The Open Championship 2019 - 1st Rd: What will be Tiger Woods’ COMBINED SCORE on Holes 13-15?

1:22 PM
10 Strokes or Fewer
11 Strokes or More

Inputs To Solve

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

hole_13 = {'1':1,
          '2':9,
          '3':43,
          '4':6}

hole_14 = {'3':5,
          '4':27,
          '5':18,
          '6':1}

hole_15 = {'3':6,
          '4':29,
          '5':11,
          '6':2}

print("The observed distribution of scores on hole 13 is: %s" % hole_13)
print("The observed distribution of scores on hole 14 is: %s" % hole_14)
print("The observed distribution of scores on hole 15 is: %s" % hole_15)

The observed distribution of scores on hole 13 is: {‘1’: 1, ‘2’: 9, ‘3’: 43, ‘4’: 6}
The observed distribution of scores on hole 14 is: {‘3’: 5, ‘4’: 27, ‘5’: 18, ‘6’: 1}
The observed distribution of scores on hole 15 is: {‘3’: 6, ‘4’: 29, ‘5’: 11, ‘6’: 2}

## Inputs Defined in the Problem

strokes = 10
golfers = ['Woods13','Woods14','Woods15']

Method to Solve

Enumrate all the possible combinations of observed scores and their respective probabilities on the 3 holes.
The probability that 10 Strokes or Fewer are recorded by Tiger Woods on holes 13-15 is the sum of the probabilities for all the outcomes where the total number of Strokes is 10 or less.

import numpy as np
import pandas as pd

t=sum(hole_13.values())
for i in hole_13:
    hole_13[i] = hole_13[i]/t

t=sum(hole_14.values())
for i in hole_14:
    hole_14[i] = hole_14[i]/t
    
t=sum(hole_15.values())
for i in hole_15:
    hole_15[i] = hole_15[i]/t
 
y = np.array([(w,x,z) for w in hole_13.keys() for x in hole_14.keys() for z in hole_15.keys()])
scores = pd.DataFrame(y)
scores.columns = golfers
scores = scores.convert_objects(convert_numeric=True)
scores['total_strokes'] = scores.sum(axis=1)

z = np.array([(w,x,y) for w in hole_13.values() for x in hole_14.values() for y in hole_15.values()])
probability = pd.DataFrame(z)
probability.columns = golfers
probability['p'] = probability.product(axis=1)

scores.head()

	Woods13	Woods14	Woods15	total_strokes
0	1	3	3	7
1	1	3	4	8
2	1	3	5	9
3	1	3	6	10
4	1	4	3	8

probability.head()

	Woods13	Woods14	Woods15	p
0	0.016949	0.098039	0.125000	0.000208
1	0.016949	0.098039	0.604167	0.001004
2	0.016949	0.098039	0.229167	0.000381
3	0.016949	0.098039	0.041667	0.000069
4	0.016949	0.529412	0.125000	0.001122

p = 0
for stroke in range(1,strokes+1):
    p += probability['p'][scores['total_strokes']==stroke].sum()

Solution

print("The probability that Tiger Woods' COMBINED SCORE on Holes 13-15 is 10 Strokes or Fewer is ~%s" % round(p,3))

The probability that Tiger Woods’ COMBINED SCORE on Holes 13-15 is 10 Strokes or Fewer is ~0.196

Posted on 7/18/2019