MLB (Yankees @ Tigers): Will a HIT be recorded in the TOP of the 4th Inning?

2:10PM
Yes: At least 1 hit in Top of 4th Inning
No: No hits in Top of 4th Inning

Inputs To Solve

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

NYY_HperG = 9.27

## Inputs Defined in the Problem
period_of_innings = 1
HITS = 0

Method to Solve

[1] Estimate lambda_h - expected arrival rate of a HIT over 1 Inning for the Yankees
[2] Use the Poisson Distribution to compute the probability of 0 HITS recorded in the 4TH Inning for NYY (p0)

## [1]

lambda_h = NYY_HperG * period_of_innings / 9
print("lambda_h = the total expected XBH over %s innings" % period_of_innings)
print("lambda_h = %s * %s / %s" % (round(NYY_HperG,3),period_of_innings,9))
print("lambda_h ~ %s" % (round(lambda_h,3)))

lambda_h = the total expected XBH over 1 innings
lambda_h = 9.27 * 1 / 9
lambda_h ~ 1.03

## [2]

import math

p0 = math.exp(-lambda_h)*(lambda_h**HITS)/(math.factorial(HITS))

print("The probability of k events occuring in an Poisson interval = e^(-lambda) * ((lambda^k)/k!)")
print('where k = 0 and lambda = %s' % round(lambda_h,3))
print('')
print("p0 = e^(-%s) * (%s^%s)/%s!" % (round(lambda_h,2),round(lambda_h,2),HITS,HITS))

The probability of k events occuring in an Poisson interval = e^(-lambda) * ((lambda^k)/k!)
where k = 0 and lambda = 1.03

p0 = e^(-1.03) * (1.03^0)/0!

Solution

print("The probability that there are no HITS in the top of the 4th Inning is ~%s" % round(p0,3))

The probability that there are no HITS in the top of the 4th Inning is ~0.357

Info

download md file
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 9/12/2019