MLB (Pirates @ Cardinals): Will an EXTRA-BASE HIT and STRIKEOUT occur during Innings 1-2?

1:15 PM
Yes: Both occur during Innings 1-2
No: At least 1 doesn’t occur during Innings 1-2

Inputs To Solve

Extra-Base Hit per Game by Team

Strikeout rate by Starting Pitcher

##### User Estimates #####
Pit_XBHperGame = (191+21+102)/93
Stl_XBHperGame = (132+9+112)/93

expected_total_XBH = Pit_XBHperGame + Stl_XBHperGame

print("Use %s + %s = %s as total expected XBH to be hit for the game." 
      % (round(Pit_XBHperGame,3),round(Stl_XBHperGame,3),round(expected_total_XBH,3)))

Use 3.376 + 2.72 = 6.097 as total expected XBH to be hit for the game.

CA2019_K_Rate = 98/((84*3)+2)
PdL2019_K_Rate = 38/((31*3)+2)

print("Chris Archer's 2019 K per Out rate is %s" % round(CA2019_K_Rate,3))
print("Daniel Ponce de Leon's 2019 K per Out rate is %s" % round(PdL2019_K_Rate,3))

Chris Archer’s 2019 K per Out rate is 0.386
Daniel Ponce de Leon’s 2019 K per Out rate is 0.4

## Inputs Defined in the Problem
period_of_innings = 2
_XBH = 0
_K = 0

Method to Solve

Estimate lambda (expected arrival rate of XBH)
Use Poisson Distribution to estimate the probability of zero XBH being hit in any two innings
Compute the probability that there are no Strikeouts in Innngs 1-2
The probability that both occur is (1 - the probability there are no XBHs) multiplied by (1 - the probability there are no Ks)

lambda_ = expected_total_XBH * period_of_innings / 9
print("lambda = the total expected XBH hit by both teams over 2 innings")
print("lambda = %s * %s / %s" % (round(expected_total_XBH,3),period_of_innings,9))
print("lambda ~ %s" % (round(lambda_,3)))

lambda = the total expected XBH hit by both teams over 2 innings
lambda = 6.097 * 2 / 9
lambda ~ 1.355

import math

xbh_zero = math.exp(-lambda_)*(lambda_**_XBH)/(math.factorial(_XBH))

print("The probability of k events occurring in an Poisson interval = e^(-lambda) * (lambda^k)/k!")
print('where k = 0')
print('')
print("p = e^(-%s) * (%s^%s)/%s!" % (round(lambda_,2),round(lambda_,2),_XBH,_XBH))
print("xbh_zero = %s" % round(xbh_zero,3))

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

p = e^(-1.35) * (1.35^0)/0!
xbh_zero = 0.258

k_zero = ((1-CA2019_K_Rate)**6)*((1-PdL2019_K_Rate)**6)
print("The probability that no Strikeouts are recorded in Innings 1-2 is (1-Archer K rate)^(# of Outs) * (1-Ponce K rate)^(# of Outs)")
print('')
print("k_zero = %s" % round(K_zero,3))

The probability that no Strikeouts are recorded in Innings 1-2 is (1-Archer K rate)^(# of Outs) * (1-Ponce K rate)^(# of Outs)

k_zero = 0.003

Solution

print("The probability that both an Extra Base Hit and a Strikeout occur is %s" % round((1-xbh_zero)*(1-k_zero),3))

The probability that both an Extra Base Hit and a Strikeout occur is 0.74

Posted on 7/17/2019