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MLB (Nationals @ Giants): Will BOTH TEAMS SCORE a RUN during Innings 1-2?

3:35PM
Yes: Both teams score during Innings 1-2
No: At least 1 team doesn’t score during Innings 1-2

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Inputs Needed To Solve

Runs per Game by Team

##### User Estimates #####
WAS_RperG = 4.99
SFG_RperG = 4.27

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

Method to Solve

• define lambda_was as an estimate for the arrival rate of runs for the Nationals in a 2 inning period
• Use Poisson Distribution and lambda_was to compute the probability of a zero runs being scored in a 2 Inning period for the Nationals.
• define lambda_sfg as an estimate for the arrival rate of runs for the Giants in a 2 inning period
• Use Poisson Distribution and lambda_sfg to compute the probability of a zero runs being scored in a 2 Inning period for the Giants.
• The probability that BOTH TEAMS SCORE a RUN during Innings 1-2 is:
  (1 - the probability the Nationals score zero runs) * (1 - the probability the Giants score zero runs)

lambda_was = WAS_RperG * period_of_innings / 9
print("lambda_was = the total expected RUNs scored by the Nationals teams over %s inning" % period_of_innings)
print("lambda_was = %s * %s / %s" % (round(WAS_RperG,3),period_of_innings,9))
print("lambda_was = %s" % (round(lambda_was,3)))

lambda_was = the total expected RUNs scored by the Nationals teams over 2 inning
lambda_was = 4.99 * 2 / 9
lambda_was = 1.109     

import math

p0_was = math.exp(-lambda_was)*(lambda_was**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_was,3))
print('')
print("p0_was = e^(-%s) * (%s^%s)/%s!" % (round(lambda_was,3),round(lambda_was,3),RUNs,RUNs))
print('')
print("The probability the Nationals SCORE zero RUNS during Innings 1-2 is %s" % round(p0_was,3))

The probability of k events occurring in an Poisson interval = e^(-lambda) * ((lambda^k)/k!)
where k = 0 and lambda = 1.109

p0_was = e^(-1.109) * (1.109^0)/0!

The probability the Nationals SCORE zero RUNS during Innings 1-2 is 0.33     

lambda_sfg = SFG_RperG * period_of_innings / 9
print("lambda_sfg = the total expected RUNs scored by the Giants teams over %s inning" % period_of_innings)
print("lambda_sfg = %s * %s / %s" % (round(SFG_RperG,3),period_of_innings,9))
print("lambda_sfg = %s" % (round(lambda_sfg,3)))

lambda_sfg = the total expected RUNs scored by the Giants teams over 2 inning
lambda_sfg = 4.27 * 2 / 9
lambda_sfg = 0.949     

import math

p0_sfg = math.exp(-lambda_sfg)*(lambda_sfg**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_sfg,3))
print('')
print("p0_sfg = e^(-%s) * (%s^%s)/%s!" % (round(lambda_sfg,3),round(lambda_sfg,3),RUNs,RUNs))
print('')
print("The probability the Nationals SCORE zero RUNS during Innings 1-2 is %s" % round(p0_sfg,3))

The probability of k events occurring in an Poisson interval = e^(-lambda) * ((lambda^k)/k!)
where k = 0 and lambda = 0.949

p0_sfg = e^(-0.949) * (0.949^0)/0!
The probability the Nationals SCORE zero RUNS during Innings 1-2 is 0.387     

p_both_score = (1-p0_was) * (1-p0_sfg)

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Solution

print("The probability BOTH TEAMS SCORE a RUN during Innings 1-2 ~%s" % round(p_both_score,3))

The probability BOTH TEAMS SCORE a RUN during Innings 1-2 ~0.411

Posted on 8/7/2019