PGA Rocket Mortgage Classic - 2nd Rd: Which PLAYER will record a LOWER FRONT 9 SCORE?

1:00PM
Rickie Fowler (USA)
Webb Simpson (USA) or Tie

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Inputs to Solve

2019 Course Stats

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

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

hole_1 = {'2':38,
          '3':311,
          '4':98,
          '5':5}

hole_2 = {'3':62,
          '4':290,
          '5':89,
          '6':11}

hole_3 = {'3':52,
          '4':310,
          '5':84,
          '6':6}

hole_4 = {'2':72,
          '3':301,
          '4':70,
          '5':10}

hole_5 = {'3':72,
          '4':300,
          '5':75,
          '6':6}

hole_6 = {'3':68,
          '4':312,
          '5':65,
          '6':5}

hole_7 = {'3':60,
          '4':334,
          '5':56,
          '6':3,
          '7':1}

hole_8 = {'2':76,
          '3':317,
          '4':56,
          '5':3}

hole_9 = {'3':94,
          '4':301,
          '5':57,
          '6':1}

## Inputs Defined in the Problem

stroke_diff = 0

golfers = ['h1','h2','h3','h4',
           'h5','h6','h7','h8','h9']

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Method to Solve

• [1] Enumrate all the possible combinations of observed scores and their respective probabilities on holes 1-9.
• [2] Compute the combined probability of each score for each golfer.
• [3] The probability Fowler has a lower score on the FRONT 9 (p_rf) is the sum of the probabilities where Fowler’s score is lower than Simpson’s.

## [1]

import numpy as np
import pandas as pd

t=sum(hole_1.values())
for i in hole_1:
    hole_1[i] = hole_1[i]/t

t=sum(hole_2.values())
for i in hole_2:
    hole_2[i] = hole_2[i]/t
    
t=sum(hole_3.values())
for i in hole_3:
    hole_3[i] = hole_3[i]/t
    
t=sum(hole_4.values())
for i in hole_4:
    hole_4[i] = hole_4[i]/t

t=sum(hole_5.values())
for i in hole_5:
    hole_5[i] = hole_5[i]/t
    
t=sum(hole_6.values())
for i in hole_6:
    hole_6[i] = hole_6[i]/t

t=sum(hole_7.values())
for i in hole_7:
    hole_7[i] = hole_7[i]/t

t=sum(hole_8.values())
for i in hole_8:
    hole_8[i] = hole_8[i]/t
    
t=sum(hole_9.values())
for i in hole_9:
    hole_9[i] = hole_9[i]/t
 
y = np.array([(a,b,c,d,e,f,g,h,i) for a in hole_1.keys() for b in hole_2.keys() for c in hole_3.keys()
              for d in hole_4.keys() for e in hole_5.keys() for f in hole_6.keys()
              for g in hole_7.keys() for h in hole_8.keys() for i in hole_9.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,c,d,e,f,g,h,i) for a in hole_1.values() for b in hole_2.values() for c in hole_3.values()
              for d in hole_4.values() for e in hole_5.values() for f in hole_6.values()
              for g in hole_7.values() for h in hole_8.values() for i in hole_9.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)

## [2]

golfers = ['Fowler','Simpson']

y = np.array([(a,b) for a in total_scores for b in total_scores])
Scores = pd.DataFrame(y)
Scores.columns = golfers
Scores['rf_less'] = Scores['Fowler'] < Scores['Simpson']

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

probability

## [3]

p_rf = probability['p'][Scores['rf_less']==True].sum()

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Solution

print("The probability Fowler has a lower score on the FRONT 9 is ~ %s" % round(p_rf,3))

The probability Fowler has a lower score on the FRONT 9 is ~ 0.42

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import sys
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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 7/3/2020