PGA BMW Championship - 1st Rd: What will be B. Koepka, R. McIlroy and P. Reed’s COMBINED SCORE on the Par 4 3rd?)

12:20PM
10, 12 or 14 Strokes
Any Other Number

Inputs To Solve

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

# estimate given the course has not been played at the time of the prop
hole_3 = {'3':45,
           '4':254,
           '5':89,
           '6':7,
           '7':2}

## Inputs Defined in the Problem

strokes = [10,12,14]

Method to Solve

[1] Enumerate all the possible combinations of observed scores and their respective probabilities for 3 golfers on the 3rd hole.
[3] The probability that B. Koepka, R. McIlroy and P. Reed’s score is 10, 12 or 14 is the sum of the probabilities of outcomes where the 3 golfer’s total score is 10, 12 or 14 (p_10_12_14).

import numpy as np
import pandas as pd

## [1]

t=sum(hole_3.values())
for i in hole_3:
    hole_3[i] = hole_3[i]/t

y = np.array([(a,b,c) for a in hole_3.keys()for b in hole_3.keys() for c in hole_3.keys()])
y = y.astype(int)
scores = pd.DataFrame(y)
scores['total_strokes'] = scores.sum(axis=1)
scores.head()

	0	1	2	total_strokes
0	3	3	3	9
1	3	3	4	10
2	3	3	5	11
3	3	3	6	12
4	3	3	7	13

z = np.array([(a,b,c) for a in hole_3.values() for b in hole_3.values() for c in hole_3.values()])
probability = pd.DataFrame(z)
probability['p'] = probability.product(axis=1)
probability.head()

	0	1	2	p
0	0.11335	0.11335	0.113350	0.001456
1	0.11335	0.11335	0.639798	0.008220
2	0.11335	0.11335	0.224181	0.002880
3	0.11335	0.11335	0.017632	0.000227
4	0.11335	0.11335	0.005038	0.000065

## [2]

p_10 = probability['p'][scores['total_strokes']==strokes[0]].sum()
p_12 = probability['p'][scores['total_strokes']==strokes[1]].sum()
p_14 = probability['p'][scores['total_strokes']==strokes[2]].sum()

p_10_12_14 = p_10 + p_12 + p_14

Solution

print("The probability B. Koepka, R. McIlroy and P. Reed's's combined score is 10, 12 or 14 is ~%s" % round(p_10_12_14,3))

The probability B. Koepka, R. McIlroy and P. Reed's's combined score is 10, 12 or 14 is ~0.508

Info

download markdown file
email: krellabsinc@gmail.com
twitter: @KRELLabs

import sys
print(sys.version)

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

Posted on 8/15/2019