CONCACAF Gold Cup (Cuba v. Mexico - Pasadena, CA): When will the FIRST GOAL of the 1st Half be SCORED?

19th Minutes or Earlier
20th Minute or Later or No Goals Scored

Inputs Needed to Solve

##### User Estimates #####
expected_goals = 4.5

print("The expected total goals for the Match is %s" % round((expected_goals),3))

The expected total goals for the Match is 4.5

## Inputs Defined in the Problem
goals = 0

Method to Solve

Estimate lambda (expected goals per 19 minutes) and use the Poisson Distribution to compute the probabilty of zero goals being scored in the 1st 19 Minutes
The probability of a goal being scored in the first 19th minute compared to after is the ratio of time in the first interval compared to the second interval (based on Poisson assumptions)

lambda_ = expected_goals / 2
print("The total expected goals for the 1st HALF is %s" % round((lambda_),3))

The total expected goals for the 1st HALF is 2.25

import math

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

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),goals,goals))
print("The probability of %s goals being scored in the 1st HALF is %s" % (goals,round(p,3)))

The probability of k events occuring in an Poisson interval = e^(-lambda) * ((lambda^k)/k!)
where k = 0 and lambda = 2.25
p = e^(-2.25)*(2.25^0)/0!
The probability of 0 goals being scored in the 1st HALF is 0.105

p1 = 1 - p
p_19 = 19*p1/45

print("The probability of the FIRST GOAL being scored in the first 19 minutes of the 1st HALF is %s" % round(p_19,3))

The probability of the FIRST GOAL being scored in the first 19 minutes of the 1st HALF is 0.378

Posted on 6/15/2019