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MLB (Mariners @ Athletics): Will a RUN be SCORED in the 8th Inning?

6:00 PM
Yes: Runs scored in 8th Inning
No:: 0 Runs in 8th Inning

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Inputs Needed To Solve

Runs per Game

##### User Estimates #####
SEA_RperG = 4.96
OAK_RperG = 5.18
total_RUNS = OAK_RperG+SEA_RperG

print("Total expected RUNs for the game as %s + %s = %s." % (SEA_RperG,OAK_RperG,total_RUNS))

Total expected RUNs for the game as 4.96 + 5.18 = 10.14.    

## Inputs Defined in the Problem
period_of_innings = 1
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_ = total_RUNS * period_of_innings / 9
print("lambda = the total expected RUNs scored by the both teams over %s inning" % period_of_innings)
print("lambda = %s * %s / %s" % (round(total_RUNS,3),period_of_innings,9))
print("lambda ~ %s" % (round(lambda_,3)))

lambda = the total expected RUNs scored by the both teams over 1 inning
lambda = 10.14 * 1 / 9
lambda ~ 1.127    

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 = 1.127

p = e^(-1.127) * (1.127^0)/0!    

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Solution

print("The probability that zero RUNS are scored during the 8th Inning is ~%s" % round(p,3))

The probability that zero RUNS are scored during the 8th Inning is ~0.324

Posted on 7/17/2019