PGA Rocket Mortgage Classic - 1st Rd: Which PLAYER will record the LOWER COMBINED SCORE on Holes 17-18?

5:00PM
Hideki Matsuyama (JPN)
Patrick Reed (USA) or Tie

Inputs to Solve

2019 Course Stats

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

hole_17 = {'2':38,
          '3':311,
          '4':98,
          '5':5}

hole_18 = {'3':62,
          '4':290,
          '5':89,
          '6':11}

## Inputs Defined in the Problem

stroke_diff = 0

golfers = ['hole17','hole18']

Method to Solve

[1] Enumrate all the possible combinations of observed scores and their respective probabilities on holes 17 and 18.
[2] Compute the combined probability of each score for each golfer.
[3] The probability Matsuyama has a lower score on Holes 17 and 18 (p_mat) is the sum of the probabilities where Matsuyama’s score is lower than Reed’s.

## [1]

import numpy as np
import pandas as pd

t=sum(hole_17.values())
for i in hole_17:
    hole_17[i] = hole_17[i]/t

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_17.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_17.values() for b in hole_18.values()])
probability = pd.DataFrame(z)
probability.columns = golfers
probability['p'] = probability.product(axis=1)

p_total_scores =[]
total_scores=[]
for s in set(scores['total_strokes']):
    p_total_scores.append(probability['p'][scores['total_strokes']==s].sum())
    total_scores.append(s)

golfers = ['Matsuyama','Reed']

y = np.array([(a,b) for a in total_scores for b in total_scores])
Scores = pd.DataFrame(y)
Scores.columns = golfers
Scores['mat_less'] = Scores['Matsuyama'] < Scores['Reed']

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

Scores

	Matsuyama	Reed	mat_less
0	5	5	False
1	5	6	True
2	5	7	True
3	5	8	True
4	5	9	True
5	5	10	True
6	5	11	True
7	6	5	False
8	6	6	False
9	6	7	True
10	6	8	True
11	6	9	True
12	6	10	True
13	6	11	True
14	7	5	False
15	7	6	False
16	7	7	False
17	7	8	True
18	7	9	True
19	7	10	True
20	7	11	True
21	8	5	False
22	8	6	False
23	8	7	False
24	8	8	False
25	8	9	True
26	8	10	True
27	8	11	True
28	9	5	False
29	9	6	False
30	9	7	False
31	9	8	False
32	9	9	False
33	9	10	True
34	9	11	True
35	10	5	False
36	10	6	False
37	10	7	False
38	10	8	False
39	10	9	False
40	10	10	False
41	10	11	True
42	11	5	False
43	11	6	False
44	11	7	False
45	11	8	False
46	11	9	False
47	11	10	False
48	11	11	False

probability

	Matsuyama	Reed	p
0	0.011532	0.011532	1.329832e-04
1	0.011532	0.148318	1.710381e-03
2	0.011532	0.487744	5.624580e-03
3	0.011532	0.278149	3.207571e-03
4	0.011532	0.066533	7.672499e-04
5	0.011532	0.007455	8.596496e-05
6	0.011532	0.000269	3.104447e-06
7	0.148318	0.011532	1.710381e-03
8	0.148318	0.148318	2.199829e-02
9	0.148318	0.487744	7.234127e-02
10	0.148318	0.278149	4.125459e-02
11	0.148318	0.066533	9.868085e-03
12	0.148318	0.007455	1.105649e-03
13	0.148318	0.000269	3.992825e-05
14	0.487744	0.011532	5.624580e-03
15	0.487744	0.148318	7.234127e-02
16	0.487744	0.487744	2.378940e-01
17	0.487744	0.278149	1.356655e-01
18	0.487744	0.066533	3.245116e-02
19	0.487744	0.007455	3.635924e-03
20	0.487744	0.000269	1.313039e-04
21	0.278149	0.011532	3.207571e-03
22	0.278149	0.148318	4.125459e-02
23	0.278149	0.487744	1.356655e-01
24	0.278149	0.278149	7.736699e-02
25	0.278149	0.066533	1.850616e-02
26	0.278149	0.007455	2.073485e-03
27	0.278149	0.000269	7.487963e-05
28	0.066533	0.011532	7.672499e-04
29	0.066533	0.148318	9.868085e-03
30	0.066533	0.487744	3.245116e-02
31	0.066533	0.278149	1.850616e-02
32	0.066533	0.066533	4.426667e-03
33	0.066533	0.007455	4.959769e-04
34	0.066533	0.000269	1.791118e-05
35	0.007455	0.011532	8.596496e-05
36	0.007455	0.148318	1.105649e-03
37	0.007455	0.487744	3.635924e-03
38	0.007455	0.278149	2.073485e-03
39	0.007455	0.066533	4.959769e-04
40	0.007455	0.007455	5.557073e-05
41	0.007455	0.000269	2.006822e-06
42	0.000269	0.011532	3.104447e-06
43	0.000269	0.148318	3.992825e-05
44	0.000269	0.487744	1.313039e-04
45	0.000269	0.278149	7.487963e-05
46	0.000269	0.066533	1.791118e-05
47	0.000269	0.007455	2.006822e-06
48	0.000269	0.000269	7.247223e-08

## [2]

p_mat = probability['p'][Scores['mat_less']==True].sum()

Solution

print("The probability Matsuyama has a lower score on Holes 17 and 18 is ~ %s" % round(p_mat,3))

The probability Matsuyama has a lower score on Holes 17 and 18 is ~ 0.329

Info

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twitter: @KRELLabs

import sys
print(sys.version)

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

Posted on 7/2/2020