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ECAC Byes and Home-Ice 2011-12

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  • burgie12
    replied
    Re: ECAC Byes and Home-Ice 2011-12

    Good luck to all in the final weekend.

    Both semis have pretty clear favorites while the potential Saturday match-ups are a little closer.

    Code:
    -----------------------------------------------------------------
    | # |   Team  | Final |  Win  \  2nd  |||Consol |  3rd  \  4th  |
    -----------------------------------------------------------------
    | 1 | Union   | 66.61 | 39.85 \ 26.76 ||| 33.39 | 20.42 \ 12.97 |
    | 2 | Cornell | 58.32 | 28.70 \ 29.62 ||| 41.68 | 22.87 \ 18.80 |
    | 3 | Harvard | 41.68 | 17.14 \ 24.54 ||| 58.32 | 27.25 \ 31.08 |
    | 4 | Colgate | 33.39 | 14.31 \ 19.08 ||| 66.61 | 39.46 \ 37.15 |
    -----------------------------------------------------------------

    Leave a comment:


  • burgie12
    replied
    Re: ECAC Byes and Home-Ice 2011-12

    Updates going into Game 3 of the Quarters with KRACH values that include all of Saturday's results. Colgate is actually favored over Quinnipiac now, so extra good luck to both teams.

    Oh, and another disclaimer about the spreadsheet. I'm assuming that there's no tie in the consolation game. That's not true, but, oh well.

    Code:
    ---------------------------------------------------------------------------------
    | # | Team         |   1st  |Quarter |  Semi  | Final |  Win  |||Consol |  3rd  |
    ---------------------------------------------------------------------------------
    | 1 | Union        |   Bye  | 100.00 | 100.00 | 69.94 | 42.29 ||| 30.06 | 18.79 |
    | 2 | Cornell      |   Bye  | 100.00 | 100.00 | 60.42 | 29.99 ||| 39.58 | 22.94 |
    | 3 | Harvard      |   Bye  | 100.00 |  58.67 | 23.79 |  9.57 ||| 34.88 | 16.27 |
    | 4 | Colgate      |   Bye  | 100.00 |  50.23 | 17.48 |  7.10 ||| 32.75 | 15.14 |
    | 5 | Quinnipiac   | 100.00 | 100.00 |  49.77 | 17.22 |  6.95 ||| 32.55 | 14.97 |
    | 6 | Yale         | 100.00 | 100.00 |  41.33 | 11.16 |  4.10 ||| 30.18 | 12.90 |
    | 7 | Clarkson     | 100.00 |   0.00 |   0.00 |  0.00 |  0.00 |||  0.00 |  0.00 |
    | 8 | St. Lawrence | 100.00 |   0.00 |   0.00 |  0.00 |  0.00 |||  0.00 |  0.00 |
    | 9 | Dartmouth    | 100.00 | 100.00 |   0.00 |  0.00 |  0.00 |||  0.00 |  0.00 |
    |10 | Rensselaer   | 100.00 | 100.00 |   0.00 |  0.00 |  0.00 |||  0.00 |  0.00 |
    |11 | Princeton    | 100.00 |   0.00 |   0.00 |  0.00 |  0.00 |||  0.00 |  0.00 |
    |12 | Brown        | 100.00 |   0.00 |   0.00 |  0.00 |  0.00 |||  0.00 |  0.00 |
    ---------------------------------------------------------------------------------
    |   |              |    8   |    8   |    4   |   2   |   1   |||   2   |   1   |
    ---------------------------------------------------------------------------------

    Leave a comment:


  • burgie12
    replied
    Originally posted by goblue78 View Post
    One more suggestion, inspired by last night. Add another switch that will allow you recalculate after the first game, and, if needed, second game of a 2-out-of-three...
    It's on my wish-list. If next weekend was another 2-of-3 series then I would definitely finish it up this weekend or early next week. Since it's not, I'll probably focus on adjusting this for the NCAA Tournament and deal with making this spreadsheet capable of recalculating in the middle of a weekend (along with the changes I want to make to the floor/ceiling script) during the off-season.

    Leave a comment:


  • goblue78
    replied
    Re: ECAC Byes and Home-Ice 2011-12

    One more suggestion, inspired by last night. Add another switch that will allow you recalculate after the first game, and, if needed, second game of a 2-out-of-three, so that the team up 1-0 has a probability of p+(1-p)p of moving on (where p is its probability of winning one game), while the team down 0-1 is (1-p)^2 to advance, or, in the latter case, turns the series into a one-game advancement.

    Leave a comment:


  • goblue78
    replied
    Re: ECAC Byes and Home-Ice 2011-12

    Nicely done, and well organized. As you can tell, organization is not my strong point.

    Leave a comment:


  • burgie12
    replied
    Re: ECAC Byes and Home-Ice 2011-12

    Alright, so I lied when I said I knew why I wasn't getting the percentages that I was expecting. I completely remade my spreadsheet, using goblue's as a starting point and it has been re-uploaded and is now fantastically more accurate. It also should be easier to use and follow. It's been completely remade, but still has the same file name, so it has the same download link.

    A quick tutorial for those looking to give it a whirl: You can adjust the KRACH values to any positive value that you wish. Percentages will auto-update (unless you have turned off automatic calculations). There is a dropdown box for each team so you can specify when they are eliminated. I've tried to make it intelligent, but I didn't try too hard. So, you can't tell it that five teams lost in the 1st Round because it knows that there were only 4 series. But, you could tell it that both #8 SLU and #9 Dartmouth were eliminated in the 1st Round and it would never stop you, but then all of the percentages / odds in the rest of the spreadsheet will go to 0.

    If you leave the macros disabled, it will be unable to do that double-checking and there will be some other unintentional mishaps, but no different than telling it that both #8 and #9 lost in the 1st Round.

    CAUTION! Choosing an option in the dropdown box will cause the document to go through most (nearly all) of the worksheets and hide all of the non-important rows / columns (basically, anything where the odds are 0). This is a very slow macro (it took about 1.5 minutes when I ran it just before I uploaded it). So, if you're going to go through and make wholesale changes to who survived what round just to screw around and see what happens, you should probably disable macros first.

    Anyways, here's a reminder on "your team's" odds going into the weekend using KRACH values that are current as of last night's PC-UML game.

    Code:
    --------------------------------------------------------------------------------
    | # | Team         |   1st  |Quarter | Semi  | Final |  Win  |||Consol |  3rd  |
    --------------------------------------------------------------------------------
    | 1 | Union        |   Bye  | 100.00 | 90.22 | 63.04 | 38.84 ||| 27.18 | 16.94 |
    | 2 | Cornell      |   Bye  | 100.00 | 77.58 | 46.48 | 23.46 ||| 31.09 | 17.56 |
    | 3 | Harvard      |   Bye  | 100.00 | 64.30 | 29.70 | 12.84 ||| 34.60 | 17.32 |
    | 4 | Colgate      |   Bye  | 100.00 | 49.81 | 20.21 |  8.56 ||| 29.60 | 14.37 |
    | 5 | Quinnipiac   | 100.00 | 100.00 | 50.19 | 20.42 |  8.68 ||| 29.77 | 14.49 |
    | 6 | Yale         | 100.00 | 100.00 | 35.70 | 11.63 |  4.33 ||| 24.06 | 10.07 |
    | 7 | Clarkson     | 100.00 |   0.00 |  0.00 |  0.00 |  0.00 |||  0.00 |  0.00 |
    | 8 | St. Lawrence | 100.00 |   0.00 |  0.00 |  0.00 |  0.00 |||  0.00 |  0.00 |
    | 9 | Dartmouth    | 100.00 | 100.00 | 22.42 |  6.01 |  2.44 ||| 16.41 |  6.78 |
    |10 | Rensselaer   | 100.00 | 100.00 |  9.78 |  2.49 |  0.84 |||  7.29 |  2.47 |
    |11 | Princeton    | 100.00 |   0.00 |  0.00 |  0.00 |  0.00 |||  0.00 |  0.00 |
    |12 | Brown        | 100.00 |   0.00 |  0.00 |  0.00 |  0.00 |||  0.00 |  0.00 |
    --------------------------------------------------------------------------------
    |   |              |    8   |    8   |   4   |   2   |   1   |||   2   |   1   |
    --------------------------------------------------------------------------------
    Last edited by burgie12; 03-09-2012, 10:56 PM.

    Leave a comment:


  • burgie12
    replied
    Re: ECAC Byes and Home-Ice 2011-12

    Originally posted by goblue78 View Post
    OK, I've done my own (somewhat brute force) spreadsheet which gets every number right (I think). I think it's easier to use than yours because all you have to do is change the KRACH numbers and the whole spreadsheet updates without any macros or sorting. So, when a team is eliminated, all you have to do is set their KRACH to 0. Let me know what people think.
    That's pretty kick-*****. I got lost somewhere in the middle, but I'll look at it again later when my head stops spinning.

    Sad note of the day: Despite the fact that I use VLOOKUP quite often, I didn't know about the existence of the HLOOKUP formula.

    But, seriously, thank you for the spreadsheet. I will probably steal it for next season.

    Leave a comment:


  • goblue78
    replied
    Re: ECAC Byes and Home-Ice 2011-12

    OK, I've done my own (somewhat brute force) spreadsheet which gets every number right (I think). I think it's easier to use than yours because all you have to do is change the KRACH numbers and the whole spreadsheet updates without any macros or sorting. So, when a team is eliminated, all you have to do is set their KRACH to 0. Let me know what people think.

    Leave a comment:


  • burgie12
    replied
    Re: ECAC Byes and Home-Ice 2011-12

    Originally posted by goblue78 View Post
    I just saw this post, burgie12, and I've worked it out, but the formulas are a little tedious to code up. I should be done tomorrow and I'll post it here. Too late for this year, pretty much, but there's always the future.
    I've worked it out by brute force (check out the spreadsheet if you're curious) and I understand why the sum of the semifinal scenarios isn't 200%, I was just surprised that it was as low as 49%.

    Leave a comment:


  • goblue78
    replied
    Re: ECAC Byes and Home-Ice 2011-12

    Originally posted by burgie12 View Post
    If there's someone that can help me with some maths with which I'm having an issue, that'd be cool. Here's what I mean: In order for #2 Cornell to host #12 Brown in Atlantic City, Brown has to beat Quinnipiac (18.29% chance) and then also beat Union (7.33% chance) and Cornell has to advance past their quarterfinal opponent, whomever it may be. Now, obviously, Cornell can't play Clarkson, because then Harvard would have to play Yale, which means that Colgate would have to play Quinnipiac, who obviously didn't make it to the quarters. So, despite the fact that Cornell has a 78.63% chance of advancing to the semis, we can take out the scenarios where they advance over Clarkson. That reduces it to 52.43% chance. (0.1829) * (0.0733) * (0.5243) = 0.70% Now, we can assume that there will be something else that I haven't taken into account which will lower this slightly, right? I mean, clearly, I didn't take everything into effect. But, when I sum up the probability of each of the individual cases, I get an answer of 0.019%. That's a little too much error for my liking.
    I just saw this post, burgie12, and I've worked it out, but the formulas are a little tedious to code up. I should be done tomorrow and I'll post it here. Too late for this year, pretty much, but there's always the future.

    Leave a comment:


  • DrDemento
    replied
    Re: ECAC Byes and Home-Ice 2011-12

    Thanks Burgie-I actually think I understand some of this.

    Leave a comment:


  • burgie12
    replied
    Re: ECAC Byes and Home-Ice 2011-12

    With the first round complete, we're moving on to the Quarterfinals. Quinnipiac is actually favored in their series (and, a 5 seed has never lost the first game of their series and finished it off in four of their seven opportunities).

    Good luck to all of the eight remaining teams.

    Your ECAC Playoff Match-ups:
    Code:
    ------------------------------------------------------------------------
    | H |Home Team| Last6 | A | Away Team  | Last6 | @H (Date) | @A (Date) |
    ------------------------------------------------------------------------
    | 1 | Union   | 4-1-1 |10 | Rensselaer | 3-2-1 | 5-1 01/14 | 5-1 11/15 |
    | 2 | Cornell | 4-1-1 | 9 | Dartmouth  | 2-4-0 | 4-3 01/20 | 3-2 11/12 |
    | 3 | Harvard | 3-1-2 | 6 | Yale       | 3-2-1 | 4-3 01/27 | 1-7 02/18 |
    | 4 | Colgate | 2-4-0 | 5 | Quinnipiac | 3-2-1 | 3-1 11/18 | 1-7 01/14 |
    ------------------------------------------------------------------------
    "Last6" refers to a team's record in their last six regular season games
    All scores are listed H-A
    Quarterfinal Outcome Probabilities: (KRACH)
    Code:
    -------------------------------------------------------------------------------------------------
    |    Home     |      Away       |  Game Winner  |  Series Sweep | 3-game Series |    Advances   |
    -------------------------------------------------------------------------------------------------
    | # |  Team   |  # |    Team    |  Home \  Away |  Home \  Away |  Home \  Away |  Home \  Away |
    -------------------------------------------------------------------------------------------------
    | 1 | Union   | 10 | Rensselaer | 80.65 \ 19.35 | 65.05 \  3.74 | 25.17 \  6.04 | 90.22 \  9.78 |
    | 2 | Cornell | 9  | Dartmouth  | 69.38 \ 30.62 | 48.14 \  9.37 | 29.48 \ 13.01 | 77.62 \ 22.38 |
    | 3 | Harvard | 6  | Yale       | 59.66 \ 40.34 | 35.59 \ 16.28 | 28.72 \ 19.42 | 64.30 \ 35.70 |
    | 4 | Colgate | 5  | Quinnipiac | 49.87 \ 50.13 | 24.87 \ 25.13 | 24.94 \ 25.06 | 49.81 \ 50.19 |
    -------------------------------------------------------------------------------------------------
    Resulting Semifinal Match-ups: (KRACH)
    Code:
    --------------------------------------------------------------------------------
    | Semis |   1   |   2   |   3   |   4   |   5   |   6   |   9   |  10  |  HOST |
    --------------------------------------------------------------------------------
    |   1   |       |       |       | 22.43 | 22.60 | 25.00 | 20.19 |      | 90.22 |
    |   2   |       |       | 45.03 | 12.45 | 12.55 |       |       | 7.59 | 77.62 |
    |   3   |       |       |       |  8.90 |  8.97 |       |       | 1.41 | 19.27 |
    |   4   |       |       |       |       |       |  4.94 |  0.70 | 0.39 |  6.03 |
    |   5   |       |       |       |       |       |  4.98 |  0.71 | 0.39 |  6.08 |
    |   6   |       |       |       |       |       |       |  0.78 |      |  0.78 |
    --------------------------------------------------------------------------------
    |  ROAD |       |       | 45.03 | 43.78 | 44.11 | 34.91 | 22.38 | 9.78 |       |
    --------------------------------------------------------------------------------
    |ADVANCE| 90.22 | 77.62 | 64.30 | 49.81 | 50.19 | 35.70 | 22.38 | 9.78 |       |
    --------------------------------------------------------------------------------
    Last edited by burgie12; 03-06-2012, 01:03 AM. Reason: formatting

    Leave a comment:


  • sshablak
    replied
    Re: ECAC Byes and Home-Ice 2011-12

    Four upset possibilities ! One upset already !

    Leave a comment:


  • burgie12
    replied
    Re: ECAC Byes and Home-Ice 2011-12

    Quarterfinal Outcome Probabilities: (ECAC B-T Ratings)
    Code:
    --------------------------------------------------------------------------------------------------------------------------------
    |     Home    |        Away       |    Any Game   |  Series Sweep | 3-game Series |    Advances   |            |    Overall    |
    --------------------------------------------------------------------------------------------------| Likelihood |----------------
    | # |   Team  |	 # |     Team     |  Home \  Away |  Home \  Away |  Home \  Away |  Home \  Away |            |  Home \  Away |
    --------------------------------------------------------------------------------------------------------------------------------
    | 1 | Union   | 12 | Brown        | 84.01 \ 15.99 | 70.58 \  2.56 | 22.57 \  4.30 | 93.15 \  6.85 |    22.48   | 20.94 \  1.54 |
    | 1 | Union   | 11 | Princeton    | 81.29 \ 18.71 | 66.07 \  3.50 | 24.73 \  5.69 | 90.80 \  9.20 |    23.89   | 21.69 \  2.20 |
    | 1 | Union   | 10 | Rensselaer   | 79.83 \ 20.17 | 63.73 \  4.07 | 25.71 \  6.50 | 89.44 \ 10.56 |    18.19   | 16.27 \  1.92 |
    | 1 | Union   |  9 | Dartmouth    | 76.79 \ 23.21 | 58.97 \  5.39 | 27.37 \  8.27 | 86.34 \ 13.66 |    15.39   | 13.29 \  2.10 |
    | 1 | Union   |  8 | St. Lawrence | 73.50 \ 26.50 | 54.03 \  7.02 | 28.63 \ 10.32 | 82.66 \ 17.34 |    20.06   | 16.58 \  3.48 |
    --------------------------------------------------------------------------------------------------------------------------------
    | 2 | Cornell | 11 | Princeton    | 77.99 \ 22.01 | 60.83 \  4.84 | 26.77 \  7.56 | 87.60 \ 12.40 |     6.93   |  6.07 \  0.86 |
    | 2 | Cornell | 10 | Rensselaer   | 76.35 \ 23.65 | 58.30 \  5.59 | 27.57 \  8.54 | 85.87 \ 14.13 |    13.37   | 11.48 \  1.89 |
    | 2 | Cornell |  9 | Dartmouth    | 72.97 \ 27.03 | 53.24 \  7.31 | 28.79 \ 10.66 | 82.03 \ 17.97 |    19.22   | 15.76 \  3.45 |
    | 2 | Cornell |  8 | St. Lawrence | 69.35 \ 30.65 | 48.10 \  9.39 | 29.48 \ 13.03 | 77.58 \ 22.42 |    25.04   | 19.42 \  5.61 |
    | 2 | Cornell |  7 | Clarkson     | 67.46 \ 32.54 | 45.51 \ 10.59 | 29.62 \ 14.29 | 75.12 \ 24.88 |    35.45   | 26.63 \  8.82 |
    --------------------------------------------------------------------------------------------------------------------------------
    | 3 | Harvard | 10 | Rensselaer   | 66.99 \ 33.01 | 44.88 \ 10.90 | 29.63 \ 14.60 | 74.51 \ 25.49 |     2.35   |  1.75 \  0.60 |
    | 3 | Harvard |  9 | Dartmouth    | 62.92 \ 37.08 | 39.58 \ 13.75 | 29.36 \ 17.30 | 68.94 \ 31.06 |     7.79   |  5.37 \  2.42 |
    | 3 | Harvard |  8 | St. Lawrence | 58.72 \ 41.28 | 34.48 \ 17.04 | 28.47 \ 20.01 | 62.95 \ 37.05 |    10.16   |  6.39 \  3.76 |
    | 3 | Harvard |  7 | Clarkson     | 56.58 \ 43.42 | 32.01 \ 18.85 | 27.80 \ 21.33 | 59.81 \ 40.19 |    26.07   | 15.59 \ 10.48 |
    | 3 | Harvard |  6 | Yale         | 56.58 \ 43.42 | 32.01 \ 18.85 | 27.80 \ 21.33 | 59.81 \ 40.19 |    53.64   | 32.08 \ 21.56 |
    --------------------------------------------------------------------------------------------------------------------------------
    | 4 | Colgate |  9 | Dartmouth    | 58.71 \ 41.29 | 34.47 \ 17.05 | 28.46 \ 20.02 | 62.93 \ 37.07 |     1.02   |  0.64 \  0.38 |
    | 4 | Colgate |  8 | St. Lawrence | 54.38 \ 45.62 | 29.57 \ 20.81 | 26.98 \ 22.63 | 56.56 \ 43.44 |     1.33   |  0.75 \  0.58 |
    | 4 | Colgate |  7 | Clarkson     | 52.20 \ 47.80 | 27.25 \ 22.85 | 26.05 \ 23.85 | 53.30 \ 46.70 |     4.58   |  2.44 \  2.14 |
    | 4 | Colgate |  6 | Yale         | 52.20 \ 47.80 | 27.25 \ 22.85 | 26.05 \ 23.85 | 53.30 \ 46.70 |    15.55   |  8.29 \  7.26 |
    | 4 | Colgate |  5 | Quinnipiac   | 50.00 \ 50.00 | 25.00 \ 25.00 | 25.00 \ 25.00 | 50.00 \ 50.00 |    77.52   | 38.76 \ 38.76 |
    --------------------------------------------------------------------------------------------------------------------------------
    Resulting Semifinal Match-ups: (KRACH)
    Code:
    ----------------------------------------------------------------------------------------------------
    | Semis |   1  |   2  |   3  |   4  |   5  |   6  |   7  |   8  |   9  |  10  |  11  |  12  | HOST |
    ----------------------------------------------------------------------------------------------------
    |   1   |      |      |      |11.049|11.122| 7.810| 7.103| 4.243| 2.111| 0.321| 0.007|      |43.765|
    |   2   |      |      |22.425| 5.624| 5.675| 0.117| 0.004| 1.697| 0.811| 0.841| 1.386| 0.078|38.657|
    |   3   |      |      |      | 4.796| 4.865| 0.086| 0.002| 0.342| 0.164| 0.165| 0.254| 0.014|10.690|
    |   4   |      |      |      |      |      | 1.692| 0.910| 0.285| 0.141| 0.056| 0.060| 0.004| 3.149|
    |   5   |      |      |      |      |      | 1.769| 0.890| 0.286| 0.141| 0.058| 0.062|      | 3.207|
    |   6   |      |      |      |      |      |      | 0.303| 0.065| 0.032| 0.001|      | 0.003| 0.402|
    |   7   |      |      |      |      |      |      |      | 0.078| 0.039|      | 0.000| 0.000| 0.117|
    |   8   |      |      |      |      |      |      |      |      |      | 0.008| 0.000| 0.000| 0.008|
    |   9   |      |      |      |      |      |      |      |      |      | 0.004| 0.000| 0.000| 0.004|
    |  10   |      |      |      |      |      |      |      |      |      |      |	0.000|      | 0.000|
    ----------------------------------------------------------------------------------------------------
    | ROAD  |      |      |22.425|21.470|21.661|11.474| 9.211| 6.997| 3.439| 1.454| 1.770| 0.099|      |
    ----------------------------------------------------------------------------------------------------
    |ADVANCE|43.765|38.657|33.114|24.619|24.868|11.876| 9.329| 7.005| 3.443| 1.454| 1.770| 0.099|      |
    ----------------------------------------------------------------------------------------------------
    Resulting Semifinal Match-ups: (ECAC B-T Ratings)
    Code:
    ----------------------------------------------------------------------------------------------------
    | Semis |   1  |   2  |   3  |   4  |   5  |   6  |   7  |   8  |   9  |  10  |  11  |  12  | HOST |
    ----------------------------------------------------------------------------------------------------
    |   1   |      |      |      |10.290| 9.764|10.253| 7.888| 3.271| 2.023| 0.293| 0.007|      |43.788|
    |   2   |      |      |20.515| 6.825| 6.489| 0.287| 0.007| 1.653| 0.999| 1.206| 0.821| 0.119|38.921|
    |   3   |      |      |      | 4.349| 4.186| 0.140| 0.003| 0.327| 0.198| 0.186| 0.120| 0.017| 9.525|
    |   4   |      |      |      |      |      | 2.248| 0.831| 0.254| 0.157| 0.072| 0.039| 0.006| 3.607|
    |   5   |      |      |      |      |      | 2.248| 0.740| 0.241| 0.148| 0.071| 0.039|      | 3.487|
    |   6   |      |      |      |      |      |      | 0.433| 0.088| 0.054| 0.001|      | 0.005| 0.581|
    |   7   |      |      |      |      |      |      |      | 0.050| 0.031|      | 0.000| 0.000| 0.081|
    |   8   |      |      |      |      |      |      |      |      |      | 0.006| 0.000| 0.000| 0.006|
    |   9   |      |      |      |      |      |      |      |      |      | 0.004| 0.000| 0.000| 0.004|
    |  10   |      |      |      |      |      |      |      |      |      |      |	0.000|      | 0.000|
    ----------------------------------------------------------------------------------------------------
    | ROAD  |      |      |20.515|21.464|20.439|15.176| 9.901| 5.884| 3.611| 1.838| 1.025| 0.147|      |
    ----------------------------------------------------------------------------------------------------
    |ADVANCE|43.788|38.921|30.039|25.071|23.925|15.758| 9.982| 5.890| 3.615| 1.838| 1.025| 0.147|      |
    ----------------------------------------------------------------------------------------------------

    Leave a comment:


  • burgie12
    replied
    Re: ECAC Byes and Home-Ice 2011-12

    With all of that out of the way, here's the reason why you showed up in the thread:

    This is straight maths, no Monte Carlo simulation.

    Team i's probability of winning a game against Team j is Rating(i) / [Rating(i) + Rating(j)]. There is no possibility of a tie. Ratings are not recalculated after a day of games, so "momentum" is completely ignored.

    Since KRACH is not being recalculated with the conclusion of each game, the chance of winning Game 1 of your series will be the same as the chance of winning Game 2 or 3. That helps make calculations a tiny bit easier.

    All values presented are percentages.

    Current Ratings:
    Code:
    -------------------------------------
    |  # |     Team     | KRACH |  ECAC |
    -------------------------------------
    |  1 | Union        | 192.8 | 254.1 |
    |  2 | Cornell      | 146.4 | 207.3 |
    |  3 | Harvard      | 109.5 | 130.3 |
    |  4 | Colgate      |  99.0 | 109.2 |
    |  5 | Quinnipiac   | 102.0 | 109.2 |
    |  6 | Yale         |  71.5 | 100.0 |
    |  7 | Clarkson     |  67.4 | 100.0 |
    |  8 | St. Lawrence |  73.2 |  91.6 |
    |  9 | Dartmouth    |  56.5 |  76.8 |
    | 10 | Rensselaer   |  42.0 |  64.2 |
    | 11 | Princeton    |  50.9 |  58.5 |
    | 12 | Brown        |  38.3 |  48.4 |
    -------------------------------------
    First Round Outcome Probabilities: (KRACH)
    Code:
    ------------------------------------------------------------------------------------------------------
    |       Home       |       Away      |  Game Winner  |  Series Sweep | 3-game Series |    Advances   |
    ------------------------------------------------------------------------------------------------------
    | # |     Team     |  # |     Team   |  Home \  Away |  Home \  Away |  Home \  Away |  Home \  Away |
    ------------------------------------------------------------------------------------------------------
    | 5 | Quinnipiac   | 12 | Brown      | 72.70 \ 27.30 | 52.85 \  7.45 | 28.86 \ 10.84 | 81.71 \ 18.29 |
    | 6 | Yale         | 11 | Princeton  | 58.42 \ 41.58 | 34.12 \ 17.29 | 28.38 \ 20.20 | 62.50 \ 37.50 |
    | 7 | Clarkson     | 10 | Rensselaer | 61.61 \ 38.39 | 37.96 \ 14.74 | 29.14 \ 18.16 | 67.10 \ 32.90 |
    | 8 | St. Lawrence |  9 | Dartmouth  | 56.44 \ 43.56 | 31.85 \ 18.98 | 27.75 \ 21.42 | 59.60 \ 40.40 |
    ------------------------------------------------------------------------------------------------------
    First Round Outcome Probabilities: (ECAC B-T Ratings)
    Code:
    ------------------------------------------------------------------------------------------------------
    |       Home       |       Away      |  Game Winner  |  Series Sweep | 3-game Series |    Advances   |
    ------------------------------------------------------------------------------------------------------
    | # |     Team     |  # |     Team   |  Home \  Away |  Home \  Away |  Home \  Away |  Home \  Away |
    ------------------------------------------------------------------------------------------------------
    | 5 | Quinnipiac   | 12 | Brown      | 69.31 \ 30.69 | 48.03 \  9.42 | 29.49 \ 13.06 | 77.52 \ 22.48 |
    | 6 | Yale         | 11 | Princeton  | 63.09 \ 36.91 | 39.81 \ 13.62 | 29.38 \ 17.19 | 69.19 \ 30.81 |
    | 7 | Clarkson     | 10 | Rensselaer | 60.90 \ 39.10 | 37.09 \ 15.29 | 29.00 \ 18.62 | 66.09 \ 33.91 |
    | 8 | St. Lawrence |  9 | Dartmouth  | 54.39 \ 45.61 | 39.59 \ 20.80 | 26.99 \ 22.63 | 56.57 \ 43.43 |
    ------------------------------------------------------------------------------------------------------
    Resulting Quarterfinal Match-ups: (KRACH)
    Code:
    ----------------------------------------------------------------------------------
    | Quarter |   5   |   6   |   7   |   8   |   9   |  10   |  11   |  12   | HOST |
    ----------------------------------------------------------------------------------
    |    1    |       |       |       | 20.43 | 13.84 | 16.80 | 30.64 | 18.29 | 100.0|
    |    2    |       |       | 34.27 | 26.84 | 18.19 | 13.84 |  6.86 |       | 100.0|
    |    3    |       | 51.07 | 28.23 | 10.99 |  7.45 |  2.26 |       |       | 100.0|
    |    4    | 81.71 | 11.43 |  4.60 |  1.34 |  0.91 |       |       |       | 100.0|
    ----------------------------------------------------------------------------------
    |   ROAD  | 81.71 | 62.50 | 67.10 | 59.60 | 40.40 | 32.90 | 37.50 | 18.29 |      |
    ----------------------------------------------------------------------------------
    Resulting Quarterfinal Match-ups: (ECAC B-T Ratings)
    Code:
    ----------------------------------------------------------------------------------
    | Quarter |   5   |   6   |   7   |   8   |   9   |  10   |  11   |  12   | HOST |
    ----------------------------------------------------------------------------------
    |    1    |       |       |       | 20.06 | 15.39 | 18.19 | 23.89 | 22.48 | 100.0|
    |    2    |       |       | 35.45 | 25.04 | 19.22 | 13.37 |  6.93 |       | 100.0|
    |    3    |       | 53.64 | 26.07 | 10.16 |  7.79 |  2.35 |       |       | 100.0|
    |    4    | 77.52 | 15.55 |  4.58 |  1.33 |  1.02 |       |       |       | 100.0|
    ----------------------------------------------------------------------------------
    |   ROAD  | 77.52 | 69.19 | 66.09 | 56.57 | 43.43 | 33.91 | 30.81 | 22.48 |      |
    ----------------------------------------------------------------------------------
    "Likelihood" refers to the probability that the First Round series finish in a manner that will result in the shown Quarterfinal match-up
    "Overall" is just "Advances" times "Likelihood"
    Quarterfinal Outcome Probabilities: (KRACH)
    Code:
    --------------------------------------------------------------------------------------------------------------------------------
    |     Home    |        Away       |  Game Winner  |  Series Sweep | 3-game Series |    Advances   |            |    Overall    |
    --------------------------------------------------------------------------------------------------| Likelihood |----------------
    | # |   Team  |  # |     Team     |  Home \  Away |  Home \  Away |  Home \  Away |  Home \  Away |            |  Home \  Away |
    --------------------------------------------------------------------------------------------------------------------------------
    | 1 | Union   | 12 | Brown        | 83.43 \ 16.57 | 69.60 \  2.75 | 23.07 \  4.58 | 92.67 \  7.33 |    18.29   | 16.95 \  1.34 |
    | 1 | Union   | 11 | Princeton    | 79.11 \ 20.89 | 62.59 \  4.36 | 26.15 \  6.90 | 88.74 \ 11.26 |    30.64   | 27.19 \  3.45 |
    | 1 | Union   | 10 | Rensselaer   | 82.11 \ 17.89 | 67.42 \  3.20 | 24.12 \  5.25 | 91.55 \  8.45 |    16.80   | 15.38 \  1.42 |
    | 1 | Union   |  9 | Dartmouth    | 77.34 \ 22.66 | 59.81 \  5.14 | 27.11 \  7.94 | 86.92 \ 13.08 |    13.84   | 12.03 \  1.81 |
    | 1 | Union   |  8 | St. Lawrence | 72.48 \ 27.52 | 52.54 \  7.57 | 28.91 \ 10.98 | 81.45 \ 18.55 |    20.43   | 16.64 \  3.79 |
    --------------------------------------------------------------------------------------------------------------------------------
    | 2 | Cornell | 11 | Princeton    | 74.20 \ 25.80 | 55.06 \  6.66 | 28.41 \  9.88 | 83.47 \ 16.53 |     6.86   |  5.72 \  1.13 |
    | 2 | Cornell | 10 | Rensselaer   | 77.71 \ 22.29 | 60.38 \  4.97 | 26.92 \  7.72 | 87.31 \ 12.69 |    13.84   | 12.08 \  1.76 |
    | 2 | Cornell |  9 | Dartmouth    | 72.15 \ 27.85 | 52.06 \  7.75 | 28.99 \ 11.19 | 81.06 \ 18.94 |    18.19   | 14.75 \  3.45 |
    | 2 | Cornell |  8 | St. Lawrence | 66.67 \ 33.33 | 44.44 \ 11.11 | 29.63 \ 14.81 | 74.07 \ 25.93 |    26.84   | 19.88 \  6.96 |
    | 2 | Cornell |  7 | Clarkson     | 68.48 \ 31.52 | 46.89 \  9.94 | 29.56 \ 13.61 | 76.45 \ 23.55 |    34.27   | 26.20 \  8.07 |
    --------------------------------------------------------------------------------------------------------------------------------
    | 3 | Harvard | 10 | Rensselaer   | 72.28 \ 27.72 | 52.24 \  7.69 | 28.96 \ 11.11 | 81.20 \ 18.80 |     2.26   |  1.83 \  0.42 |
    | 3 | Harvard |  9 | Dartmouth    | 65.96 \ 34.04 | 43.51 \ 11.58 | 29.62 \ 15.28 | 73.13 \ 26.87 |     7.45   |  5.45 \  2.00 |
    | 3 | Harvard |  8 | St. Lawrence | 59.93 \ 40.07 | 35.92 \ 16.05 | 28.78 \ 19.24 | 64.71 \ 35.29 |    10.99   |  7.11 \  3.88 |
    | 3 | Harvard |  7 | Clarkson     | 61.90 \ 38.10 | 38.32 \ 14.52 | 29.20 \ 17.97 | 67.51 \ 32.49 |    28.23   | 19.06 \  9.17 |
    | 3 | Harvard |  6 | Yale         | 60.50 \ 39.50 | 36.60 \ 15.60 | 28.92 \ 18.88 | 65.51 \ 34.49 |    51.07   | 33.46 \ 17.61 |
    --------------------------------------------------------------------------------------------------------------------------------
    | 4 | Colgate |  9 | Dartmouth    | 63.67 \ 36.33 | 40.53 \ 13.20 | 29.45 \ 16.81 | 69.99 \ 30.01 |     0.91   |  0.64 \  0.27 |
    | 4 | Colgate |  8 | St. Lawrence | 57.49 \ 42.51 | 33.05 \ 18.07 | 28.10 \ 20.78 | 61.15 \ 38.85 |     1.34   |  0.82 \  0.52 |
    | 4 | Colgate |  7 | Clarkson     | 59.50 \ 40.50 | 35.40 \ 16.41 | 28.67 \ 19.52 | 64.07 \ 35.93 |     4.60   |  2.95 \  1.65 |
    | 4 | Colgate |  6 | Yale         | 58.06 \ 41.94 | 33.71 \ 17.59 | 28.28 \ 20.42 | 61.99 \ 38.01 |    11.43   |  7.09 \  4.34 |
    | 4 | Colgate |  5 | Quinnipiac   | 49.25 \ 50.75 | 24.26 \ 25.75 | 24.62 \ 25.37 | 48.88 \ 51.12 |    81.71   | 39.94 \ 41.77 |
    --------------------------------------------------------------------------------------------------------------------------------

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