MLB (Yankees @ Dodgers): How many TOTAL BASES will be recorded during INNINGS 4-6?

Inputs Needed to Solve

##### User Estimates #####
NYY_BasesperGame = 16.79
LAD_BasesperGame = 16.05

total_expected_bases = NYY_BasesperGame + LAD_BasesperGame

print("The total expected Bases for the game is %s" % total_expected_bases)

The total expected Bases for the game is 32.84

## Inputs Defined in the Problem
period_of_innings = 3
BASES = 9

Method to Solve

[1] estimate lambda_base as the expected Total Bases per 3 Innings for the Yankees and Dodgers
[2] use the Poisson Distribution to compute the probability of 9 or less Total Bases being recorded in 3 Innings (p_9orLess)

## [1]

lambda_base = total_expected_bases * period_of_innings / 9
print("lambda_base = the total expected bases recorded by both teams over %s innings" % period_of_innings)
print("lambda_base = %s * %s / %s" % (round(total_expected_bases,2),period_of_innings,9))
print("lambda_base ~ %s" % (round(lambda_base,2)))

lambda_base = the total expected bases recorded by both teams over 3 innings
lambda_base = 32.84 * 3 / 9
lambda_base ~ 10.95

## [2]

from scipy.stats import poisson

print("The probability of k events occurring in a Poisson interval = e^(-lambda) * (lambda^k)/k!")
print("where k = 0-9")
print(' ')

p_9orLess = poisson.cdf(BASES,lambda_base)

The probability of k events occurring in a Poisson interval = e^(-lambda) * (lambda^k)/k!
where k = 0-9

Solution

print("The probability of 9 or Fewer Total Bases being recorded during Innings 4-6 is %s" % (round(p_9orLess,3)))

The probability of 9 or Fewer Total Bases being recorded during Innings 4-6 is 0.346

Info

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Posted on 8/25/2019