MLB (White Sox @ Cubs): Which side will record a HIGHER TOTAL during Innings 1-3?

Inputs To Solve

Runs per Game by Team (White Sox and Cubs)

Strikeouts Rate by Starting Pitchers

##### User Estimates #####
CHW_RperGame = 4.31
CHC_RperGame = 5.11
total_expected_Rs = CHW_RperGame + CHC_RperGame

Nova_KperInn = 891/1219
Hamels_KperInn = 2498/(((2637*3)+2)/3)
total_expected_KsperInn = Nova_KperInn + Hamels_KperInn

print("The total expected Runs for both teams in the game is %s" % round(total_expected_Rs,3))
print('')
print("Ivan Nova's K/Inning ratio is %s" % round(Nova_KperInn,3))
print("Cole Hamels' K/Inning ratio is %s" % round(Hamels_KperInn,3))
print("The total expected Strikeouts for both pitchers in one Inning is %s" % round(total_expected_KsperInn,3))

The total expected Runs for both teams in the game is 9.42

Ivan Nova’s K/Inning ratio is 0.731
Cole Hamels’ K/Inning ratio is 0.947
The total expected Strikeouts for both pitchers in one Inning is 1.678

## Inputs Defined in the Problem
period_of_innings = 3
difference = 0

Method to Solve

Estimate mu_K (expected arrival rate of Strikeout per 3 Innings) and mu_R (expected arrival rate of Runs per 3 Innings)
Use the Skellam Distribution (the difference between 2 independant Poisson processes) to compute the probabilty of more Strikeouts than Runs being recorded in Innings 1-3

mu_K = total_expected_KsperInn * period_of_innings
mu_R = total_expected_Rs * period_of_innings / 9

print("The total expected Strikeouts over Innings 1-3 is %s" % round(mu_K,3))
print("The total expected Runs over Innings 1-3 is %s" % round(mu_R,3))

The total expected Strikeouts over Innings 1-3 is 5.034
The total expected Runs over Innings 1-3 is 3.14

from scipy.stats import skellam

p = 1-skellam.cdf(difference,mu_K,mu_R)

Solution

print("The probabilty that more Strikeouts than Runs are recorded in Innings 1-3 is ~%s" % round(p,3))

The probabilty that more Strikeouts than Runs are recorded in Innings 1-3 is ~0.687

Posted on 6/18/2019