EPL (Manchester United @ Wolves): Will a CORNER KICK be TAKEN from EVERY CORNER in the 1st Half?

3:00PM
Yes: Corner taken from all 4 corners in 1H
No: No corner kick taken from at least 1 corner in 1H

Inputs To Solve

Corner Kicks by Club for 2018-2019 Season

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

MU_CKperG = 200/39
Wol_CKperG = 195/38

total_CKs = MU_CKperG + Wol_CKperG

print("The total expected CKs for Manchester United is %s" % round(MU_CKperG,3))
print("The total expected CKs for the Wolves is %s" % round(Wol_CKperG,3))
print('')
print("The total expected CKs for the match is %s" % round(total_CKs,3))

The total expected CKs for Manchester United is 5.128
The total expected CKs for the Wolves is 5.132

The total expected CKs for the match is 10.26

## Inputs Defined in the Problem

time_of_game = .5

Method to Solve

[1] Estimate lambda_ck - expected arrival rate of Corner Kick over 1 half for both teams
[2] Use the Monte Carlo Method to simualte 9999 1st Halfs with lambda_ck and the Poisson Distribution as an estimate for how many CORNER KICKS will attempted in each simulation. Randomly assign each CORNER KICK to a corner 0-3. The ratio of simulations that contain all four corners 0-3 to the total number of simulations is an estimate of the probability that there are CORNER KICKS attempted from all four corners (p_ALL4)

## [1]

lambda_ck = total_CKs * time_of_game
print("lambda_ck ~ the total expected CORNER KICKS attepmted over 1 half for both teams")
print("lambda_ck ~ %s * %s" % (round(total_CKs,3),time_of_game))
print("lambda_ck ~ %s" % (round(lambda_ck,3)))

lambda_ck ~ the total expected CORNER KICKS attepmted over 1 half for both teams
lambda_ck ~ 10.26 * 0.5
lambda_ck ~ 5.13

## [2]

import numpy as np

iterations = 9999

ans = 0
for j in range(iterations):

    corners = ''
    for i in range(1,int(np.random.poisson(lambda_ck,1))):
        c = str(int(np.random.choice([0,1,2,3],1)))
        corners += c

    corners
    if '0' in corners and '1' in corners and '2' in corners and '3' in corners:
        ans += 1

p_ALL4 = ans/iterations

Solution

print("The probability a CORNER KICK is taken from EVERY CORNER in the 1st HALF is ~%s" % round(p_ALL4,3))

The probability a CORNER KICK is taken from EVERY CORNER in the 1st HALF is ~0.182

Info

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email: krellabsinc@gmail.com
twitter: @KRELLabs

import sys
print(sys.version)

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

Posted on 8/19/2019