WNBA (Sky @ Sun): Which TEAM will be the FIRST to SCORE 15 POINTS?

7:02 PM
Sky: First to 15 Points
Sun: First to 15 Points

Inputs Needed to Solve

Expected Points by Team (Sky and Sun)

##### User Estimates #####

# over / under
expected_points = 170

# spread (sun favored)
expected_point_difference = 3 

sky_expected_points = (expected_points - expected_point_difference)/2
sun_expected_points = expected_points - sky_expected_points

print("The expected points scored by the Sky is %s" % round(sky_expected_points,3))
print("The expected points scored by the Sun is %s" % round(sun_expected_points,3))

The expected points scored by the Sky is 83.0
The expected points scored by the Sun is 87.0

## Inputs Defined in the Problem
first_to = 15

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Method to Solve

• estimate lambda_sky (arrival rate of points for Sky)
• estimate lambda_sun (arrival rate of points for Sun)
• Use the Poisson Distribution assumptions and the below equation to compute the probability of Guadalajara scoring before Fiorentina given at least one happens.

lambda_sky = sky_expected_points
lambda_sun = sun_expected_points

import math

n = first_to
m = first_to

p = 0
for k in range(n,n+m):
    ans = math.factorial(n+m-1)/(math.factorial((n+m-1)-k)*math.factorial(k))
    ans1 = (lambda_sky/(lambda_sky+lambda_sun))**k
    ans2 = (lambda_sun/(lambda_sky+lambda_sun))**(n+m-1-k)
    p += (ans*ans1*ans2)

print("The probability that the Sky score 15 Points First is %s" % (round(p,3)))

The probability that the Sky score 15 Points First is 0.0

Posted on 7/30/2019