Women’s World Cup (Spain v. USA): Will a CORNER KICK be TAKEN between the 30th and 40th MINUTE?

Yes: Corner kick taken during that time frame
No: Corner kick not taken during that time frame

Inputs Needed to Solve

##### User Estimates #####
Spain_Corners = 20/3
USA_Corners = 30/3

total_CK = Spain_Corners + USA_Corners

print("The expected total CORNER KICKS for the Match is %s" % round((total_CK),3))

The expected total CORNER KICKS for the Match is 16.0

## Inputs Defined in the Problem
Corner_Kicks = 0
time = 10

Method to Solve

Estimate lambda (expected CORNER KICKS per 10 minutes) and use the Poisson Distribution to compute the probabilty of zero CORNER KICKS being scored in the 30-40th Minute

lambda_ = total_CK * 10 / 90
print("The total expected CORNER KICKS a 10 minutes period is %s" % round((lambda_),3))

The total expected CORNER KICKS a 10 minutes period is 1.0

import math

p = math.exp(-lambda_)*(lambda_**Corner_Kicks)/(math.factorial(Corner_Kicks))

print("The probability of k events occuring in an Poisson interval = e^(-lambda) * ((lambda^k)/k!)")
print('where k = 0 and lambda = %s' % round(lambda_,2))
print("p = e^(-%s)*(%s^%s)/%s!" % (round(lambda_,2),round(lambda_,2),Corner_Kicks,Corner_Kicks))

The probability of k events occuring in an Poisson interval = e^(-lambda) * ((lambda^k)/k!)
where k = 0 and lambda = 1.0

p = e^(-1.0)*(1.0^0)/0!

print("The probability of %s CORNER KICKS in the 30th-40th Minute is %s" % (Corner_Kicks,round(p,3)))

The probability of 0 CORNER KICKS in the 30th-40th Minute is 0.368

Posted on 6/24/2019