MLB (Yankees @ Mets): How many PITCHES will be THROWN in the 1st Inning?

7:10 PM ESPN
29 Pitches or Fewer
30 Pitches or More

Inputs To Solve

PITCHES THROWN per Inning by Starting Pitcher

##### User Estimates #####
DG_PitperStart = 89.6
JV_PitperStart = 80.9

dg_starts = 13
dg_IP = 70

jv_starts = 14
jv_IP = 66.1

## Inputs Defined in the Problem
period_of_innings = 1
Pitches = 29

Method to Solve

Estimate lambda (rate of Pitches per Inning for both pitchers combined)
Use the Poisson Distribution to compute the probability of 29 or less PITCHES THROWN in the 1st Inning

lambda_dg = DG_PitperStart * dg_starts / dg_IP
print("lambda_dg = the total expected PITCHES THROWN (German) over %s inning" % period_of_innings)
print("lambda_dg = DG Pitches per Start * DG starts / DG innings pitched")
print("lambda_dg = %s * %s / %s" % (round(DG_PitperStart,3),dg_starts,dg_IP))
print("lambda_dg ~ %s" % (round(lambda_dg,3)))

lambda_dg = the total expected PITCHES THROWN (German) over 1 inning
lambda_dg = DG Pitches per Start * DG starts / DG innings pitched
lambda_dg = 89.6 * 13 / 70
lambda_dg ~ 16.64

lambda_jv = JV_PitperStart * jv_starts / jv_IP
print("lambda_jv = the total expected PITCHES THROWN (Vargas) over %s inning" % period_of_innings)
print("lambda_jv = JV Pitches per Start * JV starts / JV innings pitched")
print("lambda_jv = %s * %s / %s" % (round(JV_PitperStart,3),jv_starts,jv_IP))
print("lambda_jv ~ %s" % (round(lambda_jv,3)))

lambda_jv = the total expected PITCHES THROWN (Vargas) over 1 inning
lambda_jv = JV Pitches per Start * JV starts / JV innings pitched
lambda_jv = 80.9 * 14 / 66.1
lambda_jv ~ 17.135

from scipy.stats import poisson

print("The probability of k events occurring in a Poisson interval = e^(-lambda) * (lambda^k)/k!")
print("where k = range(0,29)")
print(' ')

p = poisson.cdf(Pitches,lambda_dg+lambda_jv)

The probability of k events occurring in a Poisson interval = e^(-lambda) * (lambda^k)/k!
where k = range(0,29)

Solution

print("The probability that 29 or FEWER PITCHES are THROWN in the 1st Inning is ~%s" % round(p,3))

The probability that 29 or FEWER PITCHES are THROWN in the 1st Inning is ~0.235

Posted on 7/4/2019