Question

Working with python 2.7.

The following code allows me to input the winning percentage of two teams (WP_1 and WP_2) a number of wins (k) and determine given the two team’s winning percentages, the probability that team one will have more wins at the end of the season (Playoff_Probability):

def PlayoffProb(WP_1, k, WP_2):
    TProb_2 = 0
    p = float(WP_1)/1000
    q = float(WP_2)/1000
    n = 162.0
    G = math.factorial(n)/(math.factorial(k)*math.factorial(n-k))
    Prob = G*(p**k)*((1-p)**(n-k))
    for c in range(0, k):
        G_2 = math.factorial(n)/(math.factorial(c)*math.factorial(n-c))
        Prob_2 = G_2*(q**c)*(1-q)**(n-c)
        TProb_2 += Prob_2
    Playoff_Probability = Prob*TProb_2
    print Playoff_Probability
    print TProb_2

But what would be a lot easier is if the function could be written recursively so that it would perform the same operation over every possible value of k and return the total probability of ending the season with more wins (which I believe should be given by the Playoff_Probability for each value run through the function of k, which I’ve tried to set equal to Total_Playoff_Probability).

I’ve tried the following code, but I get a TypeError telling me that ‘float’ object is not callable at the return Total_Playoff_Probability step. I’m also not at all sure that I’ve set up the recursion appropriately.

def PlayoffProb2(WP_1, k, WP_2):
    TProb_2 = 0
    Total_Playoff_Probability = 0
    p = float(WP_1)/1000
    q = float(WP_2)/1000
    n = 162.0
    G = math.factorial(n)/(math.factorial(k)*math.factorial(n-k))
    Prob = G*(p**k)*((1-p)**(n-k))
    for c in range(0, k):
        G_2 = math.factorial(n)/(math.factorial(c)*math.factorial(n-c))
        Prob_2 = G_2*(q**c)*(1-q)**(n-c)
        TProb_2 += Prob_2
    Playoff_Probability = Prob*TProb_2
    Total_Playoff_Probability += Playoff_Probability 
    if k == 162:
        return Total_Playoff_Probability
    else:
        return PlayoffProb2(WP_1, k+1, WP_2)

Any help would be greatly appreciated!

Answer 1

  return Total_Playoff_Probability(WP_1, k+1, WP_2)

I think you meant

  return PlayoffProb2(WP_1, k+1, WP_2)

You’ve got that error because you are trying to treat a floating point number as a function. Obviously, that doesn’t compute.

EDIT

Actually, it should be:

   return Total_Playoff_Probability + PlayoffProb2(WP_1, k+1, WP_2)

As it is, you aren’t doing anything with Total_Playoff_Probability after you calculate it. If k != 167, you just return the value for k+1.