MLB (Cubs @ Pirates): Will the Pirates SCORE a RUN during Innings 4-5?

8:15 PM ESPN
Yes: Pirates score 1+ Runs during Innings 4-5
No:: Pirates score 0 Runs during Innings 4-5

---

Inputs Needed To Solve

Pirates Runs per Game

##### User Estimates #####
PIT_RperG = 4.59

print("Use %s as total expected RUNs for the Pirates." % PIT_RperG)

 Use 4.59 as total expected RUNs for the Pirates.     

## Inputs Defined in the Problem
period_of_innings = 2
RUNs = 0

Method to Solve

• define lambda as expected runs per game
• Use Poisson Distribution to estimate the probability of a RUN being scored in any one inning

lambda_ = PIT_RperG * period_of_innings / 9
print("lambda = the total expected RUNs scored by the Pirates over %s innings" % period_of_innings)
print("lambda = %s * %s / %s" % (round(PIT_RperG,3),period_of_innings,9))
print("lambda ~ %s" % (round(lambda_,3)))

lambda = the total expected RUNs scored by the Pirates over 2 innings
lambda = 4.59 * 2 / 9
lambda ~ 1.02     

import math

p = math.exp(-lambda_)*(lambda_**RUNs)/(math.factorial(RUNs))

print("The probability of k events occurring in an Poisson interval = e^(-lambda) * ((lambda^k)/k!)")
print('where k = 0 and lambda = %s' % round(lambda_,3))
print('')
print("p = e^(-%s) * (%s^%s)/%s!" % (round(lambda_,3),round(lambda_,3),RUNs,RUNs))

The probability of k events occurring in an Poisson interval = e^(-lambda) * ((lambda^k)/k!)
where k = 0 and lambda = 1.02

p = e^(-1.02) * (1.02^0)/0!     

---

Solution

print("The probability that the Pirates score zero RUNS during Innings 4-5 is ~%s" % round(p,3))

The probability that the Pirates score zero RUNS during Innings 4-5 is ~0.361

Posted on 7/1/2019