College World Series (#3 Michigan v. #1 Vanderbilt): How many STRIKEOUTS will be recorded in the 1st Inning?

Inputs To Solve

Strike Outs per Innings Pitched by starting pitcher

##### User Estimates #####
Kauf_KperInning = 106/(127+(2/3))
Hick_KperInning = 119/(90+(2/3))

print("Kauffmann's Ks per Inning is %s" % round(Kauf_KperInning,3))
print("Hickman's Ks per Inning is %s" % round(Hick_KperInning,3))

expected_KperInning = Kauf_KperInning + Hick_KperInning
print('')
print("Use %s as total expected Ks per Inning." % (round(expected_KperInning,2)))

Kauffmann’s Ks per Inning is 0.83
Hickman’s Ks per Inning is 1.312

Use 2.14 as total expected Ks per Inning.

## Inputs Defined in the Problem
period_of_innings = 1
Ks_ = 2

Method to Solve

Estimate lambda (arrival rate - Ks per inning)
Use lambda and Poisson Distribution to estimate the probability of 2 or fewer Ks being recorded in any innings:

lambda_ = expected_KperInning

print("lambda = the total expected Ks recorded by both pitchers over one innings")
print("lambda ~ %s" % (round(lambda_,3)))

lambda = the total expected Ks recorded by both pitchers over one innings
lambda ~ 2.143

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] and lambda = %s" % round(lambda_,3))
print(' ')

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

print(' ')
print(str_)

The probability of k events occurring in a Poisson interval = e^(-lambda) * (lambda^k)/k!
where k = [0,1,2] and lambda = 2.143

e^(-2.14) * (2.14^1)/1! +
e^(-2.14) * (2.14^2)/2! +
e^(-2.14) * (2.14^3)/3!

0.251 + 0.269 + 0.192

Solution

print("The probability of 2 or less Ks being recorded in an inning is ~ %s" % (round(five_or_less,2)))

The probability of 2 or less Ks being recorded in an inning is ~ 0.71

Posted on 6/26/2019