PGA BMW Championship - 2nd Rd (Medinah, IL): What will be Tiger Woods’ SCORE on Holes 1-3?

10:37AM
10 Strokes or Fewer
11 Strokes or More

Inputs To Solve

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

hole_1 = {'3':45,
           '4':39,
           '5':6}

hole_2 = {'2':12,
           '3':55,
           '4':2}

hole_3 = {'3':14,
           '4':51,
           '5':4}

## Inputs Defined in the Problem

strokes = 10
holes = ['TW1','TW2','TW3']

Method to Solve

[1] Enumerate all the possible combinations of observed scores and their respective probabilities for Tiger Woods on the holes 1-3.
[2] The probability that Tiger Wood’s score is 10 strokes or less is the sum of the probabilities of outcomes where his total score is 10 or less (p_under10).

## [1]

import numpy as np
import pandas as pd

t=sum(hole_1.values())
for i in hole_1:
    hole_1[i] = hole_1[i]/t
    
t=sum(hole_2.values())
for i in hole_2:
    hole_2[i] = hole_2[i]/t

t=sum(hole_3.values())
for i in hole_3:
    hole_3[i] = hole_3[i]/t

y = np.array([(a,b,c) for a in hole_1.keys()for b in hole_2.keys() for c in hole_3.keys()])
y = y.astype(int)
scores = pd.DataFrame(y)
scores.columns = holes
scores['total_strokes'] = scores.sum(axis=1)
scores.head()

	TW1	TW2	TW3	total_strokes
0	3	2	3	8
1	3	2	4	9
2	3	2	5	10
3	3	3	3	9
4	3	3	4	10

z = np.array([(a,b,c) for a in hole_1.values() for b in hole_2.values() for c in hole_3.values()])
probability = pd.DataFrame(z)
probability.columns = holes
probability['p'] = probability.product(axis=1)
probability.head()

	TW1	TW2	TW3	p
0	0.5	0.173913	0.202899	0.017643
1	0.5	0.173913	0.739130	0.064272
2	0.5	0.173913	0.057971	0.005041
3	0.5	0.797101	0.202899	0.080865
4	0.5	0.797101	0.739130	0.294581

## [2]

p_under10 = probability['p'][scores['total_strokes']<=strokes].sum()

Solution

print("The probability Tiger Wood's combined score on holes 1-3 is 10 Strokes or Fewer is ~%s" % round(p_under10,3))

The probability Tiger Wood's combined score on holes 1-3 is 10 Strokes or Fewer is ~0.609

Info

download markdown 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 8/16/2019