CONCACAF Gold Cup - Qtrs (Panama v. Jamaica - Philadelphia, PA): How many CORNER KICKS will be TAKEN in the 1st Half?

5:35PM FS1
4 Corners or Fewer
5 Corners or More

Inputs Needed to Solve

Corners per Game by team (Panama and Jamaica)

##### User Estimates #####
P_CperGame = 5
J_CperGame = 8

total_Corners = P_CperGame + J_CperGame

print("The total expected Corner Kicks for the game is %s" % total_Corners)

The total expected Corner Kicks for the game is 13

## Inputs Defined in the Problem
half_ = 1
Corners = 4

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Method to Solve

• Estimate lambda (expected Corner Kicks per Half)
• Use the Poisson Distribution to compute the probability of 4 Corner Kicks or Fewer taken in the 1st Half.

lambda_ = total_Corners * half_ / 2
print("lambda = the total expected Corner Kicks by both teams in one half")
print("lambda = %s * %s / %s" % (round(total_Corners,2),half_,2))
print("lambda ~ %s" % (round(lambda_,2)))

lambda = the total expected Corner Kicks by both teams in one half
lambda = 13.0 * 1 / 2
lambda ~ 6.0

import math
str_ = ""
print("The probability of k events occurring in a Poisson interval = e^(-lambda) * (lambda^k)/k!")
print("where k = [0,1,2,3,4]")
print(' ')

p = 0
for i in range(Corners+1):
    p += math.exp(-lambda_)*(lambda_**(i))/(math.factorial(i))
    
    if(i<Corners):
        str_ += str(round(math.exp(-lambda_)*(lambda_**(i))/(math.factorial(i)),3)) + " + "
        print("e^(-%s) * (%s^%s)/%s! + " % (round(lambda_,2),round(lambda_,2),(i),(i)))
    else:
        str_ += str(round(math.exp(-lambda_)*(lambda_**(i))/(math.factorial(i)),3))
        print("e^(-%s) * (%s^%s)/%s!" % (round(lambda_,2),round(lambda_,2),(i),(i)))

print(' ')
print(str_)

The probability of k events occurring in a Poisson interval = e^(-lambda) * (lambda^k)/k!
where k = [0,1,2,3,4]
 
e^(-6.0) * (6.0^0)/0! + 
e^(-6.0) * (6.0^1)/1! + 
e^(-6.0) * (6.0^2)/2! + 
e^(-6.0) * (6.0^3)/3! + 
e^(-6.0) * (6.0^4)/4!
 
0.002 + 0.015 + 0.045 + 0.089 + 0.134

print("The probability of 4 or Fewer Corner Kicks taken in the 1st Half is %s" % (round(p,3)))

The probability of 4 or Fewer Corner Kicks taken in the 1st Half is 0.285

Posted on 6/30/2019