Simple pure python functions for simulating tennis matches

## Project description

# tennisim

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)?

# Installing

`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.

# Example

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
sim_game(p)
```

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
means.append(mean_res)
game_lengths.append(mean_length)
# add data to probab dict
results[p] = (means, game_lengths)
```

# Help

For more info see the documentation

# License

`tennisim`

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

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