English Premier League (Manchester United @ Brighton): When will the FIRST GOAL of the 1st HALF be SCORED?

3:15 PM
25th Minute or Earlier
26th Minute or Later OR No Goal in 1st Half

Inputs to Solve

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

expected_G_Per_Game = 2.5
# over / under

## Inputs Defined in the Problem

GOALS = 0
time = 25

Method to Solve

[1] Estimate lambda (l_) (arrival rate of GOALS per 25 minutes)
[2] Use the Poisson Distribution to compute the probability of zero GOALS SCORED in the FIRST 25 MINUTES (p_0_25)
[3] 1 - p_0_25 is the probability that the first goal is scored after the 25th minute or their are no goals in the 1st half (p_25_none)

## [1]

l_ = float(expected_G_Per_Game * time) / 90
print("The total expected GOALS in a 25 minute period is %s" % round((l_),3))

The total expected GOALS in a 25 minute period is 0.694

## [2]

import math

p_0_25 = 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_0_25 = e^(-%s) * (%s^%s)/%s!" % (round(l_,3),round(l_,3),GOALS,GOALS))
print('')
print("The probability of zero GOALS SCORED in the FIRST 25 MINUTES is %s" % round(p_0_25,3))

The probability of k events occuring in an Poisson interval = e^(-lambda) * ((lambda^k)/k!) where k = 0 and lambda = 0.694

p_0_25 = e^(-0.694) * (0.694^0)/0!

The probability of zero GOALS SCORED in the FIRST 25 MINUTES is 0.499

## [3]

p_25_none = 1 - p_0_25

Solution

print("The probability of the FIRST GOAL of the FIRST HALF SCORED after the 25th Minute or NO GOALS scored is %s" % round(p_25_none,3))

The probability of the FIRST GOAL of the FIRST HALF SCORED after the 25th Minute or NO GOALS scored is 0.501

Info

download markdown file
email: krellabsinc@gmail.com
twitter: @KRELLabs

import sys
print(sys.version)

3.6.5 (v3.6.5:f59c0932b4, Mar 28 2018, 16:07:46) [MSC v.1900 32 bit (Intel)]

Posted on 6/30/2020