MLB (Cubs @ Cardinals): Which TEAM will SCORE MORE RUNS during Innings 5-7?

9:35 PM
Cubs
Cardinals or Tie

Inputs Needed to Solve

Expected Runs per Game by team (Cubs and Cardinals)

##### User Estimates #####
CHC_RperGame = 5.01
STL_RperGame = 4.56

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

Method to Solve

Estimate mu_Chi (expected arrival rate of RUNS per 3 Innings for the Cubs)
Estimate mu_Stl (expected arrival rate of RUNS per 3 Innings for the Cardinals)
Use mu_Chi and mu_Stl in the Skellam Distribution (the difference between 2 independant Poisson processes) to compute the probability of the Cubs leading (p_Chi).

mu_Chi = CHC_RperGame * period_of_innings / 9
mu_Stl = STL_RperGame * period_of_innings / 9
print("mu_Chi = the total expected RUNS scored by the Cubs in 3 Innings is ~%s" % round(mu_Chi,3))
print("mu_Stl = the total expected RUNS scored by the Cardinals in 2 Innings is ~%s" % round(mu_Stl,3))

mu_Chi = the total expected RUNS scored by the Cubs in 3 Innings is ~1.67
mu_Stl = the total expected RUNS scored by the Cardinals in 2 Innings is ~1.52

from scipy.stats import skellam

p_Chi = skellam.cdf(run_diff,mu_Chi,mu_Stl)
p_Stl = skellam.cdf(run_diff,mu_Stl,mu_Chi)
print("Recall the cdf (cumulative distribution fuction) is P[X<=x] where X is the 'difference' in this example")

Recall the cdf (cumulative distribution fuction) is P[X<=x] where X is the 'difference' in this example

Solution

print("The probability of the CUBS LEADING after 3 Innings ~%s" % round(p_Chi,3))

The probability of the CUBS LEADING after 3 Innings ~0.585

Posted on 7/31/2019