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Simple pure python functions for simulating tennis matches

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Simulate tennis points, games, sets and matches.

Small pure python package (no dependencies outside of standard lib) to simulate tennis using points-based modelling i.e. given a probability of a server winning a given point, simulate the outcome of:

  • points
  • games
  • sets
  • tiebreaks
  • matches

with the ability to alter various parameters to gain some intuition behind how the tennis scoring system impacts matches. Using this we can answer various questions like:

  • what effect does removing the second serve have on match duration?
  • if the probability of winning a point on serve is reflective of skill, then how do rule alterations affect the likelihood that the more skillful player will actually end up winning the match (not just a given point)?


pip install tennisim

Points-based Modelling

Points-based modelling is a popular model for modelling tennis matches where predictions for games, sets and matches depends on modelling every constituent point. This can lead to a wealth of data that can be used to generate in-play match odds as we can output distributions e.g. for a given starting point, if we simulate 1000 outcomes how many show that player 1 wins the next set?

For more background I wrote this article on Towards Data Science.


Suppose we want to simulate a game of tennis. We define the probability that the server will win a given point:

from tennisim.sim import sim_game

p = 0.7

This will simulate 1 game of tennis where the probability that the server will win any given point is 0.7. It will return a tuple containing:

  • boolean result for if the server won the game
  • list of tuples for the score progression of the game

We can then take this further and simulate 1,000 groups of 100 games to generate a distribution of results. This can be interesting when looking at how changes in the probability p or the length of a game impacts the servers win probability for the game.

import numpy as np
from tennisim.sim import sim_game

# set params for simulation
games = 100
sims = 1000
probabs = np.linspace(0.5, 0.8, 4)
results = {}

# for each serve win probability
for p in probabs:
   # we now need to generate sims
   means = []
   game_lengths = []
   for i in range(0, sims):
       g_results = [sim_game(p) for x in range(games)]
       # get mean result
       mean_res = np.mean([x[0] for x in g_results])
       # get mean game length
       mean_length = np.mean([len(x[1]) for x in g_results])
       # join to results holders
   # add data to probab dict
   results[p] = (means, game_lengths)


For more info see the documentation


tennisim is free and open source software, distributed under the terms of the MIT license.

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