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Fun With Numbers 2018: Pairwise, KRACH, GRaNT, and other mathematical excitement

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  • #16
    Re: Fun With Numbers 2018: Pairwise, KRACH, GRaNT, and other mathematical excitement

    Originally posted by vicb View Post
    ECAC is gonna be a real crap shoot and it would not surprise me when all the ice has settled you end up with the following ...
    2) Clarkson/Colgate
    ...
    5) Colgate/Clarkson
    Historically, it hasn't tended to go that way, in part because the top teams in the ECAC play each other 2 or 3 times rather than 3 or 4 as in HEA or 4 or 5 as in the WCHA. The exception might be the years the North Country teams decide to do an extra nonconference home and home. So in a year where there is a clear top two in the ECAC and a drop to everyone else, those top two don't beat each other up as far as RPI goes. I'm pretty confident that both Clarkson and Colgate are destined for the top four, unless something unexpected happens (like OSU beating Wisconsin three times in a row). Those two ECAC teams are comfortably ahead of the rest of the pack.
    "... And lose, and start again at your beginnings
    And never breathe a word about your loss;" -- Rudyard Kipling

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    • #17
      Re: Fun With Numbers 2018: Pairwise, KRACH, GRaNT, and other mathematical excitement

      Originally posted by vicb View Post
      ECAC is gonna be a real crap shoot and it would not surprise me when all the ice has settled you end up with the following

      1) Wisconsin
      2) Clarkson/Colgate
      3) BC
      4) Ohio State
      5) Colgate/Clarkson
      6) Minnesota
      7) Maine/NE/Providence/Cornell
      8) Robert Morris
      The ECAC is a crapshoot but Clarkson and Cornell have wildly easy schedules the rest of the way (this weekend excluded), Colgate in particular. It would take a pretty dramatic fall for any of the top 4 to drop out of home ice.

      My best guess right now is we're going to see something along the lines of:

      (1) Wisconsin
      (2-4) Boston College, Clarkson, Colgate
      (5) Ohio State
      (6-7) Two of: Minnesota, Cornell, St. Lawrence, Maine, Northeastern, MAYYYYBE Providence if they can take some points against BC this weekend.
      (8) CHA

      Providence and Maine each have a shot to climb up into that 6-7 slot but they have a rough last two weekends, with 4 games against BC plus each other. Northeastern is more likely, but they have a lot of teams to leapfrog. Gun to my head, I don't think anyone other than BC gets in as an at-large from WHEA.

      There is such a big gap between the top 4 and the rest -- even if Ohio State swept Wisconsin next weekend and BC got swept by PC this weekend, Ohio State would still be handily behind BC. So barring something catastrophic, you're not going to see any of the top 4 fall out. Also Wisconsin has #1 pretty much locked up.

      Ohio State has a pretty good lead on Cornell, too, though they're closer to Cornell than they are to BC. Ohio State's road to the end of the regular season is a bit tougher than Cornell's, though.

      This weekend is really going to set things up for the rest of the year. BC has Providence, Clarkson/Colgate/Cornell/SLU all play two games against each other, Ohio State has Duluth (who is, admittedly, bad, but not Mankato bad). Then the ECAC teams all have it WICKED easy the rest of the way, which Minnesota gets to get blasted by the Badgers and the WHEA teams beat up on each other.

      My guess is the top 7 today is the top 7 you'll see at the end of the year, but everything is total chaos so who the heck knows. We'll learn a lot this weekend.
      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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      • #18
        Re: Fun With Numbers 2018: Pairwise, KRACH, GRaNT, and other mathematical excitement

        Originally posted by TonyTheTiger20 View Post
        Habemus BRACKETOLOGUM!


        http://www.bostonherald.com/sites/de...?itok=YjCeyWoT

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        • #19
          Re: Fun With Numbers 2018: Pairwise, KRACH, GRaNT, and other mathematical excitement

          Originally posted by Genbeau View Post
          What about the GRaNT. Someone insisted it's a soft "G." I don't agree with them.
          So you don't want people pronouncing your moniker as "enbeau"?

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          • #20
            Re: Fun With Numbers 2018: Pairwise, KRACH, GRaNT, and other mathematical excitement

            Originally posted by FredsDeadFriend View Post
            So you don't want people pronouncing your moniker as "enbeau"?
            I believe it's "zhZHzhZHzhZHenbeauoluulxxghhh," en francais
            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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            • #21
              Re: Fun With Numbers 2018: Pairwise, KRACH, GRaNT, and other mathematical excitement

              Originally posted by TonyTheTiger20 View Post

              We're using our Pairwise, which is correct, instead of USCHO's, which is incorrect.
              never use USCHO stats unless you have no other source for the stats you need
              and don't bet your paycheck on them

              Originally posted by ARM View Post
              I'm pretty confident that both Clarkson and Colgate are destined for the top four, unless something unexpected happens (like OSU beating Wisconsin three times in a row). Those two ECAC teams are comfortably ahead of the rest of the pack.
              yes, and OSU seems pretty much a lock on #5

              forgotten in all of this is the very real possibility of an upset in the conference tourneys
              I could see 3 teams other than Wisco winning WCHA
              I could see any of the also-rans upsetting BC
              and there are 3-4 teams that could get hot at the right time other than Clarkson or Colgate in the ECAC
              Last edited by pokechecker; 01-26-2018, 07:23 AM.

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              • #22
                Re: Fun With Numbers 2018: Pairwise, KRACH, GRaNT, and other mathematical excitement

                So for a while I've wondered to myself if there was an easy way to rank teams in order of who gives you the biggest PWR boost for beating them. Not as a way of ranking teams -- but just to see how much it's worth to beat each team. It isn't just "beating #1 is best," because who is "best" involves how good your opponent's winning % is and how good your opponent's opponent's winning % is -- not your opponent's final ranking.

                Anyway I should have figured this out sooner because it's actually a simple formula. Since RPI is calculated as 30% Win%, 24% OppWin%, and 46% OppOppWin%, you can calculate how much each team will affect your RPI by doing:

                1 (since you would have won that game, so your winning percentage in that game is 1.000) times 0.3
                plus that team's winning percentage times 0.24 (since that team's Win% is now your OppWin%)
                plus that team's opponent's winning percentage times 0.46 (since that team's OppWin% is now your OppOppWin%

                Do that for all 40 teams, and voila --



                The colored numbers at the right are each team's ranking relative to their PWR position.
                Last edited by TonyTheTiger20; 01-27-2018, 10:02 PM.
                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 2018: Pairwise, KRACH, GRaNT, and other mathematical excitement

                  Originally posted by TonyTheTiger20 View Post
                  So for a while I've wondered to myself if there was an easy way to rank teams in order of who gives you the biggest PWR boost for beating them. Not as a way of ranking teams -- but just to see how much it's worth to beat each team. It isn't just "beating #1 is best," because who is "best" involves how good your opponent's winning % is and how good your opponent's opponent's winning % is -- not your opponent's final ranking.

                  Anyway I should have figured this out sooner because it's actually a simple formula. Since RPI is calculated as 30% Win%, 24% OppWin%, and 46% OppOppWin%, you can calculate how much each team will affect your RPI by doing:

                  1 (since you would have won that game, so your winning percentage in that game is 1.000) times 0.3
                  plus that team's winning percentage times 0.24 (since that team's Win% is now your OppWin%)
                  plus that team's opponent's winning percentage times 0.46 (since that team's OppWin% is now your OppOppWin%

                  Do that for all 40 teams, and voila --



                  The colored numbers at the right are each team's ranking relative to their PWR position.


                  Why is anyone wasting any kind of spots on St A's. Because they beat Post 21-0? There is no way they are going to be placed in the NCAA D1 tournament.

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                  • #24
                    Originally posted by Quiet Riot View Post
                    Why is anyone wasting any kind of spots on St A's. Because they beat Post 21-0? There is no way they are going to be placed in the NCAA D1 tournament.
                    They are not -- but whether they're selected or not, we do know from the committee chair that games against them do count. That's all this list is! It's not a ranking, but a list of how much beating each team helps your ranking
                    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 2018: Pairwise, KRACH, GRaNT, and other mathematical excitement

                      Originally posted by TonyTheTiger20 View Post
                      Do that for all 40 teams, and voila --
                      So this afternoon, there is one and only one game (an interesting circumstance that let's you see how much or little a game can affect teams in isolation, and "third-party" teams): St Cloud and Wisconsin. If we assume Wisconsin wins, does that means we should see Wisconsin's RPI go up be something like the St Cloud value (.6237) divided by the number of games UW has played (28), or about 0.0223? Because that seems like a lot for a win over St Cloud (sorry, SCS fans).

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                      • #26
                        Re: Fun With Numbers 2018: Pairwise, KRACH, GRaNT, and other mathematical excitement

                        Originally posted by robertearle View Post
                        So this afternoon, there is one and only one game (an interesting circumstance that let's you see how much or little a game can affect teams in isolation, and "third-party" teams): St Cloud and Wisconsin. If we assume Wisconsin wins, does that means we should see Wisconsin's RPI go up be something like the St Cloud value (.6237) divided by the number of games UW has played (28), or about 0.0223? Because that seems like a lot for a win over St Cloud (sorry, SCS fans).
                        No. I'd have to play around with some numbers to be sure, and I won't have time for that until this evening, but I'm pretty sure that your RPI will increase by:

                        (Above calculated value for your opponent - Your RPI before the game) / Number of games you've played

                        So, if your RPI is higher than your opponent's value, that win would drop your RPI and it gets tossed out.

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                        • #27
                          Re: Fun With Numbers 2018: Pairwise, KRACH, GRaNT, and other mathematical excitement

                          Originally posted by Eeyore View Post
                          No. I'd have to play around with some numbers to be sure, and I won't have time for that until this evening, but I'm pretty sure that your RPI will increase by:

                          (Above calculated value for your opponent - Your RPI before the game) / Number of games you've played

                          So, if your RPI is higher than your opponent's value, that win would drop your RPI and it gets tossed out.
                          The RPI page shows both the 'unadjusted' and 'adjusted' values. So, we'll see the unadjusted go down a bit for UW, but the adjusted not change? This is going to be interesting...

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                          • #28
                            Originally posted by Eeyore View Post
                            No. I'd have to play around with some numbers to be sure, and I won't have time for that until this evening, but I'm pretty sure that your RPI will increase by:

                            (Above calculated value for your opponent - Your RPI before the game) / Number of games you've played

                            So, if your RPI is higher than your opponent's value, that win would drop your RPI and it gets tossed out.
                            Originally posted by robertearle View Post
                            The RPI page shows both the 'unadjusted' and 'adjusted' values. So, we'll see the unadjusted go down a bit for UW, but the adjusted not change? This is going to be interesting...
                            Yep, that's correct, (both of you). Also one other caveat is it's not exact, because "OppWin%" is actually your opponent's winning percentage in games not against you -- so for the UW vs. SCSU example, you'd subtract out the prior UW vs. SCSU games from the winning percentage before doing the calculation. But the difference at this point in the season is very small.
                            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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                            • #29
                              Originally posted by Eeyore View Post
                              No. I'd have to play around with some numbers to be sure, and I won't have time for that until this evening, but I'm pretty sure that your RPI will increase by:

                              (Above calculated value for your opponent - Your RPI before the game) / Number of games you've played

                              So, if your RPI is higher than your opponent's value, that win would drop your RPI and it gets tossed out.
                              Put another way -- Wisconsin's new (unadjusted) RPI would be:

                              {[UW's unadjusted RPI times (games played minus 1)]
                              Plus the RPI above for beating SCSU}
                              All divided by number of games played.

                              I'm on my phone multitasking so if that's wrong then oops lol... But I'm pretty sure that's right.
                              Grant Salzano, Boston College '10
                              Writer Emeritus, BC Interruption
                              Twitter: @Salzano14


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

                              Comment


                              • #30
                                Re: Fun With Numbers 2018: Pairwise, KRACH, GRaNT, and other mathematical excitement

                                Originally posted by TonyTheTiger20 View Post
                                Put another way -- Wisconsin's new (unadjusted) RPI would be:

                                {[UW's unadjusted RPI times (games played minus 1)]
                                Plus the RPI above for beating SCSU}
                                All divided by number of games played.

                                I'm on my phone multitasking so if that's wrong then oops lol... But I'm pretty sure that's right.
                                What about the other way? How much is losing to Wisconsin worth to St Cloud? Does the gain of 'opponents' and 'opponents-opponents' outweigh the hit to their own won-loss? Similar table?

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