PGA Tour Championship - 1st Rd (Atlanta, GA): Which PLAYER will card a LOWER SCORE on the Par 3 2nd?

1:20PM
Adam Scott (AUS) or Tie
Dustin Johnson (USA)

Inputs To Solve

East Lake Golf Club 2018 Course Stats

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

hole_2 = {'2':18,
          '3':84,
          '4':18}

## Inputs Defined in the Problem

golfers = ['AS2','DJ2']

Method to Solve

[1] Enumerate all the possible combinations (scores) of observed scores and their respective probabilities (probability) for Adam Scott and Dustin Johnson on Hole 2.
[2] The probability that Dustin Johnson’s score is lower than Adam Scott’s is the sum of the probabilities of outcomes where his total score is less (p_DJ).

## [1]

import numpy as np
import pandas as pd

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

y = np.array([(a,b) for a in hole_2.keys()for b in hole_2.keys()])
y = y.astype(int)
scores = pd.DataFrame(y)
scores.columns = golfers
scores['DJ_less'] = scores['DJ2'] < scores['AS2']
scores.head()

	AS2	DJ2	DJ_less
0	2	2	False
1	2	3	False
2	2	4	False
3	3	2	True
4	3	3	False

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

	AS2	DJ2	p
0	0.15	0.15	0.0225
1	0.15	0.70	0.1050
2	0.15	0.15	0.0225
3	0.70	0.15	0.1050
4	0.70	0.70	0.4900

## [2]

p_DJ = probability['p'][scores['DJ_less']==True].sum()

Solution

print("The probability that Dustin Johnson's score is lower than Adam Scott's is ~%s" % round(p_DJ,3))

The probability that Dustin Johnson's score is lower than Adam Scott's is ~0.232

Info

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3.6.5 |Anaconda, Inc.| (default, Mar 29 2018, 13:32:41) [MSC v.1900 64 bit (AMD64)]

Posted on 8/22/2019