MLB (Astros @ White Sox): How many STRIKEOUTS will be recorded during Innings 1-2?

4:40PM
3 or Fewer
4 or More

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Inputs To Solve

Starting Pitcher STRIKEOUT per OUT Rate

Greinke HOU
Cease CWS

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

Gre_2019_KRate = 137/(152*3)
# Total Ks / Number of Outs Recorded

Cea_2019_KRate = 33/(33*3)
# Total Ks / Number of Outs Recorded

print("Zach Greinke's 2019 K per Out rate is ~%s" % round(Gre_2019_KRate,3))
print("Dylan Cease's 2019 K per Out rate is ~%s" % round(Cea_2019_KRate,3))

Zach Greinke’s 2019 K per Out rate is ~0.3
Dylan Cease’s 2019 K per Out rate is ~0.333

## Inputs Defined in the Problem
Innings = 2
Ks = 3

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Method to Solve

• [1] Enumerate all the possible combinations of STRIKEOUTS vs NON STRIKEOUT OUTS recorded in Innings 1-2
• [2] Sum the probabilities for all the combination’s outcomes where the total number of STRIKEOUTS is less than or equal to 2.

## [1]

import numpy as np
import pandas as pd

# Zach Greinke K / no K probability
p_K_Gre = Gre_2019_KRate
p_no_K_Gre = 1 - p_K_Gre
prob_Gre = (p_K_Gre,p_no_K_Gre)
K_grid = (1,0)

# Dylan Cease K / no K probability
p_K_Cea = Cea_2019_KRate
p_no_K_Cea = 1 - p_K_Cea
prob_Cea = (p_K_Cea,p_no_K_Cea)
K_grid = (1,0)

# Enumerate all possible combinations of K / no K for both pitchers over 2 Innings 
# max 12 Total Ks - if all outs are STRIKEOUTS
y = np.array([(a,b,c,d,e,f,t,u,v,w,x,z) 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
             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])
K = pd.DataFrame(y)
K['total_Ks'] = K.sum(axis=1)

K.head()

# Compute the probability of all possible combinations of K / no K for both pitchers over 2 Innings
x = np.array([(a,b,c,d,e,f,t,u,v,w,y,z) for t in prob_Cea for u in prob_Cea for v in prob_Cea for w in prob_Cea for y in prob_Cea for z in prob_Cea
             for a in prob_Gre for b in prob_Gre for c in prob_Gre for d in prob_Gre for e in prob_Gre for f in prob_Gre])

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

probability.head()

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

The possible outcomes of STRIKEOUTS in Innings 1-2 and their respective probabilities are: {0: 0.01, 1: 0.06, 2: 0.15, 3: 0.23, 4: 0.24, 5: 0.18, 6: 0.1, 7: 0.04, 8: 0.01, 9: 0.0, 10: 0.0, 11: 0.0, 12: 0.0}

## [2]

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

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Solution

print("The probability that 3 or FEWER STRIKEOUTS are recorded in Innings 1-2 is ~%s" % p)

The probability that 3 or FEWER STRIKEOUTS are recorded in Innings 1-2 is ~0.441

Posted on 8/13/2019