Generic Series Probabilities

generic_seriesProbs.py

## calculate the probability of winning a series, 
## given p(winning single game) and current score

## Granger Huntress
## based on Jeff Sackmann's gameProb code 
## (https://gist.github.com/JeffSackmann/768862)


def fact(x):
    if x in [0, 1]:  return 1
    r = 1
    for a in range(1, (x+1)):  r = r*a
    return r
 
def ch(a, b):
    return fact(a)/(fact(b)*fact(a-b))

def seriesOutcome(s, a, b):
    return ch((a+b), a)*(s**a)*((1-s)**b)*s

def seriesProb(s, v=0, w=0, g=1):
    ## function calculates the probability of team(s) winning
    ## a series, given p(winning a given game) [s],
    ## and the current series score.
    ## v, w = current series score
    ## [g] is the number of games to clinch the series


    ## check if series is clinched:
    win = []
    if v == g:
        return 1,0
    elif w == g:
        return 0,1
    else:   pass
    ## specific probabilities on favorite side:
    for i in range(g):
        vMax = g-1
        if ((g-1 != v or g-1 != w) and w<=i):
            win.append(seriesOutcome(s, vMax-v, i-w))
        elif g-v != 1 or g-w != 1:
            win.append(0)

    lose = []
    ## specific probabilities on the dog side:
    for i in range(g):
        wMax = g-1
        if ((g-1 != v or g-1 != w) and v<=i):
            lose.append(seriesOutcome(1-s, wMax-w, i-v))
        elif g-v != 1 or g-w != 1:
            lose.append(0)

    
    ## if we get to the final game
    if g-v == 1 and g-w == 1:
        a = 0
        b = 0
        d = ch((a+b), a)*(s**a)*((1-s)**b)

        win.append(d*s)
        lose.append(d*(1-s))


    
    ## returns the individual series probabilities
    ## as well as the total for every possible outcome
    ## the sum part can be eliminated, as it is just a sanity
    ## check to make sure it all works
    return win,sum(win),lose,sum(lose)

print seriesProb(.54,0,0,4)
## for the example seriesProb(.54,0,0,4), where team A has a 54%
## chance to win a particular game, the series is just beginning
## and it is a best of 7 series.

## this will return probability Team A exactly wins 4-0, 4-1, 4-2, 4-3
## then the total probability Team A wins the series
## then the probability Team A loses the series exactly 0-4, 1-4, 2-4, 3-4
## and the overall probability they lose the series