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UEL(Gent@Larnaca/Wolves@Pyunik/Trabzonspor@Sp. Prague): Will ANY of these 3 MATCHES have EXACTLY 3 GOALS SCORED?

11:30AM
Yes: At least 1 match has exactly 3 goals scored
No:  None have exactly 3 goals scored

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Inputs Needed To Solve

Over / Under for the Matches - Expected Goals Scored

##### User Estimates #####
expected_goals_scored_per_match = 2.5

## Inputs Defined in the Problem
goals = 3
num_of_matches = 3

Method To Solve

• [1] Use expected goals per match as lambda (expected arrival rate of goals per match)
• [2] Use Poisson Distribution and lambda to estimate the probability of three goals being scored (p_3) in any one match
• [3] The probability there are no matches with exactly three goals (p_no3goalmatch) scored is (1-p_3)^(num_of_matches)

## [1]

lambda_ = expected_goals_scored_per_match

## [2]

import math

p_3 = math.exp(-lambda_)*(lambda_**goals)/(math.factorial(goals))

print("The probability of k events occurring in an Poisson interval = e^(-lambda) * (lambda^k)/k!")
print('where k = 3')
print(' ')
print("p_3 = e^(-%s)*(%s^%s)/%s!" % (round(lambda_,3),round(lambda_,3),goals,goals))
print('')
print("The probability there are exactly 3 goals scored in a match is %s" % round(p_3,3))

The probability of k events occurring in an Poisson interval = e^(-lambda) * (lambda^k)/k!
where k = 3

p_3 = e^(-2.5)*(2.5^3)/3!

The probability there are exactly 3 goals scored in a match is 0.214    

## [3]

p_no3goalmatch = (1-p_3)**3

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Solution

print("The probability NONE of these 3 MATCHES will have EXACTLY 3 GOALS SCORED is ~%s" % round(p_no3goalmatch,3))

The probability NONE of these 3 MATCHES will have EXACTLY 3 GOALS SCORED is ~0.486

Posted on 8/8/2019