Results 1 to 8 of 8

Thread: Standings and Probability Question

  1. #1
    LawMan's Avatar
    LawMan is offline
    Join Date
    Sep 2011
    Posts
    5,193
    Rep Power
    50

    Dobber Sports Superstar

    Default Standings and Probability Question

    With the end of the fantasy season our league has begun our annual evaluation of rules and consideration of rule tweaking. Our league setup is currently as follows: 12 teams in 3 divisions of 4, come playoffs the top-8 teams advance and the 3 divisional winners are given the top-3 seeds regardless of total number of points. It?s a one-year league and divisions are reset every year. Given this setup it often occurs where one weaker division emerges by random luck, at the same time one strong division occurs with 2 top teams, one which is forced to fall to the 4-seed. If the top-4 teams advance to the semi-finals this creates a situation where the 1-seed ends up playing a ?better? team (by record) than the 2-seed (#3 weak division champ).

    I was trying to calculate the percentages that the top 3 teams will each end up in a different division, thus no weak 3-seed. Is the below math correct?
    1. Chances #1 team wins division 1/1- has to happen by definition.
    2. Chances #2 team wins a different division 8/11 ? not in division 1.
    3. Chances #3 team wins the final division 4/10- not in division 1 or 2.
    1 x 8/11 x 4/10 = .290909

    The thinking is as follows:
    1. The #1 team in the league wins the division 1/1 times.
    2. The #2 team needs to be from the other 2 divisions 8-teams out of 11 left; and
    3. The #3 team needs to be from the final division 4-teams out of 10 left.
    4. All 3 of these things needs to occur so 1/1 x 8/11 x 4/10 = chance top 3 teams are in separate division.

    So, by my math there is only a 29% chance that the top-3 teams are in 3 separate divisions, and, accordingly a 71% chance that the #4 seed will have a better record than the #3 seed.

    Is the above analysis and calculation correct or am I approaching this probability problem incorrectly?
    12 team H-2-H 1 year league, daily roster changes, 3 goalie start minimum/week
    2xC, 2xRW, 2xLW, 4xD, 3xUtil, 2xG, 5 Bench
    G, A, P, PIM, PPP, SHP, GWG, SOG, Hits, W, SV%, GAA, SVs
    C: C. Keller, C. Mittelstadt, B. Nelson, R. Strome,
    LW: K. Connor, B. Tkachuk, J. Gaudreau, J. Marchessault, E. Rodrigues, A. Lafreniere
    RW: K. Fiala, J. Bratt, T. Jeannot V. Arvidsson
    D: R. Josi, J. Trouba, E. Gustafsson,
    G: L. Thompson, F. Gustavsson, V. Vanecek
    NO IR

  2. #2
    Location
    Stratford
    Rep Power
    19

    Dobber Sports Apprentice

    Default Re: Standings and Probability Question

    Does each team play ever other team twice during the season, or are there more intradivision matchups scheduled?
    Yahoo 12 team H2H Keeper (Keep 7 vets; 3 prospects (Skater < 201 GP; Goalie < 101GP)

    Categories: G, A, P, PIM, +/-, PPP, SOG, FW, Hits, Blocks, W, GAA, Sv% Saves

    Start 3LW, 3C, 3RW, 5D, 2G, 8Bn

    C: Crosby, RNH, Stepan, Faksa
    LW: Ovechkin, Benn, Jenner (c), Komarov (c, rw), Dano
    RW: Voracek (lw), Neal, Hornqvist, Silfverberg, Buchnevich (lw), Boeser
    D: Karlsson, Letang, Ellis, Muzzin, Slavin, Boychuk
    G: Price, Bernier, Grubauer, Pickard

  3. #3
    LawMan's Avatar
    LawMan is offline
    Join Date
    Sep 2011
    Posts
    5,193
    Rep Power
    50

    Dobber Sports Superstar

    Default Re: Standings and Probability Question

    Quote Originally Posted by PensInThree View Post
    Does each team play ever other team twice during the season, or are there more intradivision matchups scheduled?
    Everyone plays everyone the same number of times. For the sake of the probability issue assume the 12 teams are randomly disbursed.
    12 team H-2-H 1 year league, daily roster changes, 3 goalie start minimum/week
    2xC, 2xRW, 2xLW, 4xD, 3xUtil, 2xG, 5 Bench
    G, A, P, PIM, PPP, SHP, GWG, SOG, Hits, W, SV%, GAA, SVs
    C: C. Keller, C. Mittelstadt, B. Nelson, R. Strome,
    LW: K. Connor, B. Tkachuk, J. Gaudreau, J. Marchessault, E. Rodrigues, A. Lafreniere
    RW: K. Fiala, J. Bratt, T. Jeannot V. Arvidsson
    D: R. Josi, J. Trouba, E. Gustafsson,
    G: L. Thompson, F. Gustavsson, V. Vanecek
    NO IR

  4. #4
    Location
    Brampton, Ontario
    Rep Power
    40

    Dobber Sports Titan

    Default Re: Standings and Probability Question

    I think you are correct in your math. What I might advise as a fix, if you can actually implement this type of standing, is something similar to what the NBA used to do with each division winner in the conference (not sure if they still do or not). They ran into the same problem where a very strong team was stuck in the 4 seed, so they made it such that the top 4 seeds were the top 3 division winners, and the team with the next best record. If you have two teams in the same division with the two best records, they would still be seeded 1 and 2, with the other two division winners filling out the 3 and 4 slots. It would take a case of 3 teams in the same division having top 4 records to cause an incorrect balance in the standings. And in that case they would only then be 5th instead of 3rd/4th. So if you had the top 3 teams from the same division (a lot less likely) then you would have them seeded 1, 2 and 5. 3 and 4 still being filled out by the other two division winners. That way even if the third best record finishes in 5th, and should have finished 4th, he gets the same matchup anyways.
    Does that all make sense?
    Associate Editor for DobberHockey (Wednesdays). Click that Ramblings button on the the menu bar!
    (No I don't have a hockey problem...)

  5. #5
    Location
    Prairies
    Rep Power
    40

    Dobber Sports Demi-God

    Default Re: Standings and Probability Question

    I give the a math a thumbs up.
    It would be similar to putting 12 balls in a container: 4 blue, 4 red, 4 yellow.
    What are the chances you pull exactly 1 blue, 1 red, 1 yellow in 3 pulls?
    And I believe the math is exactly as you lay it out.
    29% seems about right.

    For fun, try this one from fivethirtyeight.org from a couple weeks ago - pretty good one for people that like numbers (and a great site for all things numbers, incl. sports):
    https://fivethirtyeight.com/features...math-problems/

  6. #6
    LawMan's Avatar
    LawMan is offline
    Join Date
    Sep 2011
    Posts
    5,193
    Rep Power
    50

    Dobber Sports Superstar

    Default Re: Standings and Probability Question

    Quote Originally Posted by Pengwin7 View Post
    I give the a math a thumbs up.
    It would be similar to putting 12 balls in a container: 4 blue, 4 red, 4 yellow.
    What are the chances you pull exactly 1 blue, 1 red, 1 yellow in 3 pulls?
    And I believe the math is exactly as you lay it out.
    29% seems about right.

    For fun, try this one from fivethirtyeight.org from a couple weeks ago - pretty good one for people that like numbers (and a great site for all things numbers, incl. sports):
    https://fivethirtyeight.com/features...math-problems/
    Thanks, that's how I approached the problem. I was surprised it was so unlikely so wanted confirmation.

    Just spent far too long on the Riddler problem attached. I will have to go back and check next week when the answer is revealed. Spoiler My answer to the Riddler problem below:

    The 2nd student's card has a 6. Highlight the white text to read.
    12 team H-2-H 1 year league, daily roster changes, 3 goalie start minimum/week
    2xC, 2xRW, 2xLW, 4xD, 3xUtil, 2xG, 5 Bench
    G, A, P, PIM, PPP, SHP, GWG, SOG, Hits, W, SV%, GAA, SVs
    C: C. Keller, C. Mittelstadt, B. Nelson, R. Strome,
    LW: K. Connor, B. Tkachuk, J. Gaudreau, J. Marchessault, E. Rodrigues, A. Lafreniere
    RW: K. Fiala, J. Bratt, T. Jeannot V. Arvidsson
    D: R. Josi, J. Trouba, E. Gustafsson,
    G: L. Thompson, F. Gustavsson, V. Vanecek
    NO IR

  7. #7
    Location
    Brampton, Ontario
    Rep Power
    40

    Dobber Sports Titan

    Default Re: Standings and Probability Question

    I'm pretty sure LawMan is right with his number. Only way I could make it work was with that one too.
    Associate Editor for DobberHockey (Wednesdays). Click that Ramblings button on the the menu bar!
    (No I don't have a hockey problem...)

  8. #8
    Location
    Stratford
    Rep Power
    19

    Dobber Sports Apprentice

    Default Re: Standings and Probability Question

    That's what I got too. Either of you take on the second question?
    Yahoo 12 team H2H Keeper (Keep 7 vets; 3 prospects (Skater < 201 GP; Goalie < 101GP)

    Categories: G, A, P, PIM, +/-, PPP, SOG, FW, Hits, Blocks, W, GAA, Sv% Saves

    Start 3LW, 3C, 3RW, 5D, 2G, 8Bn

    C: Crosby, RNH, Stepan, Faksa
    LW: Ovechkin, Benn, Jenner (c), Komarov (c, rw), Dano
    RW: Voracek (lw), Neal, Hornqvist, Silfverberg, Buchnevich (lw), Boeser
    D: Karlsson, Letang, Ellis, Muzzin, Slavin, Boychuk
    G: Price, Bernier, Grubauer, Pickard

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •