PGA RBC Heritage - 1st Rd: What will be Branden Grace AND Alex Noren’s COMBINED SCORE on the Par 4 18th?

6:54PM
8 Strokes
Any Other Score

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Inputs to Solve

2019 Course Stats

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

hole_18 = {'3':40,
           '4':253,
           '5':92,
           '6':12,
           '7':5}

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

The observed distribution of scores on hole 18 is: {‘3’: 40, ‘4’: 253, ‘5’: 92, ‘6’: 12, ‘7’: 5}

## Inputs Defined in the Problem

strokes = 8
golfers = ['Grace','Noren']

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Method to Solve

• [1] Enumrate all the possible combinations of observed strokes and their respective probabilities for the 2 golfers on hole 18.
• [2] The probability that 8 Strokes are recorded by Grace and Noren on hole 18 is the sum of the probabilities for all the outcomes where the total number of Strokes is exactly equal to 8 (p_8).

## [1]

import numpy as np
import pandas as pd

t=sum(hole_18.values())
for i in hole_18:
    hole_18[i] = hole_18[i]/t
 
y = np.array([(a,b) for a in hole_18.keys() for b 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) for a in hole_18.values() for b in hole_18.values()])
probability = pd.DataFrame(z)
probability.columns = golfers
probability['p'] = probability.product(axis=1)

scores

probability

p_8 = probability['p'][scores['total_strokes']==strokes].sum()

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Solution

print("The probability that Branden Grace AND Alex Noren's COMBINED SCORE on the Par 4 18th is 8 Strokes is ~ %s" % round(p_8,3))

The probability that Branden Grace AND Alex Noren’s COMBINED SCORE on the Par 4 18th is 8 Strokes is ~ 0.442

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Info

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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 6/18/2020