MLB (Red Sox @ Indians): Will there be a HOME RUN hit during INNINGS 4-6?

8:10PM
Yes: 1+ HR hit during Innings 4-6
No: 0 HR hit during Innings 4-6

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Inputs To Solve

HR per Game by Team (Red Sox and Indians)

##### User Estimates #####
BOS_HRperG = 1.55
CLE_HRperG = 1.33

expected_total_HR = BOS_HRperG + CLE_HRperG

print("Use %s + %s = %s as total expected HR hit in the game." % (round(BOS_HRperG,3),round(CLE_HRperG,3),round(expected_total_HR,3)))

Use 1.55 + 1.33 = 2.88 as total expected HR hit in the game.     

## Inputs Defined in the Problem
period_of_innings = 3
HR = 0

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Method to Solve

• [1] Estimate lambda - expected arrival rate of HR for 3 Innings (lambda_)
• [2] Use the Poisson Distribution to compute the probability of 0 HR being hit during Innings 4-6 (p_0)

## [1]

lambda_ = expected_total_HR * period_of_innings / 9
print("lambda = the total expected HOME  RUNS hit over %s innings" % period_of_innings)
print("lambda = %s * %s / %s" % (round(expected_total_HR,3),period_of_innings,9))
print("lambda ~ %s" % (round(lambda_,3)))

lambda = the total expected HOME RUNS hit over 3 innings
lambda = 2.88 * 3 / 9
lambda ~ 0.96     

## [2]

import math

str_ = ""
print("The probability of k events occurring in a Poisson interval = e^(-lambda) * (lambda^k)/k!")
print("where k = [0]")

p_0 = math.exp(-lambda_)*(lambda_**(HR))/(math.factorial(HR))

print('')
print("p_0 = e^(-%s) * (%s^%s)/%s!" % (round(lambda_,2),round(lambda_,2),(HR),(HR)))

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

p_0 = e^(-0.96) * (0.96^0)/0!     

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Solution

print("The probability that 0 HOME RUNS are Hit during Innings 4-6 is ~%s" % round(p_0,3))

The probability that 0 HOME RUNS are Hit during Innings 4-6 is ~0.383

Posted on 8/12/2019