MLB (Astros @ Indians): Will there be an EXTRA-BASE HIT in the 1st Inning?

7:10PM
Yes: 1+ XBH in 1st Inning
No: 0 XBH in 1st Inning

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Inputs Needed to Solve

XBHs per Game by team (Astros & Indians)

##### User Estimates #####
HOU_XBHperGame = float(208+18+153)/108
CLE_XBHperGame = float(170+13+140)/106

total_XBHs = HOU_XBHperGame + CLE_XBHperGame

print("The total expected XBHs for the Astros is %s" % round(HOU_XBHperGame,3))
print("The total expected XBHs for the Braves is %s" % round(CLE_XBHperGame,3))
print('')
print("The total expected XBHs for the game is %s" % round(total_XBHs,3))

The total expected XBHs for the Astros is 3.509
The total expected XBHs for the Braves is 3.047

The total expected XBHs for the game is 6.556

## Inputs Defined in the Problem
period_of_innings = 1
XBHs= 0

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Method to Solve

• Estimate lambda (expected XBHs per Inning)
• Use the Poisson Distribution to compute the probability of zero XBHs being hit in the 1st Inning.

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

lambda = the total expected XBHs by both teams over 1 innings
lambda = 6.56 * 1 / 9
lambda ~ 0.73

import math

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

print("The probability of k events occuring in an Poisson interval = e^(-lambda) * ((lambda^k)/k!)")
print('where k = 0 and lambda = %s' % round(lambda_,2))
print('')
print("p = e^(-%s) * (%s^%s)/%s!" % (round(lambda_,2),round(lambda_,2),XBHs,XBHs))

The probability of k events occuring in an Poisson interval = e^(-lambda) * ((lambda^k)/k!)
where k = 0 and lambda = 0.73

p = e^(-0.73) * (0.73^0)/0!

print("The probability of zero XBHs being hit in the 1st Inning is %s" % (round(p,3)))

The probability of zero XBHs being hit in the 1st Inning is 0.483

Posted on 7/31/2019