PGA Travelers: What will be D. Johnson, J. Spieth, J. Thomas, and X. Schauffele’s COMBINED SCORE on Hole 18?

5:08PM
15 Strokes or Fewer
16 Strokes or More

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Inputs to Solve

Travelers Championship Course Stats

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

hole_18 = {'3':0.19,
           '4':0.71,
           '5':0.05,
           '6':0.035,
           '7':0.015}

print("The observed distribution of scores on hole 18 is: %s" % hole_18)

The observed distribution of scores on hole 18 is: {‘3’: 0.19, ‘4’: 0.71, ‘5’: 0.05, ‘6’: 0.035, ‘7’: 0.015}

## Inputs Defined in the Problem

strokes = 15
golfers = ['Johnson','Speith','Thomas','Schauffele']

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Method to Solve

• [1] Enumrate all the possible combinations of observed strokes and their respective probabilities for 4 golfers on hole 18.
• [2] The probability that 15 Strokes or Fewer are recorded by D. Johnson, J. Spieth, J. Thomas, and X. Schauffele on hole 18 is the sum of the probabilities for all the outcomes where the total number of Strokes is less than or equal to 15 (p_15).

## [1]

import numpy as np
import pandas as pd

y = np.array([(a,b,c,d) for a in hole_18.keys() for b in hole_18.keys() for c in hole_18.keys() for d in hole_18.keys()])
scores = pd.DataFrame(y)
scores.columns = golfers
scores = scores.apply(pd.to_numeric)
scores['total_strokes'] = scores.sum(axis=1)

z = np.array([(a,b,c,d) for a in hole_18.values() for b in hole_18.values() for c in hole_18.values() for d in hole_18.values()])
probability = pd.DataFrame(z)
probability.columns = golfers
probability['p'] = probability.product(axis=1)

scores

probability

p_15 = probability['p'][scores['total_strokes']<=strokes].sum()

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Solution

print("The probability that D. Johnson, J. Spieth, J. Thomas, and X. Schauffele's COMBINED SCORE on the Par 4 18th is 15 Strokes or Fewer is ~ %s" % round(p_15,3))

The probability that D. Johnson, J. Spieth, J. Thomas, and X. Schauffele’s COMBINED SCORE on the Par 4 18th is 15 Strokes or Fewer is ~ 0.42

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3.6.5 (v3.6.5:f59c0932b4, Mar 28 2018, 16:07:46) [MSC v.1900 32 bit (Intel)]

Posted on 6/25/2020