Dominion Strategy Forum
Dominion => Tournaments and Events => Dominion League => Topic started by: samath on April 08, 2018, 05:59:42 pm
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I'm calculating mid season forecasts of the league that simulate the outstanding games based on your rating. The results can be found here (https://docs.google.com/spreadsheets/d/1ZgimtlIsDx1B6SRNSxV0NyXeKubQe0KYITUjjaJ-7b8/edit#gid=1993822266). They show the expected number of points after the season and the probability of finishing 1st to 6th for each player. (A-Division accounts for the champion match when it comes to the win probability but not for the expected points.)
To show the evolution over time, there are graphs for each division (https://onedrive.live.com/?authkey=%21AFw4ne3wMFgQLKE&v=photos&id=4375584A8C199C03%21701&cid=4375584A8C199C03). They show the expected points for each player after each result that has been reported.
There are also graphs for each player (https://onedrive.live.com/?authkey=%21ACtc3mGUmoOX%2D0E&v=photos&id=4375584A8C199C03%21487&cid=4375584A8C199C03). They show the probability of finishing 1st to 6th, calculated after each day of the season.
The spreadsheet and graphs should be updated at least once daily.
Methodology:
All outstanding games are simulated 100,000 times. In each simulation, a player's skill is drawn from a normal distribution with mean mu and standard deviation phi as given by the current official leaderboard.
Tie probability is set to 2%, and the win probability is 98%/(1+exp(-(skill1+FPA-skill2))). FPA is the first player advantage set to 0.5 for each player in 3 of the 6 games. That corresponds to about a 60% win chance for the first player against an equal opponent.