International Champions Cup (Bayern Munich v. Arsenal - Los Angeles, CA): Will a CORNER KICK be TAKEN in the FIRST 10 MINS?

11:05
Yes: Corner Kick taken in first 10 minutes
No: No Corner Kick taken in first 10 minutes

Inputs Needed to Solve

Expected CORNER KICKS for the game

##### User Estimates #####
Bayer_CornersperGame = 9
Arsenal_CornersperGame = 7

total_CK = Bayer_CornersperGame + Arsenal_CornersperGame

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 (arrival rate of CORNER KICKS per 10 minutes)
Use the Poisson Distribution to compute the probability of zero CORNER KICKS being scored in the FIRST 10 Min

lambda_ = float(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 1.778

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_,3))
print('')
print("p = e^(-%s)*(%s^%s)/%s!" % (round(lambda_,3),round(lambda_,3),Corner_Kicks,Corner_Kicks))

The probability of k events occuring in an Poisson interval = e^(-lambda) * ((lambda^k)/k!)
where k = 0 and lambda = 1.778

p = e^(-1.778)*(1.778^0)/0!

print("The probability of %s CORNER KICKS in the FIRST 10 Min is %s" % (Corner_Kicks,round(p,3)))

The probability of 0 CORNER KICKS in the FIRST 10 Min is 0.169

Posted on 7/18/2019