H2H9 / Fun With Probabilities

  • wheres_walto%s's Photo

    I'm a stats nerd by profession and today I got bored, so I decided to examine team results through the lens of vote distributions. Basically, this is a calculation of "for an average voter, how many times should we expect that they had voted for a specific club, given the distribution of votes cast by other members?" So for example, someone voting against the Tile Inspectors in each match to this point would have had a roughly 1-in-70 percent chance of occurring organically through five rounds. 

     

    Alternatively, this is a way to answer "what is the distribution of expected wins for each club, given their match results?" I probably should have waited until the end of round 6 but here we are.

     

     

    EAST DIVISION

     

    Cereal Killers

    5 wins: 1.8% (1 in 54)

    4 wins: 14.4%

    3 wins: 33.7%

    2 wins: 33.3%

    1 win: 14.5%

    0 wins: 2.3% (1 in 44)

    Actual Wins: 3

    Match Outcomes: 53.2%, 61.5%, 43.8%, 72.7%, 17.7%

    - Beautiful standard normal distribution, two somewhat extreme matches but otherwise balanced results

     

    Logan's Run

    5 wins: 4.5%

    4 wins: 20.2%

    3 wins: 34.8%

    2 wins: 28.4%

    1 win: 10.7%

    0 wins: 1.4% (1 in 72)

    Actual Wins: 2

    Match Outcomes: 48.2%, 79.2%, 56.2%, 45.6%, 46.0%

    - a convincing victory raises their floor, but four tight matches means there's a lot of randomness, signified by a 1-3 record in tight votes so far

     

    Scream Queens

    5 wins: 0.4% (1 in 264)

    4 wins: 4.8%

    3 wins: 20.1%

    2 wins: 36.5%

    1 win: 29.6%

    0 wins: 8.7%

    Actual Wins: 2

    Match Outcomes: 51.8%, 38.5%, 13.6%, 25.8%, 54.0%

    - some bad losses with no strong victories yet, they're about where we'd expect given those results

     

     

    WEST DIVISION
     

    Adventure Club

    5 wins: 6.7%

    4 wins: 30.2%

    3 wins: 40.1%

    2 wins: 19.6%

    1 win: 3.3%

    0 wins: 0.2% (1 in 600)

    Actual Wins: 3

    Match Outcomes: 49.4%, 63.0%, 86.4%, 27.3%, 91.0%

    - strongest team of the contest so far by match results, two dominant wins and a one-vote loss skew their outcomes

     

    Tile Inspectors

    5 wins: 1.3% (1 in 79)

    4 wins: 12.0%

    3 wins: 35.8%

    2 wins: 36.6%

    1 win: 13.0%

    0 wins: 1.4% (1 in 70)

    Actual Wins: 3

    Match Outcomes: 50.7%, 20.8%, 19.7%, 74.2%, 82.4%

    - four blowouts in five matches keeps the tails thin, a one-vote margin in round one could have easily flipped the other way

     

    Manual Laborers

    5 wins: 0.7% (1 in 147)

    4 wins: 9.6%

    3 wins: 30.6%

    2 wins: 37.7%

    1 win: 18.7%

    0 wins: 2.7%

    Actual Wins: 2

    Match Outcomes: 46.8%, 37.0%, 80.3%, 54.4%, 9.0%

    - one dominant win, one dominant loss, they skew toward the lower end, but not significantly different than the Tile Inspectors
     
     
    I think this is a good way of showing just how evenly matched this season has been. Logan's Run has been the unluckiest team so far, but I hesitate to say that any one team has gotten unusually lucky by vote results. It's truly anyone's game at this point!
     

     

     

  • saxman1089%s's Photo

    This is cool, thanks for putting it together!

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