MLS All-Star Game (Atletico Madrid v. MLS All-Stars - Orlando, FL): Will a GOAL be SCORED in the FIRST 20 MINUTES?

8:05 PM
Yes: Goal scored in first 20 minutes
No: 0 Goals in first 20 minutess

Inputs Needed to Solve

##### User Estimates #####
expected_G_Per_Game = 3.5
# over / under

## Inputs Defined in the Problem
GOALS = 0
time = 20

Method to Solve

Estimate lambda (arrival rate of GOALS per 20 minutes)
Use the Poisson Distribution to compute the probability of zero CORNER KICKS being scored in the FIRST 10 Min

lambda_ = float(expected_G_Per_Game * time) / 90
print("The total expected GOALS a 20 minute period is %s" % round((lambda_),3))

The total expected GOALS a 20 minute period is 0.778

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

The probability of k events occuring in an Poisson interval = e^(-lambda) * ((lambda^k)/k!)
where k = 0 and lambda = 0.778

p = e^(-0.778) * (0.778^0)/0!

print("The probability of %s GOALS in the FIRST 20 Minutes is %s" % (GOALS,round(p,3)))

The probability of 0 GOALS in the FIRST 20 Minutes is 0.459

Posted on 7/31/2019