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  • Octonion Power Rankings

    Poisson model, pooled NCAA divisions, home/away/neutral factors.

    div = NCAA division
    str = team strength
    ofs = offensive strength
    dfs = defensive strength
    sos = strength of schedule

    Code:
      rk |             school              | div |  str  |  ofs  |  dfs  |  sos  
    -----+---------------------------------+-----+-------+-------+-------+-------
       1 | minnesota                       |   1 | 4.230 | 1.916 | 0.453 | 1.489
       2 | quinnipiac                      |   1 | 3.858 | 1.536 | 0.398 | 1.460
       3 | miami                           |   1 | 3.469 | 1.402 | 0.404 | 1.458
       4 | minnesota-state                 |   1 | 3.443 | 1.753 | 0.509 | 1.502
       5 | north-dakota                    |   1 | 3.321 | 1.727 | 0.520 | 1.526
       6 | denver                          |   1 | 3.259 | 1.837 | 0.564 | 1.548
       7 | st-cloud-state                  |   1 | 3.216 | 1.720 | 0.535 | 1.499
       8 | new-hampshire                   |   1 | 3.173 | 1.687 | 0.532 | 1.470
       9 | umass-lowell                    |   1 | 3.113 | 1.565 | 0.503 | 1.428
      10 | notre-dame                      |   1 | 3.084 | 1.605 | 0.521 | 1.482
      11 | union                           |   1 | 3.012 | 1.570 | 0.521 | 1.448
      12 | rensselaer                      |   1 | 2.931 | 1.551 | 0.529 | 1.496
      13 | wisconsin                       |   1 | 2.868 | 1.369 | 0.477 | 1.496
      14 | providence                      |   1 | 2.863 | 1.544 | 0.539 | 1.482
      15 | boston-college                  |   1 | 2.808 | 1.761 | 0.627 | 1.437
      16 | western-michigan                |   1 | 2.786 | 1.295 | 0.465 | 1.459
      17 | nebraska-omaha                  |   1 | 2.679 | 1.760 | 0.657 | 1.495
      18 | air-force                       |   1 | 2.673 | 1.534 | 0.574 | 1.349
      19 | ferris-state                    |   1 | 2.625 | 1.463 | 0.558 | 1.475
      20 | dartmouth                       |   1 | 2.618 | 1.526 | 0.583 | 1.462
      21 | cornell                         |   1 | 2.541 | 1.377 | 0.542 | 1.502
      22 | yale                            |   1 | 2.527 | 1.576 | 0.624 | 1.486
      23 | niagara                         |   1 | 2.508 | 1.494 | 0.596 | 1.354
      24 | colorado-college                |   1 | 2.507 | 1.798 | 0.717 | 1.567
      25 | michigan-tech                   |   1 | 2.493 | 1.611 | 0.646 | 1.516

  • #2
    Re: Octonion Power Rankings

    Originally posted by octonion View Post
    Poisson model, pooled NCAA divisions, home/away/neutral factors.

    div = NCAA division
    str = team strength
    ofs = offensive strength
    dfs = defensive strength
    sos = strength of schedule

    Code:
      rk |             school              | div |  str  |  ofs  |  dfs  |  sos  
    -----+---------------------------------+-----+-------+-------+-------+-------
       1 | minnesota                       |   1 | 4.230 | 1.916 | 0.453 | 1.489
       2 | quinnipiac                      |   1 | 3.858 | 1.536 | 0.398 | 1.460
       3 | miami                           |   1 | 3.469 | 1.402 | 0.404 | 1.458
       4 | minnesota-state                 |   1 | 3.443 | 1.753 | 0.509 | 1.502
       5 | north-dakota                    |   1 | 3.321 | 1.727 | 0.520 | 1.526
       6 | denver                          |   1 | 3.259 | 1.837 | 0.564 | 1.548
       7 | st-cloud-state                  |   1 | 3.216 | 1.720 | 0.535 | 1.499
       8 | new-hampshire                   |   1 | 3.173 | 1.687 | 0.532 | 1.470
       9 | umass-lowell                    |   1 | 3.113 | 1.565 | 0.503 | 1.428
      10 | notre-dame                      |   1 | 3.084 | 1.605 | 0.521 | 1.482
      11 | union                           |   1 | 3.012 | 1.570 | 0.521 | 1.448
      12 | rensselaer                      |   1 | 2.931 | 1.551 | 0.529 | 1.496
      13 | wisconsin                       |   1 | 2.868 | 1.369 | 0.477 | 1.496
      14 | providence                      |   1 | 2.863 | 1.544 | 0.539 | 1.482
      15 | boston-college                  |   1 | 2.808 | 1.761 | 0.627 | 1.437
      16 | western-michigan                |   1 | 2.786 | 1.295 | 0.465 | 1.459
      17 | nebraska-omaha                  |   1 | 2.679 | 1.760 | 0.657 | 1.495
      18 | air-force                       |   1 | 2.673 | 1.534 | 0.574 | 1.349
      19 | ferris-state                    |   1 | 2.625 | 1.463 | 0.558 | 1.475
      20 | dartmouth                       |   1 | 2.618 | 1.526 | 0.583 | 1.462
      21 | cornell                         |   1 | 2.541 | 1.377 | 0.542 | 1.502
      22 | yale                            |   1 | 2.527 | 1.576 | 0.624 | 1.486
      23 | niagara                         |   1 | 2.508 | 1.494 | 0.596 | 1.354
      24 | colorado-college                |   1 | 2.507 | 1.798 | 0.717 | 1.567
      25 | michigan-tech                   |   1 | 2.493 | 1.611 | 0.646 | 1.516
    Any description as to how you are coming by these numbers?

    Comment


    • #3
      Re: Octonion Power Rankings

      For a fairly simple exposition of how to do Poisson modeling, see https://dl.dropbo*****/u/5755704/ranking.doc (I wrote it a couple of years ago, so it refers to the 2011 season.) The only difference between this and what Octonion has done is normalization to create the rankings, I think. But he or she will, I'm sure, correct me if I'm wrong.

      Comment


      • #4
        Re: Octonion Power Rankings

        Sure, it's a mixed-effect Poisson regression model. I'm assuming that the goals scored by a team is modeled as a Poisson distribution depending on the team's offensive strength (random effect), opponent's defensive strength (random effect), home/away/neutral factor (fixed effect) and year (fixed effect). Offense and defense are nested within NCAA divisions, and these are pooled over the last 14 years.

        As an example, I get than teams score about 7% more goals and allow about 7% fewer goals at home. This implies by the Pythagorean expectation (with exponent about 2.2) that the home team's winning percentage should be about 57%, and this is exactly what we see.

        -Chris
        Last edited by octonion; 03-13-2013, 09:25 AM.

        Comment


        • #5
          Re: Octonion Power Rankings

          Interesting, Octonion. What do you get out of the 14 year pooling (given year fixed effects) other than more accurate (presuming invariance) estimates of the home team effect? If I understand you correctly, are you assuming that, in essence, a team's offensive and defensive prowess rises and falls by a fixed (estimated) amount, or are the defense and offense allowed to move independently from year to year?

          Comment


          • #6
            Re: Octonion Power Rankings

            what? Only 9 WCHA teams in the top 25? Eastern bias.

            Comment


            • #7
              Re: Octonion Power Rankings

              Originally posted by William Blake View Post
              what? Only 9 WCHA teams in the top 25? Eastern bias.
              Goofers are #1? Western bias.

              Comment


              • #8
                Re: Octonion Power Rankings

                Union not #26? Michigan Tech in the top half of anything?

                Comment


                • #9
                  Re: Octonion Power Rankings

                  So, was the model applied to previous years? If so, how did it compare to the NCAA tournament results (especially in regards to insulated teams that do not play each other such as MN and QU this year)?

                  I assume the reason to rank the teams is to give some insight into how the teams will perform. If the purpose is for something else, what is it?
                  Bottom Line: If you deserve to win the national championship then don't worry about who you play, when, and where. Just keep winning.
                  Exception: You are right about the refs. They, no doubt, have it in for <insert your team name here>!

                  Comment


                  • #10
                    Re: Octonion Power Rankings

                    Originally posted by gopheritall View Post
                    So, was the model applied to previous years? If so, how did it compare to the NCAA tournament results (especially in regards to insulated teams that do not play each other such as MN and QU this year)?

                    I assume the reason to rank the teams is to give some insight into how the teams will perform. If the purpose is for something else, what is it?
                    To start a discussion on the internet. Duh.

                    "I have come up with a plan so cunning you could stick a tail on it and call it a weasel. ."
                    -Blackadder
                    "I'm shocked, shocked to find that gambling is going on in here. "
                    -Casablanca
                    "They could maybe hire another officer to catch the illegal immigrant drug dealers breast feeding at Dunkin' Donuts or whatever it is! Thank you!"
                    -Somerville Speakout

                    2008 POTY

                    Comment


                    • #11
                      Re: Octonion Power Rankings

                      It's a first model - with sports you do have to be really careful regarding any rule changes. In particular, can the rule changes be absorbed into the fixed yearly effect?

                      The strength of a team's offense and defense are separately estimated for each season, but the overall pool strength of D1, D2 and D3 is assumed to be consistent. The home field advantage is assumed to be consistent, too, but that could easily be allowed to vary by team. That makes a difference for some (but not most) teams.

                      Comment


                      • #12
                        Re: Octonion Power Rankings

                        It predicted 11/15 (73.3%) of the NCAA D1 tournament outcomes correctly last year, fitting on only non-tournament games. Is that good or bad?

                        Comment


                        • #13
                          Re: Octonion Power Rankings

                          Originally posted by octonion View Post
                          It predicted 11/15 (73.3%) of the NCAA D1 tournament outcomes correctly last year, fitting on only non-tournament games. Is that good or bad?
                          In last year's tournament, I believe that all 4 top seeds qualified for the FF, and in the FF, everything went according to PWR seeding. That means that, at worst, the PWR predicted the same 11/15 (and I am fairly sure that UND was a #2, so that makes 12 right atleast), and it's not designed as a predictive model. Draw your own conclusion.

                          Comment


                          • #14
                            Re: Octonion Power Rankings

                            It looks like the tournament seeding had two #1 seeds in the final 4, whereas I had three. What's the overall accuracy of the tournament seeding over the last 10 years or so?

                            http://en.wikipedia.org/wiki/2012_NCAA_Division_I_Men's_Ice_Hockey_Tournament

                            Comment


                            • #15
                              Re: Octonion Power Rankings

                              Originally posted by octonion View Post
                              It looks like the tournament seeding had two #1 seeds in the final 4, whereas I had three. What's the overall accuracy of the tournament seeding over the last 10 years or so?

                              http://en.wikipedia.org/wiki/2012_NCAA_Division_I_Men's_Ice_Hockey_Tournament
                              I am sorry. I had thought that Minny and Ferris were #1s. Interesting that they each defeated #1 seeds from their own conference...

                              Comment

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