Men’s US Open - 1st Rd (John Millman v. #2 Rafael Nadal): How many GAMES will be PLAYED in the 1st Set?

7:10PM
8 Games or Fewer
9 Games or More

Inputs Needed To Solve

Service Games Won %

John Millman
Rafael Nadal

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

JM_SRV_Wperct = .77
RN_SRV_Wperct = .86

# Adjust to match current market odds
JM_SRV_Wperct = .5
RN_SRV_Wperct = .92

## Inputs Defined in the Problem

games = 8

Method To Solve

[1] Simulate 9999 Sets between John Millman and Rafael Nadal using their respective Service Games Won Percent
[2] The ratio of Simulated Matches where there are 8 or less games played in the 1st Set to the total number of Simulations is an estimate of the probability there are 8 Games or Fewer PLAYED in the 1st Set (p_8orless) 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
_8_orless = 0

for i in range(iterations):
    winner = (sim_set(RN_SRV_Wperct,JM_SRV_Wperct))
    if len(winner) <= games:
        _8_orless += 1
        
    if i < 10:
        print(len(winner))
        
p_8orless = _8_orless/iterations

Solution

print("The probability 8 Games or Fewer are PLAYED in the 1st Set is ~%s" % round(p_8orless,3))

The probability 8 Games or Fewer are PLAYED in the 1st Set is ~0.58

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 8/27/2019