College World Series (#1 Texas Tech v. #3 Florida State): Will an EXTRA-BASE HIT and STRIKEOUT occur during Innings 1-2?

Yes: Both occur during Innings 1-2
No: At least 1 doesn’t occur during Innings 1-2

Inputs To Solve

XBHs per Game by Team (TX Tech and FL St)
Ks per Game by Team (TX Tech and FL St)

##### User Estimates #####
TX_XBHperG = (122+20+57)/56
FL_XBHperG = (105+13+69)/57
expected_XBH = TX_XBHperG + FL_XBHperG

TX_Kper9 = 9.2
FL_Kper9 = 10.5
expected_Ks = TX_Kper9 + FL_Kper9

print("TX Tech total XBH per game is %s" % round(TX_XBHperG,3))
print("FL St total XBH per game is %s" % round(FL_XBHperG,3))
print("The total expected XBH per game is %s" % round(expected_XBH,3))
print('')
print("The total expected Ks per game is %s" % round(expected_Ks,3))

TX Tech total XBH per game is 3.554
FL St total XBH per game is 3.281
The total expected XBH per game is 6.834
The total expected Ks per game is 19.7

## Inputs Defined in the Problem
period_of_innings = 2
XBH = 0
K = 0

Method to Solve

Estimate lambda_xbh (rate of XBHs hit per 2 innings)
Use the Poisson Distribution to compute the probabilty of zero XBHs being hit in Innings 1-2
Estimate lambda_k (rate of Ks per 2 innings)
Use the Poisson Distribution to compute the probabilty of zero Ks being recorded in Innings 1-2
Multiply 1- the probability that there are zero XBHs and 1 - the probability there are zero Ks to get the probability that both occur

lambda_xbh = expected_XBH * period_of_innings / 9
print("lambda_xbh = the total expected XBH by both team over %s innings" % period_of_innings)
print("lambda_xbh = %s * %s / %s" % (round(expected_XBH,3),period_of_innings,9))
print("lambda_xbh ~ %s" % (round(lambda_xbh,2)))

lambda_xbh = the total expected XBH by both team over 2 innings
lambda_xbh = 6.834 * 2 / 9
lambda_xbh ~ 1.52

import math

p1 = math.exp(-lambda_xbh)*(lambda_xbh**XBH)/(math.factorial(XBH))

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_xbh,3))
print('')
print("p = e^(-%s) * (%s^%s)/%s!" % (round(lambda_xbh,3),round(lambda_xbh,3),XBH,XBH))
print('')
print("The probability that there are zero XBHs in Innings 1-2 is %s" % round(p1,3))

The probability of k events occuring in an Poisson interval = e^(-lambda) * (lambda^k)/k!
where k = 0 and lambda = 1.519

p = e^(-1.519) * (1.519^0)/0!

The probability that there are zero XBHs in Innings 1-2 is 0.219

lambda_k = expected_Ks * period_of_innings / 9
print("lambda_k = the total expected Ks by both team over %s innings" % period_of_innings)
print("lambda_k = %s * %s / %s" % (round(expected_Ks,3),period_of_innings,9))
print("lambda_k ~ %s" % (round(lambda_k,2)))

lambda_k = the total expected Ks by both team over 2 innings
lambda_k = 19.7 * 2 / 9
lambda_k ~ 4.38

p2 = math.exp(-lambda_k)*(lambda_k**K)/(math.factorial(K))

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_k,3))
print('')
print("p = e^(-%s)*(%s^%s)/%s!" % (round(lambda_k,3),round(lambda_k,3),K,K))
print('')
print("The probability that there are zero Ks in Innings 1-2 is %s" % round(p2,3))

The probability of k events occuring in an Poisson interval = e^(-lambda) * (lambda^k)/k!
where k = 0 and lambda = 4.378

p = e^(-4.378)*(4.378^0)/0!

The probability that there are zero Ks in Innings 1-2 is 0.013

Solution

print("The probabilty that both and XBH and a K occur in Innings 1-2 is %s" % round((1-p1)*(1-p2),3))

The probabilty that both and XBH and a K occur in Innings 1-2 is 0.771

Posted on 6/19/2019