H2H9 / Fun With Probabilities
- 26-July 21
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wheres_walto Offline
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 resultsLogan'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 DIVISIONAdventure 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 InspectorsI 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!
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