PGA Tour Championship - 1st Rd (Atlanta, GA): How many BIRDIES will Rory McIlroy and John Rahm record on Holes 2-4?

2:00PM
2 or 3 Birdies
Any Other Number

Inputs To Solve

East Lake Golf Club 2018 Course Stats

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

p_bird_2 = 18/(18+84+18)
p_bird_3 = 29/(29+72+19)
p_bird_4 = 17/(17+74+27+2)

print("The probability of a PLAYER scoring BIRDIE on hole 2 is ~%s" % round(p_bird_2,3))
print("The probability of a PLAYER scoring BIRDIE on hole 3 is ~%s" % round(p_bird_3,3))
print("The probability of a PLAYER scoring BIRDIE on hole 4 is ~%s" % round(p_bird_4,3))

The probability of a PLAYER scoring BIRDIE on hole 2 is ~0.15
The probability of a PLAYER scoring BIRDIE on hole 3 is ~0.242
The probability of a PLAYER scoring BIRDIE on hole 4 is ~0.142

## Inputs Defined in the Problem

num_birdies = [2,3]
golfers = ['RM','JR']

Method to Solve

[1] Compute the probability of 0, 1 or 2 Birdies being scored on each hole (2-4) by the 2 golfers
[2] Enumerate all the possible combinations of 0, 1 or 2 BIRDIES being scored on holes 2-4 (birdies) and their respective probabilities (probability).
[3] The probability that 2 or 3 total BIRDIES are scored by both golfers on holes 2-4 is the sum of the probabilities of all the outcomes where the total number of BIRDIES is equal to 2 or 3 (p_2or3).

## [1]

import numpy as np
import pandas as pd

# Hole 2
p_other = 1 - p_bird_2
prob = (p_bird_2,p_other)
bird = (1,0)
b = {}

y = np.array([(x,z) for x in bird for z in bird])
birdies = pd.DataFrame(y)
birdies.columns = golfers
birdies['total_birdies'] = birdies.sum(axis=1)

x = np.array([(x,z) for x in prob for z in prob])
probability = pd.DataFrame(x)
probability.columns = golfers
probability['p'] = probability.product(axis=1)

for i in set(birdies.total_birdies):
    b[i] = round(probability['p'][birdies['total_birdies']==i].sum(),2)
    
# Hole 3
p_other = 1 - p_bird_3
prob = (p_bird_3,p_other)
bird = (1,0)
c = {}

y = np.array([(x,z) for x in bird for z in bird])
birdies = pd.DataFrame(y)
birdies.columns = golfers
birdies['total_birdies'] = birdies.sum(axis=1)

x = np.array([(x,z) for x in prob for z in prob])
probability = pd.DataFrame(x)
probability.columns = golfers
probability['p'] = probability.product(axis=1)

for i in set(birdies.total_birdies):
    c[i] = round(probability['p'][birdies['total_birdies']==i].sum(),2)
    
# Hole 4
p_other = 1 - p_bird_4
prob = (p_bird_4,p_other)
bird = (1,0)
d = {}

y = np.array([(x,z) for x in bird for z in bird])
birdies = pd.DataFrame(y)
birdies.columns = golfers
birdies['total_birdies'] = birdies.sum(axis=1)

x = np.array([(x,z) for x in prob for z in prob])
probability = pd.DataFrame(x)
probability.columns = golfers
probability['p'] = probability.product(axis=1)

for i in set(birdies.total_birdies):
    d[i] = round(probability['p'][birdies['total_birdies']==i].sum(),2)

print("The number of possible birdies on hole 2 for 3 golfers and their respective probabilities are: %s" % b)
print("The number of possible birdies on hole 3 for 3 golfers and their respective probabilities are: %s" % c)
print("The number of possible birdies on hole 4 for 3 golfers and their respective probabilities are: %s" % d)

The number of possible birdies on hole 2 for 3 golfers and their respective probabilities are: {0: 0.72, 1: 0.26, 2: 0.02}
The number of possible birdies on hole 3 for 3 golfers and their respective probabilities are: {0: 0.58, 1: 0.37, 2: 0.06}
The number of possible birdies on hole 4 for 3 golfers and their respective probabilities are: {0: 0.74, 1: 0.24, 2: 0.02}

## [2]

holes = ['2','3','4']
outcomes = (0,1,2)

y = np.array([(w,x,z) for w in outcomes for x in outcomes for z in outcomes])
birdies = pd.DataFrame(y)
birdies.columns = holes
birdies['total_birdies'] = birdies.sum(axis=1)

birdies.head()

	3	4	total_birdies
0	0	0	0
1	0	1	1
2	0	2	2
3	1	0	1
4	1	1	2

x = np.array([(w,y,z) for w in b.values() for y in c.values() for z in d.values()])
probability = pd.DataFrame(x)
probability.columns = holes
probability['p'] = probability.product(axis=1)

probability.head()

	2	3	4	p
0	0.72	0.58	0.74	0.309024
1	0.72	0.58	0.24	0.100224
2	0.72	0.58	0.02	0.008352
3	0.72	0.37	0.74	0.197136
4	0.72	0.37	0.24	0.063936

## [3]

p_2or3 = probability['p'][birdies['total_birdies']==num_birdies[0]].sum() + probability['p'][birdies['total_birdies']==num_birdies[1]].sum()

Solution

print("The probability that Rory McIlroy and John Rahm record 2 or 3 BIRDIES on holes 2-4 is ~%s" % round(p_2or3,3))

The probability that Rory McIlroy and John Rahm record 2 or 3 BIRDIES on holes 2-4 is ~0.282

Info

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Posted on 8/22/2019