---

U.S. Open - 1st Rd (#3 Roger Federer v. Sumit Nagal): What will be Federer’s MARGIN of VICTORY?

9:40PM
8 Games or Fewer or Federer Loses
9 Games or More

---

Inputs Needed To Solve

Service Games Won %

Roger Federer
Sumit Nagal

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

RF_SRV_Wperct = .90
SN_SRV_Wperct = .50

## Inputs Defined in the Problem

difference = 8

Method To Solve

• [1] Simulate 9999 Sets between Roger Federer and Sumit Nagalusing their respective Service Games Won Percent
• [2] The ratio of Simulated Matches where RF net losses less than 8 games to the total number of Simulations is an estimate of the probability (p_8orless) or 9 or less based on the Monte Carlo Method.

## [1]

import numpy as np

def sim_game(server,perct1,perct2):
    if server:
        serve = np.random.choice([1,0],1,p=[perct1,1-perct1])
        if serve == 1:
            ans = '1'
        else:
            ans = '0'
        
    else:
        serve = np.random.choice([1,0],1,p=[perct2,1-perct2])
        if serve == 1:
            ans = '0'
        else:
            ans = '1'
        
    return ans

def set_over(winner):
    set_over = False
    
    if winner.count('1') >= 7:
        set_over = True
    if winner.count('0') >= 7:
        set_over = True
    if winner.count('1') >=6 and winner.count('0') < 5:
        set_over = True
    if winner.count('0') >=6 and winner.count('1') < 5:
        set_over = True
    if winner.count('0') == 6 and winner.count('1') == 6:
        set_over = True
    
    return set_over

def sim_set(perct1,perct2):
    winner = ''
    server = True
    set_over_ = False

    while not set_over_:
        game = sim_game(server,perct1,perct2)
        winner += str(game)
        server = not server
        set_over_ = set_over(winner)

    return winner

## [2]

iterations = 9999
less_than_8 = 0

for i in range(iterations):
    RF = 0
    SN = 0
    RF_detlta = 0
    
    while RF < 3 and SN < 3:
        winner = (sim_set(RF_SRV_Wperct,SN_SRV_Wperct))
        if winner.count('1') > winner.count('0'):
            RF += 1
        else:
            SN += 1
            
        RF_detlta += winner.count('1') - winner.count('0')
            
    if RF_detlta <= difference:
        less_than_8 += 1
    

p_8orless = less_than_8/iterations

---

Solution

print("The probability Federer's MARGIN OF VICTORY is 8 Games or Fewer is ~%s" % round(p_8orless,3))

The probability Federer's MARGIN OF VICTORY is 8 Games or Fewer is ~0.083

---

---

---

Info

download md 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 8/26/2019