MLB (Braves @ Nationals): How many TOTAL BASES will be recorded during the FIRST THREE INNINGS?

Inputs Needed to Solve

Expected Total Bases by Team per Game (Braves and Nationals)

##### User Estimates #####
ATL_BasesperGame = 15.78
WAS_BasesperGame = 14.76

total_expected_bases = ATL_BasesperGame + WAS_BasesperGame

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

The total expected Bases for the game is 30.54

## Inputs Defined in the Problem
period_of_innings = 3
BASES = 6

Method to Solve

estimate lambda (expected Bases per 3 Innings)
use the Poisson Distribution to compute the probability of zero Runs being scored in 3 Innings

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

lambda = the total expected bases recorded by both teams over 3 innings
lambda = 30.54 * 3 / 9
lambda ~ 10.18

from scipy.stats import poisson

print("The probability of k events occurring in a Poisson interval = e^(-lambda) * (lambda^k)/k!")
print("where k = range(0,6)")
print(' ')

p = poisson.cdf(BASES,lambda_)

The probability of k events occurring in a Poisson interval = e^(-lambda) * (lambda^k)/k!
where k = range(0,6)

print("The probability of 6 or Fewer Total Bases being recorded in the First Three Innings is %s" % (round(p,3)))

The probability of 6 or Fewer Total Bases being recorded in the First Three Innings is 0.119

Posted on 7/29/2019