series win probability

probability.hs

import Data.List
import Control.Monad
import Data.Function

space = 10
ranks = [1..(space-1)]
matchResult rank = take 10 (take rank [1,1..] ++ [0,0..])

getPosterior::Int->Int->Int->Double
getPosterior wins losses rank  = matches/all where
   result = sequence.replicate (wins+losses).matchResult$rank
   all = fromIntegral.length$result
   condition x = sum x == wins
   matches = fromIntegral.length.filter condition$result
   
normalize::[Double]->[Double]
normalize a = map (/s) a where
   s = (sum a)

getProbability::Int->Int->Int->Double
getProbability games mustWin rank = wins/all where
   result = sequence.replicate games.matchResult$rank
   all = fromIntegral.length$result
   isWin x = sum x >= mustWin
   wins = fromIntegral.length.filter isWin$result

result wins losses toWinsWin  = sum.zipWith (*) posterior$probability where
   posterior = normalize.map (getPosterior wins losses)$ranks
   mustWin = toWinsWin - wins
   games = toWinsWin - losses - 1 + mustWin
   probability = map (getProbability games mustWin) ranks