MLB (Cubs @ Padres): How many STRIKEOUTS will Yu Darvish (CHC) record during Innings 1-3?

Inputs To Solve

Darvish 2019 STRIKEOUT per OUT Rate

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

Yu_KperOut = 190/((157*3)+1)

print("Yu Darvish's 2019 K per Out rate is ~%s" % round(Yu_KperOut,3))

Yu Darvish's 2019 K per Out rate is ~0.403

## Inputs Defined in the Problem
period_of_innings = 3
Ks = 3

Method to Solve

[1] Enumerate all the possible combinations of STRIKEOUTS vs NON STRIKEOUT OUTS recorded in Innings 1-3 (K) by Yu Darvish and their respective probabilities (P).
[2] Sum the probabilities for all the combination’s outcomes where the total number of STRIKEOUTS is less than or equal to 3 (p).

## [1]

import numpy as np
import pandas as pd

# Yu Darvish K / no K probability
pK_Yu = Yu_KperOut
pnoK_Yu = 1 - pK_Yu
prob_Yu = (pK_Yu,pnoK_Yu)
K_grid = (1,0)

# Enumerate all possible combinations of K / no K for Yu D over 3 Innings 
# max 9 Total Ks - if all outs are STRIKEOUTS
y = np.array([(a,b,c,d,e,f,g,h,i) for a in K_grid for b in K_grid for c in K_grid
              for d in K_grid for e in K_grid for f in K_grid
              for g in K_grid for h in K_grid for i in K_grid])

K = pd.DataFrame(y)
K['total_Ks'] = K.sum(axis=1)


# Compute the probability of all possible combinations of K / no K for Yu D over 3 Innings
x = np.array([(a,b,c,d,e,f,g,h,i) for a in prob_Yu for b in prob_Yu for c in prob_Yu
              for d in prob_Yu for e in prob_Yu for f in prob_Yu
              for g in prob_Yu for h in prob_Yu for i in prob_Yu])

P = pd.DataFrame(x)
P['p'] = P.product(axis=1)

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

P.head()

	0	1	2	3	4	5	6	7	8	p
0	0.402542	0.402542	0.402542	0.402542	0.402542	0.402542	0.402542	0.402542	0.402542	0.000278
1	0.402542	0.402542	0.402542	0.402542	0.402542	0.402542	0.402542	0.402542	0.597458	0.000412
2	0.402542	0.402542	0.402542	0.402542	0.402542	0.402542	0.402542	0.597458	0.402542	0.000412
3	0.402542	0.402542	0.402542	0.402542	0.402542	0.402542	0.402542	0.597458	0.597458	0.000611
4	0.402542	0.402542	0.402542	0.402542	0.402542	0.402542	0.597458	0.402542	0.402542	0.000412

a = {}
for i in set(K.total_Ks):
    a[i] = round(P['p'][K['total_Ks']==i].sum(),2)
    
print("The possible outcomes of STRIKEOUTS for Yu Darvish in Innings 1-3 and their respective probabilities are: %s" % a)

The possible outcomes of STRIKEOUTS for Yu Darvish in Innings 1-3 and their respective probabilities are: {0: 0.01, 1: 0.06, 2: 0.16, 3: 0.25, 4: 0.25, 5: 0.17, 6: 0.08, 7: 0.02, 8: 0.0, 9: 0.0}

## [2]

p = P['p'][K['total_Ks']<=Ks].sum()

Solution

print("The probability that Yu Darvish records 3 or Fewer STRIKEOUTS in Innings 1-3 is ~%s" % round(p,3))

The probability that Yu Darvish records 3 or Fewer STRIKEOUTS in Innings 1-3 is ~0.476

Info

download md file
email: krellabsinc@gmail.com
twitter: @KRELLabs

import sys
print(sys.version)

3.6.5 |Anaconda, Inc.| (default, Mar 29 2018, 13:32:41) [MSC v.1900 64 bit (AMD64)]

Posted on 9/12/2019