2019 Africa Cup of Nations (Morocco v. Ivory Coast): Will the MATCH be 1-1 OR 2-2 at ANY POINT?

1:00PM BEIN
Yes: Match 1-1 or 2-2 at any point
No: Match never 1-1 or 2-2

Inputs Needed To Solve

##### User Estimates #####
expected_total_Goals = 2.25

## Inputs Defined in the Problem
Goals = [1,2]

Method to Solve

Estimate lambda_mor (estimated arrival rate of goals for Morocco)
Estimate lambda_ic (estimated arrival rate of goals for Ivory Coast)
Use Poisson Distribution to estimate - the probability of exactly 1 GOAL being SCORED by each team - the probability of exactly 2 GOALs being SCORED by each team
The probability that the MATCH is 1-1 is the probability that Morocco scores exactly one goal multiplied by the probability that Ivory Coast scores exactly one goal
The probability that the MATCH is 2-2 is the probability that Morocco scores exactly 2 goals multiplied by the probability that Ivory Coast scores exactly 2 goals
The probability that either occur is the probability the MATCH is 1-1 plus the probability the MATCH is 2-2.

lambda_mor = expected_total_Goals / 2
lambda_ic = expected_total_Goals / 2

print("lambda_mor ~%s" % (round(lambda_mor,3)))
print("lambda_ic ~%s" % (round(lambda_ic,3)))

lambda_mor ~1.125
lambda_ic ~1.125

import math

p = math.exp(-lambda_mor)*(lambda_mor**Goals[0])/(math.factorial(Goals[0]))

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_mor,3))
print('')
print("p = e^(-%s)*(%s^%s)/%s!" % (round(lambda_mor,3),round(lambda_mor,3),Goals[0],Goals[0]))
print("The probability that a team will score exactly one goal is %s" % round(p,3))
p_11 = p*p
print('')
print("The probability that the MATCH is 1-1 is %s" % round(p_11,3))

The probability of k events occurring in an Poisson interval = e^(-lambda) * ((lambda^k)/k!)
where k = 0 and lambda = 1.125

p = e^(-1.125)*(1.125^1)/1!
The probability that a team will score exactly one goal is 0.365

The probability that the MATCH is 1-1 is 0.133

p = math.exp(-lambda_mor)*(lambda_mor**Goals[1])/(math.factorial(Goals[1]))

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_mor,3))
print('')
print("p = e^(-%s)*(%s^%s)/%s!" % (round(lambda_mor,3),round(lambda_mor,3),Goals[1],Goals[1]))
print("The probability that a team will score exactly 2 goals is %s" % round(p,3))
p_22 = p*p
print('')
print("The probability that the MATCH is 2-2 is %s" % round(p_22,3))

The probability of k events occurring in an Poisson interval = e^(-lambda) * ((lambda^k)/k!)
where k = 0 and lambda = 1.125

p = e^(-1.125)*(1.125^2)/2!
The probability that a team will score exactly 2 goals is 0.205

The probability that the MATCH is 2-2 is 0.042

Solution

print("The probability that the MATCH is 1-1 OR 2-2 at ANY POINT is %s" % round(p_11+p_22,3))

The probability that the MATCH is 1-1 OR 2-2 at ANY POINT is 0.176

Posted on 6/28/2019