Announcement

Collapse
No announcement yet.

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

Collapse
X
 
  • Filter
  • Time
  • Show
Clear All
new posts

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

    Current Mease Rankings (THETA):
    Code:
    -------------------------
    |     Team     |  Theta |
    -------------------------
    | Quinnipiac   |  0.939 |
    | Yale         |  0.459 |
    | Princeton    | -0.023 |
    | Rensselaer   |  0.202 |
    | Dartmouth    |  0.284 |
    | St. Lawrence |  0.037 |
    | Union        |  0.153 |
    | Brown        |  0.056 |
    | Clarkson     | -0.279 |
    | Colgate      |  0.130 |
    | Cornell      | -0.175 |
    | Harvard      | -0.389 |
    -------------------------
    
    PHI = 0.200059
    And, here are the results, organized by expected final standings...
    Mease Simulation (35,000 trials):
    Code:
    ------------------------------------------------------------------------------------------------------------
    |              |  1st |  2nd |  3rd |  4th |  5th |  6th |  7th |  8th |  9th | 10th | 11th | 12th | ExpPl |
    ------------------------------------------------------------------------------------------------------------
    | Quinnipiac   |100.0 | XXXX | ---- | ---- | ---- | ---- | ---- | ---- | ---- | ---- | ---- | ---- |  1.00 |
    | Yale         | XXXX | 58.3 | 19.8 | 10.5 |  6.1 |  3.2 |  1.3 |  0.5 |  0.1 |  0.0 | XXXX | ---- |  2.83 |
    | Dartmouth    | ---- | 11.5 | 24.8 | 21.2 | 16.1 | 11.7 |  7.2 |  4.4 |  2.1 |  0.9 |  0.1 | XXXX |  4.47 |
    | Rensselaer   | ---- | 14.9 | 19.2 | 18.3 | 15.9 | 12.9 |  9.0 |  5.6 |  2.8 |  1.2 |  0.2 | XXXX |  4.64 |
    | Princeton    | ---- |  6.6 | 13.9 | 15.5 | 16.5 | 16.0 | 13.3 |  9.5 |  6.3 |  2.4 |  0.0 | XXXX |  5.45 |
    | Union        | ---- |  6.3 | 11.4 | 15.6 | 16.9 | 16.0 | 13.0 |  9.7 |  6.5 |  3.9 |  0.6 | XXXX |  5.63 |
    | St. Lawrence | ---- |  1.5 |  6.7 |  9.8 | 13.0 | 16.4 | 18.6 | 16.4 | 11.3 |  5.8 |  0.6 |  0.0 |  6.53 |
    | Brown        | ---- |  0.5 |  2.5 |  5.2 |  8.4 | 11.6 | 16.0 | 19.8 | 19.1 | 13.6 |  3.2 |  0.0 |  7.55 |
    | Colgate      | ---- |  0.2 |  0.9 |  1.9 |  3.7 |  6.1 | 11.2 | 17.6 | 24.0 | 26.1 |  7.7 |  0.5 |  8.54 |
    | Clarkson     | ---- |  0.1 |  0.8 |  2.0 |  3.4 |  5.9 |  9.8 | 15.1 | 23.3 | 33.2 |  6.2 |  0.1 |  8.64 |
    | Cornell      | ---- | XXXX | XXXX |  0.0 |  0.1 |  0.1 |  0.5 |  1.4 |  4.2 | 11.8 | 65.6 | 16.3 | 10.89 |
    | Harvard      | ---- | ---- | ---- | ---- | XXXX | XXXX | XXXX |  0.0 |  0.2 |  1.1 | 15.7 | 83.0 | 11.82 |
    ------------------------------------------------------------------------------------------------------------
    "XXXX" indicates that the finish is mathematically possible, but did not occur in any of the 35,000 trails. "----" indicates that it is not possible. "0.0" means that it occurred 17 times or less.

    First-Round Match-ups:
    Code:
    ------------------------------------------------------------------------------------------
    |TEAM|  YA  |  DA  |  RP  |  PN  |  UC  |  SL  |  BN  |  CG  |  CK  |  CR  |  HA  | HOST |
    ------------------------------------------------------------------------------------------
    | YA |  XX  |  0.1 |  0.0 |  0.0 |  0.0 |  0.2 |  0.4 |  0.6 |  0.9 |  3.4 |  5.5 | 11.2 |
    | DA |  0.0 |  XX  |  0.3 |  0.3 |  0.9 |  0.6 |  3.0 |  3.7 |  4.2 | 11.4 | 15.0 | 39.4 |
    | RP |  0.0 |  0.2 |  XX  |  0.5 |  0.6 |  1.3 |  2.4 |  5.3 |  5.4 | 12.4 | 15.3 | 43.4 |
    | PN |  0.0 |  0.2 |  0.5 |  XX  |  1.0 |  1.7 |  3.3 |  8.9 |  8.0 | 14.7 | 17.0 | 55.3 |
    | UC |  0.0 |  0.2 |  0.6 |  1.4 |  XX  |  1.7 |  4.1 |  7.7 |  8.0 | 15.4 | 16.5 | 55.6 |
    | SL |  0.0 |  0.5 |  0.4 |  1.1 |  1.6 |  XX  |  7.1 | 12.1 | 11.8 | 16.0 | 13.7 | 64.3 |
    | BN |  0.0 |  0.4 |  0.9 |  1.8 |  2.2 |  3.0 |  XX  | 12.7 | 14.0 | 11.8 |  8.9 | 55.8 |
    | CG |  0.1 |  0.9 |  0.7 |  1.0 |  1.9 |  2.7 | 10.8 |  XX  | 10.1 |  6.5 |  4.1 | 38.6 |
    | CK |  0.0 |  0.6 |  0.7 |  2.6 |  2.6 |  6.1 |  4.5 |  6.9 |  XX  |  6.4 |  3.9 | 34.3 |
    | CR |  0.0 |  0.1 |  0.0 |  0.0 |  0.2 |  0.4 |  0.4 |  0.5 |  0.4 |  XX  |  0.1 |  2.1 |
    | HA |  0.0 |  0.0 |  0.0 |  0.0 |  0.0 |  0.0 |  0.0 |  0.0 |  0.0 |  0.0 |  XX  |  0.0 |
    ------------------------------------------------------------------------------------------
    |ROAD|  0.2 |  3.1 |  4.2 |  8.7 | 11.1 | 17.7 | 36.0 | 58.4 | 62.9 | 97.9 |100.0 |      |
    ------------------------------------------------------------------------------------------
    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.
    Go Red!!

    National Champions: 1954, 1985, 201x

    Houston Field House, Cheel Arena, Agganis Arena, Magness Arena, Ritter Arena, Messa Rink, Matthews Arena, Von Braun Center, Lynah Rink, Starr Rink, Appleton Arena, Dwyer Arena, Buffalo State Ice Arena, Kelley Rink (also Verizon Center (DC), Herb Brooks Arena, Fenway Park (Frozen Fenway I), Times Union Center, DCU Center, Blue Cross Arena)

    Comment


    • #17
      Re: ECAC Byes and Home-Ice - A Mathematical Journey 2012-13

      I hope you derive a lot of enjoyment and personal satisfaction from performing these calculations....reminds me of quantum mechanics class in college. you calculate all these probabilities, and then "boom" they all crystallize into one and only one actuality.
      "Hope is a good thing; maybe the best of things."

      "Beer is a sign that God loves us and wants us to be happy." -- Benjamin Franklin

      "Being Irish, he had an abiding sense of tragedy, which sustained him through temporary periods of joy." -- W. B. Yeats

      "People generally are most impatient with those flaws in others about which they are most ashamed of in themselves." - folk wisdom

      Comment


      • #18
        Re: ECAC Byes and Home-Ice - A Mathematical Journey 2012-13

        My head is spinning. I think i will just wait and see how it all turns out after 6 more games.
        Take the shortest distance to the puck and arrive in ill humor

        Comment


        • #19
          Re: ECAC Byes and Home-Ice - A Mathematical Journey 2012-13

          Originally posted by DrDemento View Post
          My head is spinning. I think i will just wait and see how it all turns out after 6 more games.

          I know, right? I am suffering from GEEK OVERLOAD. But I respect the enthusiasm and effort.

          Comment


          • #20
            Re: ECAC Byes and Home-Ice - A Mathematical Journey 2012-13

            Originally posted by DarthBruno View Post
            I know, right? I am suffering from GEEK OVERLOAD. But I respect the enthusiasm and effort.
            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.
            Take the shortest distance to the puck and arrive in ill humor

            Comment


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

              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.
              Union Hockey

              2014 National Champions!!!!

              Comment


              • #22
                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, 01:22 PM.

                Comment


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

                  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...
                  Quinnipiac Bobcats
                  2023 National Champions
                  ECAC Regular Season Champions: 2012-13, 2014-15, 2015-16, 2018-19, 2020-21, 2021-22, 2022-23, 2023-24
                  ECAC Tournament Champions: 2016
                  East Regional: 2013 (Champions), 2014, 2016 (Champions), 2023 (Champions)
                  Northeast Regional:

                  West Regional: 2015, 2021
                  Midwest Regional: 2019, 2022
                  Frozen Four: 2013, 2016, 2023 (Champions)

                  Pass complete. Lipkin has a man in front! Shot... SCORE!!!

                  Comment


                  • #24
                    Re: ECAC Byes and Home-Ice - A Mathematical Journey 2012-13

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

                    2014 National Champions!!!!

                    Comment


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

                      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.

                      Comment


                      • #26
                        Re: ECAC Byes and Home-Ice - A Mathematical Journey 2012-13

                        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.
                        sigpic

                        Let's Go 'Tute!

                        Maxed out at 2,147,483,647 at 10:00 AM EDT 9/17/07.

                        2012 Poser Of The Year

                        Comment


                        • #27
                          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.
                          Go Red!!

                          National Champions: 1954, 1985, 201x

                          Houston Field House, Cheel Arena, Agganis Arena, Magness Arena, Ritter Arena, Messa Rink, Matthews Arena, Von Braun Center, Lynah Rink, Starr Rink, Appleton Arena, Dwyer Arena, Buffalo State Ice Arena, Kelley Rink (also Verizon Center (DC), Herb Brooks Arena, Fenway Park (Frozen Fenway I), Times Union Center, DCU Center, Blue Cross Arena)

                          Comment


                          • #28
                            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 |      |
                            Go Red!!

                            National Champions: 1954, 1985, 201x

                            Houston Field House, Cheel Arena, Agganis Arena, Magness Arena, Ritter Arena, Messa Rink, Matthews Arena, Von Braun Center, Lynah Rink, Starr Rink, Appleton Arena, Dwyer Arena, Buffalo State Ice Arena, Kelley Rink (also Verizon Center (DC), Herb Brooks Arena, Fenway Park (Frozen Fenway I), Times Union Center, DCU Center, Blue Cross Arena)

                            Comment


                            • #29
                              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 |      |
                              Go Red!!

                              National Champions: 1954, 1985, 201x

                              Houston Field House, Cheel Arena, Agganis Arena, Magness Arena, Ritter Arena, Messa Rink, Matthews Arena, Von Braun Center, Lynah Rink, Starr Rink, Appleton Arena, Dwyer Arena, Buffalo State Ice Arena, Kelley Rink (also Verizon Center (DC), Herb Brooks Arena, Fenway Park (Frozen Fenway I), Times Union Center, DCU Center, Blue Cross Arena)

                              Comment


                              • #30
                                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.
                                QUINNIPIAC UNIVERSITY BOBCATS


                                ECAC Regular Season Champions
                                2013, 2015, 2016, 2019

                                ECAC Tournament Champions
                                2016

                                NCAA Tournament
                                2002, 2013, 2014, 2015, 2016, 2019

                                NCAA Frozen Four
                                2013, 2016

                                https://www.bobcatshockeyblog.com/
                                https://***********/QHockeyBlog
                                https://www.instagram.com/bobcatshockeyblog/
                                https://www.facebook.com/QHockeyBlog/

                                Comment

                                Working...
                                X