Women’s US Open - 2nd Rd (#3 K. Pliskova v. T. Martincova): How many BREAK POINTS will Pliskova FACE in the 2nd Set?

Inputs Needed To Solve

Service Games Won %

Pliskova
Martincova

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

KP_SRV_Wperct = .806
KN_SRV_Wperct = .735

KP_BreakPoint = .35
TM_BreakPoint = .65

Method To Solve

[1] Simulate 9999 Sets between Pliskova and Martincova using respective Service Games Won Percent and the observable odds that any of their service games will go to a BREAK POINT.
[2] The ratio of Simulated Matches there are 0 or 1 BREAK POINTS to the total number of Simulations is an estimate of the probability of the event happening (p_breakpoint) 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

## [2]

iterations = 999
BreakPoints = 0


print("The first 10 simuations yield the following number of BREAK POINTS FACED by Pliskova in the 2nd Set:")
print('')

for i in range(iterations):
    winner = ''
    server = True
    set_over_ = False
    bp = 0

    while not set_over_:
        game = sim_game(server,KP_BreakPoint,TM_BreakPoint)
        winner += str(game)
        
        if server:
            b_point = int(np.random.choice([1,0],1,p=[KP_BreakPoint,1-KP_BreakPoint]))
        
        bp += b_point
        
        server = not server
        set_over_ = set_over(winner)
        

    if bp == 0 or bp == 1:
        BreakPoints += 1
    
    if i < 10:
        print(bp)
       
p_breakpoint = BreakPoints/iterations

The first 10 simuations yield the following number of BREAK POINTS FACED by Pliskova in the 2nd Set:

2
4
2
2
2
0
4
8
0
3

Solution

print("The probability Pliskova FACES 0 or 1 BREAK POINTS in the 2nd Set is ~ %s" % round(p_breakpoint,3))

The probability Pliskova FACES 0 or 1 BREAK POINTS in the 2nd Set is ~ 0.172

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 8/28/2019