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Fun With Numbers 2019: PWR, RPI, KRACH, GRaNT, WCHODR, & other assortments of letters

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  • #16
    Re: Fun With Numbers 2019: PWR, RPI, KRACH, GRaNT, WCHODR, & other assortments of let

    Hey, some of you other people are good at math, right?

    How in the world is USCHO getting its Round Robin Winning Percentage (RRWP)? https://www.uscho.com/rankings/krach/d-i-women/ I cannot for the life of me figure it out.
    Grant Salzano, Boston College '10
    Writer Emeritus, BC Interruption
    Twitter: @Salzano14


    Click here for the BC Interruption Pairwise, KRACH, and GRaNT Calculators

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    • #17
      Re: Fun With Numbers 2019: PWR, RPI, KRACH, GRaNT, WCHODR, & other assortments of let

      Originally posted by ChickHicks86 View Post
      I was crunching down some Frosted Flakes for lunch, and decided to channel my inner TonyTheTiger20 and crunch some numbers too. I know there’s one series left this weekend (actually a pretty interesting one), but the halfway point of the season is a fun time to look at possible NCAA tourney brackets. I looked at travel distances for the Top 10 Pairwise teams, plus the most likely CHA autobid contenders. Barring the predictably unpredictable conference tournament party crashers, this might be a year where bracket integrity survives the perennial travel budget rearrangements. More than likely, the CHA champ will go to Madison or Minneapolis. Ohio State would fly anywhere if they get in (another reason Michigan, Michigan State, and Notre Dame should add women’s hockey, but that’s a discussion for another time…). That leaves a lot of eastern bus trips for 3-4 seeds’ visiting teams, unless OSU gets up to 5 or 6 and gets sent west.

      There’s a reason they don’t seed the NCAA tournament in December, but it’s still kind of fun to see where the teams might be playing in March!
      ------------------------------------------------------------------------------------------------------------------------------
      1___Wisconsin_____Wisconsin
      2___Minnesota_____B__Minnesota
      3___Northeastern___F_____F___Northeastern
      4___Providence_____F_____F_____B___Providence
      5___Clarkson_______F_____F_____B_____B__Clarkson
      6___Cornell________F_____F_____B_____B_____B____Co rnell
      7___Princeton______F_____F_____B_____B_____B_____B __Princeton
      8___Ohio State_____F_____F_____F_____F_____F_____F_____F___ Ohio State
      9___Colgate_______F_____F_____B_____B_____B_____B_ ____B_____F___Colgate
      10__Boston College_F_____F_____B_____B_____B_____B_____B_____ F_____B__Boston College
      CHA_Mercyhurst____F_____F_____F_____F_____B_____B_ ____F_____B_____B_____F__Mercyhurst
      CHA_Robert Morris__F_____F_____F_____F_____F_____B_____B_____ B_____F_____F_____B

      B = BUS
      F = FLIGHT
      Flight occurs when NCAA Miles > 400

      I apologize the formatting stinks. I have an Excel sheet, but couldn’t figure out how to post it
      I like this a lot, A+
      Grant Salzano, Boston College '10
      Writer Emeritus, BC Interruption
      Twitter: @Salzano14


      Click here for the BC Interruption Pairwise, KRACH, and GRaNT Calculators

      Comment


      • #18
        Re: Fun With Numbers 2019: PWR, RPI, KRACH, GRaNT, WCHODR, & other assortments of let

        Originally posted by TonyTheTiger20 View Post
        Hey, some of you other people are good at math, right?

        How in the world is USCHO getting its Round Robin Winning Percentage (RRWP)? https://www.uscho.com/rankings/krach/d-i-women/ I cannot for the life of me figure it out.
        I'm not sure I have much of a claim to being good at math, but I spent some time with the RRWP, and I couldn't match the USCHO numbers either. For each team, I calculated an expected winning percentage from the KRACH ranking if they were to play all 39 other teams (which supposedly is what the RRWP is). I used three scenarios: straight-up average winning percentage, KRACH predicted results of a 1 game series, and KRACH predicted results of an N game series. The closest I could come to matching USCHO was setting N to a 17 game series, and that was only working for the teams in the middle of the pack:

        USCHO | Avg. % | 1 Game | N=17 Gm.
        0.9567 | 0.9470 | 1.0000 | 0.9487 Wisconsin
        0.9206 | 0.9040 | 0.9744 | 0.9065 Minnesota
        0.8289 | 0.8046 | 0.9487 | 0.8054 Northeastern
        0.7736 | 0.7493 | 0.9231 | 0.7481 Princeton
        0.7654 | 0.7414 | 0.8974 | 0.7406 Ohio State
        0.7582 | 0.7345 | 0.8718 | 0.7300 Providence
        0.7405 | 0.7174 | 0.8462 | 0.7164 Clarkson
        0.7394 | 0.7164 | 0.8205 | 0.7149 Saint Anselm
        0.7379 | 0.7149 | 0.7949 | 0.7119 Cornell
        0.6663 | 0.6483 | 0.7692 | 0.6501 Minnesota Duluth
        0.6616 | 0.6440 | 0.7436 | 0.6425 Colgate
        0.6524 | 0.6355 | 0.7179 | 0.6335 Boston College
        0.6226 | 0.6087 | 0.6923 | 0.6124 Boston University
        0.6097 | 0.5971 | 0.6667 | 0.5958 Maine
        0.6009 | 0.5893 | 0.6410 | 0.5913 Mercyhurst
        0.5866 | 0.5766 | 0.6154 | 0.5762 Merrimack
        0.5760 | 0.5672 | 0.5897 | 0.5686 Minnesota State
        0.5621 | 0.5549 | 0.5641 | 0.5566 St. Lawrence
        0.5129 | 0.5113 | 0.5385 | 0.5128 Robert Morris
        0.5066 | 0.5058 | 0.5128 | 0.5068 Bemidji State
        0.4925 | 0.4934 | 0.4872 | 0.4932 Connecticut
        0.4871 | 0.4887 | 0.4615 | 0.4872 New Hampshire
        0.4565 | 0.4616 | 0.4359 | 0.4615 Penn State
        0.4355 | 0.4431 | 0.4103 | 0.4434 Vermont
        0.4109 | 0.4212 | 0.3846 | 0.4208 Quinnipiac
        0.3974 | 0.4092 | 0.3590 | 0.4087 St. Cloud State
        0.3823 | 0.3957 | 0.3333 | 0.3967 Harvard
        0.3721 | 0.3865 | 0.3077 | 0.3891 Sacred Heart
        0.3658 | 0.3808 | 0.2821 | 0.3771 Rensselaer
        0.3217 | 0.3406 | 0.2564 | 0.3394 Brown
        0.3185 | 0.3377 | 0.2308 | 0.3379 Syracuse
        0.2967 | 0.3174 | 0.2051 | 0.3213 Franklin Pierce
        0.2887 | 0.3100 | 0.1795 | 0.3137 Yale
        0.2654 | 0.2880 | 0.1538 | 0.2866 RIT
        0.2159 | 0.2400 | 0.1282 | 0.2368 Dartmouth
        0.2051 | 0.2292 | 0.1026 | 0.2293 Lindenwood
        0.1832 | 0.2072 | 0.0769 | 0.2066 Saint Michael's
        0.1325 | 0.1541 | 0.0513 | 0.1554 Holy Cross
        0.1311 | 0.1526 | 0.0256 | 0.1538 Union
        0.0626 | 0.0751 | 0.0000 | 0.0724 Post


        In short, I too have no idea where the USCHO RRWP is coming from. My best guess is it has something to do with rounding (my predictions round up from 0.5 like most people) or how it handles existing ties, but a guess is exactly what that is...
        2005 Piston Cup Champion

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        • #19
          Re: Fun With Numbers 2019: PWR, RPI, KRACH, GRaNT, WCHODR, & other assortments of let

          Using the ratings from the USCHO page, I get the same calculations as ChickHicks86. This gives a RRWP that is higher than the USCHO RRWP for teams with a KRACH greater than average, and a lower RRWP for teams with a KRACH below average. This suggests that the KRACH used to calculate RRWP on the page is based upon an actual winning percentage that is farther away from .500.

          My understanding is that USCHO's KRACH calculations are based upon actual winning percentages modified by adding a dummy team that is 0-0-1 against all of the real teams to each team's record, in order to prevent teams with a 1.0000 or 0.0000 winning percentage from blowing up to positive or negative infinity. This has the effect of pushing everyone's winning percentage towards .500. So, my first guess is that the RRWP they calculate has this dummy tie removed. They probably do this so that a team with a perfect (or perfectly bad) record will show up with the same RRWP. If it were me, I'd drop the dummy team entirely once it's no longer needed, or just stop being afraid of infinity in the first place, but it's hardly the first time USCHO does something dumb with its ratings.

          In order to test this, I'd have to build a KRACH calculator, which I have no intention of taking the time to do.
          Last edited by Still Eeyore; 01-07-2019, 05:57 AM.

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          • #20
            Re: Fun With Numbers 2019: PWR, RPI, KRACH, GRaNT, WCHODR, & other assortments of let

            Originally posted by Still Eeyore View Post
            Using the ratings from the USCHO page, I get the same calculations as ChickHicks86. This gives a RRWP that is higher than the USCHO RRWP for teams with a KRACH greater than average, and a lower RRWP for teams with a KRACH below average. This suggests that the KRACH used to calculate RRWP on the page is based upon an actual winning percentage that is farther away from .500.

            My understanding is that USCHO's KRACH calculations are based upon actual winning percentages modified by adding a dummy team that is 0-0-1 against all of the real teams to each team's record, in order to prevent teams with a 1.0000 or 0.0000 winning percentage from blowing up to positive or negative infinity. This has the effect of pushing everyone's winning percentage towards .500. So, my first guess is that the RRWP they calculate has this dummy tie removed. They probably do this so that a team with a perfect (or perfectly bad) record will show up with the same RRWP. If it were me, I'd drop the dummy team entirely once it's no longer needed, or just stop being afraid of infinity in the first place, but it's hardly the first time USCHO does something dumb with its ratings.

            In order to test this, I'd have to build a KRACH calculator, which I have no intention of taking the time to do.
            As a quick check, I created an average team with a KRACH rating of 100 and plugged it into my spreadsheet. The RRWP numbers inch closer to the USCHO numbers, but they are still closer to my original predictions. Another odd observation is that the margin of error is largest around rankings 3-4 and 35-36 (plotting ranking on X axis and difference between USCHO and me on Y axis makes for an interesting visual). Maybe there are two dummy teams floating in USCHO's calculations? Beats me...

            USCHO | Modified CH86 | Original CH86
            0.9567 | 0.9475 | 0.9470 Wisconsin
            0.9206 | 0.9048 | 0.9040 Minnesota
            0.8289 | 0.8058 | 0.8046 Northeastern
            0.7736 | 0.7505 | 0.7493 Princeton
            0.7654 | 0.7426 | 0.7414 Ohio State
            0.7582 | 0.7356 | 0.7345 Providence
            0.7405 | 0.7185 | 0.7174 Clarkson
            0.7394 | 0.7176 | 0.7164 Saint Anselm
            0.7379 | 0.7161 | 0.7149 Cornell
            0.6663 | 0.6492 | 0.6483 Minnesota Duluth
            0.6616 | 0.6449 | 0.6440 Colgate
            0.6524 | 0.6364 | 0.6355 Boston College
            0.6226 | 0.6094 | 0.6087 Boston University
            0.6097 | 0.5977 | 0.5971 Maine
            0.6009 | 0.5899 | 0.5893 Mercyhurst
            0.5866 | 0.5771 | 0.5766 Merrimack
            0.576 | 0.5676 | 0.5672 Minnesota State
            0.5621 | 0.5552 | 0.5549 St. Lawrence
            0.5129 | 0.5114 | 0.5113 Robert Morris
            0.5066 | 0.5059 | 0.5058 Bemidji State
            0.0000 | 0.5000 | -N/A- Average University
            0.4925 | 0.4934 | 0.4934 Connecticut
            0.4871 | 0.4886 | 0.4887 New Hampshire
            0.4565 | 0.4613 | 0.4616 Penn State
            0.4355 | 0.4427 | 0.4431 Vermont
            0.4109 | 0.4207 | 0.4212 Quinnipiac
            0.3974 | 0.4086 | 0.4092 St. Cloud State
            0.3823 | 0.3950 | 0.3957 Harvard
            0.3721 | 0.3858 | 0.3865 Sacred Heart
            0.3658 | 0.3801 | 0.3808 Rensselaer
            0.3217 | 0.3396 | 0.3406 Brown
            0.3185 | 0.3367 | 0.3377 Syracuse
            0.2967 | 0.3164 | 0.3174 Franklin Pierce
            0.2887 | 0.3089 | 0.3100 Yale
            0.2654 | 0.2869 | 0.2880 RIT
            0.2159 | 0.2388 | 0.2400 Dartmouth
            0.2051 | 0.2280 | 0.2292 Lindenwood
            0.1832 | 0.2060 | 0.2072 Saint Michael's
            0.1325 | 0.1530 | 0.1541 Holy Cross
            0.1311 | 0.1515 | 0.1526 Union
            0.0626 | 0.0745 | 0.0751 Post
            2005 Piston Cup Champion

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            • #21
              Re: Fun With Numbers 2019: PWR, RPI, KRACH, GRaNT, WCHODR, & other assortments of let

              Originally posted by ChickHicks86 View Post
              As a quick check, I created an average team with a KRACH rating of 100 and plugged it into my spreadsheet. The RRWP numbers inch closer to the USCHO numbers, but they are still closer to my original predictions.
              My hypothesis is not that there is an additional dummy team used in the RRWP calculation. It's that there is a dummy team used by USCHO to calculate the ratings that you see on their KRACH page, and that you and I both used to calculate what the RRWP should be based upon those ratings, but that USCHO's page is calculating RRWP based upon a different set of ratings that does not include the dummy team. In order to test that, you would need to have a spreadsheet that takes every team's schedule and uses it to generate the ratings, and see if it produces the same or different ratings for each team.

              That spreadsheet is a major piece of work. I believe that Grant has one; I do not, and don't intend to build one.

              Comment


              • #22
                Originally posted by Still Eeyore View Post
                My hypothesis is not that there is an additional dummy team used in the RRWP calculation. It's that there is a dummy team used by USCHO to calculate the ratings that you see on their KRACH page, and that you and I both used to calculate what the RRWP should be based upon those ratings, but that USCHO's page is calculating RRWP based upon a different set of ratings that does not include the dummy team. In order to test that, you would need to have a spreadsheet that takes every team's schedule and uses it to generate the ratings, and see if it produces the same or different ratings for each team.

                That spreadsheet is a major piece of work. I believe that Grant has one; I do not, and don't intend to build one.
                I do have it -- I'm working from home tomorrow so I'm planning on diving into both of your guesses/suggestions!
                Grant Salzano, Boston College '10
                Writer Emeritus, BC Interruption
                Twitter: @Salzano14


                Click here for the BC Interruption Pairwise, KRACH, and GRaNT Calculators

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                • #23
                  Re: Fun With Numbers 2019: PWR, RPI, KRACH, GRaNT, WCHODR, & other assortments of let

                  Originally posted by TonyTheTiger20 View Post
                  I do have it -- I'm working from home tomorrow so I'm planning on diving into both of your guesses/suggestions!
                  Because I've thought about building one, I have some questions. Foremost, do you have to hand enter game results, or do you have some place that you pull the data from?

                  Comment


                  • #24
                    Originally posted by Still Eeyore View Post
                    Because I've thought about building one, I have some questions. Foremost, do you have to hand enter game results, or do you have some place that you pull the data from?
                    I pull from USCHO's composite schedule using an external connection
                    Grant Salzano, Boston College '10
                    Writer Emeritus, BC Interruption
                    Twitter: @Salzano14


                    Click here for the BC Interruption Pairwise, KRACH, and GRaNT Calculators

                    Comment


                    • #25
                      Re: Fun With Numbers 2019: PWR, RPI, KRACH, GRaNT, WCHODR, & other assortments of let

                      Originally posted by TonyTheTiger20 View Post
                      I pull from USCHO's composite schedule using an external connection
                      I'd use collegehockeystats instead of USCHO if you are starting from scratch. The former has been much more reliable over the years.
                      "... And lose, and start again at your beginnings
                      And never breathe a word about your loss;" -- Rudyard Kipling

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                      • #26
                        Re: Fun With Numbers 2019: PWR, RPI, KRACH, GRaNT, WCHODR, & other assortments of let

                        Originally posted by ARM View Post
                        I'd use collegehockeystats instead of USCHO if you are starting from scratch. The former has been much more reliable over the years.
                        Ha, yeah, I knew someone was going to mention how USCHO is always wrong with this stuff... I've thought about changing over to something else, but decided against it because even though it's just a matter of changing the import, I'd also have to re-match up the columns. Also USCHO's problem seems to be more in the line of having dates/times wrong. Once the official boxes get posted everything seems to match up right.
                        Grant Salzano, Boston College '10
                        Writer Emeritus, BC Interruption
                        Twitter: @Salzano14


                        Click here for the BC Interruption Pairwise, KRACH, and GRaNT Calculators

                        Comment


                        • #27
                          Re: Fun With Numbers 2019: PWR, RPI, KRACH, GRaNT, WCHODR, & other assortments of let

                          Originally posted by TonyTheTiger20 View Post
                          Ha, yeah, I knew someone was going to mention how USCHO is always wrong with this stuff... I've thought about changing over to something else, but decided against it because even though it's just a matter of changing the import, I'd also have to re-match up the columns. Also USCHO's problem seems to be more in the line of having dates/times wrong. Once the official boxes get posted everything seems to match up right.
                          It has been better in recent years. I remember times 6 or so years ago when there were wholesale problems. I don't recommend going to the effort of changing if you have a working application, but I wouldn't build something new on top of USCHO.
                          "... And lose, and start again at your beginnings
                          And never breathe a word about your loss;" -- Rudyard Kipling

                          Comment


                          • #28
                            Re: Fun With Numbers 2019: PWR, RPI, KRACH, GRaNT, WCHODR, & other assortments of let

                            Originally posted by Still Eeyore View Post
                            My hypothesis is not that there is an additional dummy team used in the RRWP calculation. It's that there is a dummy team used by USCHO to calculate the ratings that you see on their KRACH page, and that you and I both used to calculate what the RRWP should be based upon those ratings, but that USCHO's page is calculating RRWP based upon a different set of ratings that does not include the dummy team.
                            So, I took out the phantom tie against an average team. After doing that, the rankings didn't converge. So that didn't do it.

                            I also thought maybe we're overthinking this and RRWP is just your odds of beating a team with a rating of 100. That didn't do it either.

                            This is obnoxious.
                            Grant Salzano, Boston College '10
                            Writer Emeritus, BC Interruption
                            Twitter: @Salzano14


                            Click here for the BC Interruption Pairwise, KRACH, and GRaNT Calculators

                            Comment


                            • #29
                              Originally posted by TonyTheTiger20 View Post
                              So, I took out the phantom tie against an average team. After doing that, the rankings didn't converge. So that didn't do it.

                              I also thought maybe we're overthinking this and RRWP is just your odds of beating a team with a rating of 100. That didn't do it either.

                              This is obnoxious.
                              They're using Red Kryptonite.
                              CCT '77 & '78
                              4 kids
                              5 grandsons (BCA 7/09, CJA 5/14, JDL 8/14, JFL 6/16, PJL 7/18)
                              1 granddaughter (EML 4/18)

                              ”Any society that would give up a little liberty to gain a little security will deserve neither and lose both.”
                              - Benjamin Franklin

                              Banned from the St. Lawrence University Facebook page - March 2016 (But I got better).

                              I want to live forever. So far, so good.

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                              • #30
                                Re: Fun With Numbers 2019: PWR, RPI, KRACH, GRaNT, WCHODR, & other assortments of let

                                I still think Eeyore's guess is right... I need to see if I'm screwing things up by how I'm deleting the tie.
                                Grant Salzano, Boston College '10
                                Writer Emeritus, BC Interruption
                                Twitter: @Salzano14


                                Click here for the BC Interruption Pairwise, KRACH, and GRaNT Calculators

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