EPL (Manchester United @ Wolves): Will a GOAL be SCORED during the 70th-85th MINUTE?

4:27PM
Yes: Goal scored during 70-85th minute
No: No goal scored during the 70-85th minute

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Inputs To Solve

Goals per Game by Club for 2018-2019 Season

##### User Estimates #####

MU_GperG = 65/39
Wol_GperG = 47/38

total_GOALs = MU_GperG + Wol_GperG

print("The total expected GOALS for Manchester United is %s" % round(MU_GperG,3))
print("The total expected GOALS for the Wolves is %s" % round(Wol_GperG,3))
print('')
print("The total expected GOALS for the match is %s" % round(total_GOALs,3))

The total expected GOALS for Manchester United is 1.667
The total expected GOALS for the Wolves is 1.237

The total expected GOALS for the match is 2.904

## Inputs Defined in the Problem

time_of_game = 15/90
goals = 0

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Method to Solve

• [1] Estimate lambda_goals - expected arrival rate of GOALS both teams in a 15 minute span.
• [2] Use the lambda_goals and the Poisson Distribution to compute the probability of ZERO goals being scored in the 70-85 minute of the match (p_0)

## [1]

lambda_goals = total_GOALs * time_of_game
print("lambda_goals ~ the total expected GOALS scored during 15m for both teams")
print("lambda_goals ~ %s * %s" % (round(total_GOALs,3),round(time_of_game,3)))
print("lambda_goals ~ %s" % (round(lambda_goals,3)))

lambda_goals ~ the total expected GOALS scored during 15m for both teams
lambda_goals ~ 2.904 * 0.167
lambda_goals ~ 0.484

## [2]

import math

p_0 = math.exp(-lambda_goals)*(lambda_goals**goals)/(math.factorial(goals))

print("The probability of k events occurring in an Poisson interval = e^(-lambda) * ((lambda^k)/k!)")
print('where k = 0 and lambda = %s' % round(lambda_goals,3))
print('')
print("p_0 = e^(-%s) * (%s^%s)/%s!" % (round(lambda_goals,3),round(lambda_goals,3),goals,goals))

The probability of k events occurring in an Poisson interval = e^(-lambda) * ((lambda^k)/k!)
where k = 0 and lambda = 0.484

p_0 = e^(-0.484) * (0.484^0)/0!

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Solution

print("The probability Zero goals scored in the 70-85th minute is ~%s" % round(p_0,3))

The probability Zero goals scored in the 70-85th minute is ~0.616

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Info

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3.6.5 |Anaconda, Inc.| (default, Mar 29 2018, 13:32:41) [MSC v.1900 64 bit (AMD64)]

Posted on 8/19/2019