EPL (Manchester City @ Chelsea): Will a GOAL be SCORED during the 60th through 75th MINUTE?

4:31 PM
Yes: Goal scored during 60-75th minute
No: No goals during 60-75th minute

Inputs Needed to Solve

##### User Estimates #####
expected_G_Per_Game = 2.5
# 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 CORNER KICKS being scored in the FIRST 10 Min

## [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 0.417

## [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 = 0.417

p = e^(-0.417) * (0.417^0)/0!

Solution

print("The probability of %s GOALS in the 60th through 75th MINUTE is %s" % (GOALS,round(p,3)))

The probability of 0 GOALS in the 60th through 75th MINUTE is 0.659

Info

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Posted on 6/25/2020