456 |  154 |    1 |    0 |    0 |13570 |
    |  9th | 1659 | 2512 | 4356 |  892 |  176 |    1 |    0 |    0 |    0 | 9596 |
    | 10th | 1958 |  869 |  594 |   20 |    0 |    0 |    0 |    0 |    0 | 3441 |
    | 11th |  572 |   75 |   12 |    0 |    0 |    0 |    0 |    0 |    0 |  659 |
    | 12th |    5 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    5 |
    |      | 4413 | 4557 |11665 | 7752 | 9294 | 3707 | 2770 |  587 |  255 |      |
    Colgate:
    Code:
    |Pl\Pts|  13  |  14  |  15  |  16  |  17  |  18  |  19  |  20  |  21  |      |
    |  4th |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    1 |    1 |
    |  5th |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |   10 |   10 |
    |  6th |    0 |    0 |    0 |    0 |    0 |    0 |    2 |   19 |  135 |  156 |
    |  7th |    0 |    0 |    0 |    0 |    5 |   18 |  281 |  292 |  302 |  898 |
    |  8th |    0 |    0 |    0 |    0 |  230 |  561 | 1614 |  584 |  159 | 3148 |
    |  9th |    0 |    0 |    2 |  178 | 2293 | 2458 | 2198 |  279 |   29 | 7437 |
    | 10th |    0 |  193 | 1848 | 3455 | 6054 | 2074 |  533 |   14 |    0 |14171 |
    | 11th | 1468 | 2053 | 6597 | 3610 | 2008 |  205 |   13 |    0 |    0 |15954 |
    | 12th | 1199 |  986 |  795 |  228 |   17 |    0 |    0 |    0 |    0 | 3225 |
    |      | 2667 | 3232 | 9242 | 7471 |10607 | 5316 | 4641 | 1188 |  636 |      |
    Cornell:
    Code:
    |Pl\Pts|  13  |  14  |  15  |  16  |  17  |  18  |  19  |  20  |  21  |      |
    |  2nd |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
    |  3rd |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
    |  4th |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
    |  5th |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |   10 |   10 |
    |  6th |    0 |    0 |    0 |    0 |    0 |    0 |    1 |    8 |   59 |   68 |
    |  7th |    0 |    0 |    0 |    0 |    0 |    6 |  103 |  136 |  172 |  417 |
    |  8th |    0 |    0 |    0 |    0 |   71 |  327 |  990 |  356 |  103 | 1847 |
    |  9th |    0 |    0 |   61 |  183 | 2236 | 1901 | 1672 |  200 |   27 | 6280 |
    | 10th |  109 |  394 | 3508 | 3732 | 5549 | 1761 |  547 |   26 |    0 |15626 |
    | 11th | 1934 | 2726 | 6562 | 3403 | 1522 |  195 |   21 |    0 |    0 |16363 |
    | 12th | 1939 | 1320 |  921 |  191 |   18 |    0 |    0 |    0 |    0 | 4389 |
    |      | 3982 | 4440 |11052 | 7509 | 9396 | 4190 | 3334 |  726 |  371 |      |
    Dartmouth:
    Code:
    |Pl\Pts|  19  |  20  |  21  |  22  |  23  |  24  |  25  |  26  |  27  |      |
    |  2nd |    0 |    0 |    0 |    0 |    6 |   57 |  733 |  716 |  933 | 2445 |
    |  3rd |    0 |    0 |    0 |    0 |  122 |  928 | 3378 | 1163 |  462 | 6053 |
    |  4th |    0 |    0 |    0 |  111 | 1592 | 2705 | 3242 |  308 |   56 | 8014 |
    |  5th |    0 |    2 |   88 |  919 | 4669 | 2643 | 1166 |   28 |    4 | 9519 |
    |  6th |    1 |   50 | 1468 | 3305 | 4942 |  720 |   85 |    1 |    0 |10572 |
    |  7th |   52 |  409 | 2996 | 1511 |  562 |   10 |    0 |    0 |    0 | 5540 |
    |  8th |  450 |  737 |  998 |  133 |    8 |    0 |    0 |    0 |    0 | 2326 |
    |  9th |  299 |  145 |   56 |    0 |    0 |    0 |    0 |    0 |    0 |  500 |
    | 10th |   28 |    3 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |   31 |
    | 11th |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
    |      |  830 | 1346 | 5606 | 5979 |11901 | 7063 | 8604 | 2216 | 1455 |      |
    Harvard:
    Code:
    |Pl\Pts|  10  |  11  |  12  |  13  |  14  |  15  |  16  |  17  |  18  |      |
    |  7th |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    1 |    1 |
    |  8th |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |   27 |   27 |
    |  9th |    0 |    0 |    0 |    0 |    0 |    5 |   22 |   40 |   72 |  139 |
    | 10th |    0 |    0 |    0 |   34 |  216 |  455 |  779 |  171 |   48 | 1703 |
    | 11th |    0 |    0 |    0 |  881 | 2416 | 1628 | 1170 |  110 |    3 | 6208 |
    | 12th | 4956 | 4841 |12191 | 6779 | 6571 | 1235 |  338 |   11 |    0 |36922 |
    |      | 4956 | 4841 |12191 | 7694 | 9203 | 3323 | 2309 |  332 |  151 |      |
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  9. #29
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    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 |      |

  10. #30
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    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.

  11. #31
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    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 at 06:50 AM.
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  12. #32
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    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 at 06:54 AM.
    Go Red!!

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  13. #33
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    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.



    Quote 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.

  14. #34
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    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.

  15. #35
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    Re: ECAC Byes and Home-Ice - A Mathematical Journey 2012-13

    Quote 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.

  16. #36
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    Re: ECAC Byes and Home-Ice - A Mathematical Journey 2012-13

    Quote 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.
    YALE HOCKEY

  17. #37
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    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 at 08:39 AM. Reason: link instead of tables

  18. #38
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    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.
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  19. #39
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    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 |      |
    Go Red!!

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  20. #40
    RPI '11 Go Red!
    Join Date
    Feb 2009
    Location
    Buffalo, NY
    Posts
    6,158

    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.

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