MLB (Dodgers @ Phillies): How many STRIKEOUTS will Clayton Kershaw (LAD) record during Innings 1-3?

Inputs To Solve

##### User Estimates #####

Kershaw_2019_KRate = 91/(99*3)
# Total Ks / Number of Outs Recorded

print("Clayton Kershaw's 2019 K per Out rate is ~%s" % round(Kershaw_2019_KRate,3))

Clayton Kershaw’s 2019 K per Out rate is ~0.306

## Inputs Defined in the Problem
Ks = 3

Method to Solve

Enumrate all the possible combinations of STRIKEOUTS being recorded in Innings 1-3
The probability that 0, 1, 2 or 3 STRIKEOUTS are recorded is the sum of the probabilities for all the outcomes where the total number of STRIKEOUTS is less than or equal to 3.

import numpy as np
import pandas as pd

p_K = Kershaw_2019_KRate
p_no_K = 1 - p_K
prob = (p_K,p_no_K)
K_grid = (1,0)
a = {}

y = np.array([(q,r,s,t,u,v,w,x,z) for q in K_grid for r in K_grid for s in K_grid for t in K_grid for u in K_grid for v in K_grid for w in K_grid for x in K_grid for z in K_grid])
K = pd.DataFrame(y)
K['total_Ks'] = K.sum(axis=1)

x = np.array([(q,r,s,t,u,v,w,y,z) for q in prob for r in prob for s in prob for t in prob for u in prob for v in prob for w in prob for y in prob for z in prob])
probability = pd.DataFrame(x)
probability['p'] = probability.product(axis=1)

for i in set(K.total_Ks):
    a[i] = round(probability['p'][K['total_Ks']==i].sum(),2)

K.head()

	0	1	2	3	4	5	6	7	8	total_Ks
0	1	1	1	1	1	1	1	1	1	9
1	1	1	1	1	1	1	1	1	0	8
2	1	1	1	1	1	1	1	0	1	8
3	1	1	1	1	1	1	1	0	0	7
4	1	1	1	1	1	1	0	1	1	8

probability.head()

	0	1	2	3	4	5	6	7	8	p
0	0.306397	0.306397	0.306397	0.306397	0.306397	0.306397	0.306397	0.306397	0.306397	0.000024
1	0.306397	0.306397	0.306397	0.306397	0.306397	0.306397	0.306397	0.306397	0.693603	0.000054
2	0.306397	0.306397	0.306397	0.306397	0.306397	0.306397	0.306397	0.693603	0.306397	0.000054
3	0.306397	0.306397	0.306397	0.306397	0.306397	0.306397	0.306397	0.693603	0.693603	0.000122
4	0.306397	0.306397	0.306397	0.306397	0.306397	0.306397	0.693603	0.306397	0.306397	0.000054

print("The number of possible STRIKEOUTS in Innings 1-3 and their respective probabilities are: %s" % a)

The number of possible STRIKEOUTS in Innings 1-3 and their respective probabilities are: {0: 0.04, 1: 0.15, 2: 0.26, 3: 0.27, 4: 0.18, 5: 0.08, 6: 0.02, 7: 0.0, 8: 0.0, 9: 0.0}

p = round(probability['p'][K['total_Ks']<=Ks].sum(),3)

Solution

print("The probability that 3 or FEWER STRIKOUTS are recorded in Innings 1-3 is ~%s" % p)

The probability that 3 or FEWER STRIKOUTS are recorded in Innings 1-3 is ~0.715

Posted on 7/15/2019