MLS is Back Tournament (Philadelphia Union v. Orlando City SC): Will a GOAL be SCORED in the 80th MINUTE or LATER?

9:45 PM
Yes: Goal in 80th minute or later
No: No Goal in 80th minute or later

Inputs Needed to Solve

##### User Estimates #####
expected_G_Per_Game = 3
# over / under

## Inputs Defined in the Problem
GOALS = 0
time = 15

Method to Solve

[1] Estimate lambda (l_) (arrival rate of GOALS per 15 minutes)
[2] Use the Poisson Distribution to compute the probability of zero GOALS being scored in the 80th Minute or later.

## [1]

l_ = float(expected_G_Per_Game * time) / 90
print("The total expected GOALS a 15 minute period is %s" % round((l_),3))

The total expected GOALS a 15 minute period is 0.5

## [2]

import math

p = math.exp(-l_)*(l_**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(l_,3))
print('')
print("p = e^(-%s) * (%s^%s)/%s!" % (round(l_,3),round(l_,3),GOALS,GOALS))

The probability of k events occuring in an Poisson interval = e^(-lambda) * ((lambda^k)/k!)
where k = 0 and lambda = 0.5

p = e^(-0.5) * (0.5^0)/0!

Solution

print("The probability of %s GOALS in the 80th Minute or Later is %s" % (GOALS,round(p,3)))

The probability of 0 GOALS in the 80th Minute or Later is 0.607

Info

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import sys
print(sys.version)

3.6.5 (v3.6.5:f59c0932b4, Mar 28 2018, 16:07:46) [MSC v.1900 32 bit (Intel)]

Posted on 7/20/2020