Spanish Primera Division (Athletic Bilbao @ Mallorca): Will a GOAL be SCORED in the 75th Minute or Later?

4:30PM
Yes: 1+ goals in 75th minute or later
No: No goals in 75th minute or later ***

Inputs To Solve

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

match_over_under = 2.5

## Inputs Defined in the Problem

time_of_game = 20/95 # include extra time
goals = 0

Method to Solve

[1] Estimate lambda_goals - expected arrival rate of GOALS both teams in a 20 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 = match_over_under * time_of_game
print("lambda_goals ~ the total expected GOALS scored during 20m for both teams")
print("lambda_goals ~ %s * %s" % (round(match_over_under,3),round(time_of_game,3)))
print("lambda_goals ~ %s" % (round(lambda_goals,3)))

lambda_goals ~ the total expected GOALS scored during 20m for both teams
lambda_goals ~ 2.5 * 0.211
lambda_goals ~ 0.526

## [2]

import math

p_0 = math.exp(-lambda_goals)*(lambda_goals**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_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 occuring in an Poisson interval = e^(-lambda) * ((lambda^k)/k!)
where k = 0 and lambda = 0.526

p_0 = e^(-0.526) * (0.526^0)/0!

Solution

print("The probability Zero goals scored after the 75th Minute is ~%s" % round(p_0,3))

The probability Zero goals scored after the 75th Minute is ~0.591

Info

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Posted on 9/13/2019