Simulating a football league in python

January 11, 2022

I could use some help on this. I want to simulate a football league in python for an arbitrary number of teams and tally the points over a season in a table. The rules are simple:

Every team in the league plays each other twice. so each team plays 2*(Nteams_in_league -1)
Teams have a 50% chance of a winning.
There are only two possible outcomes, win or lose.
A win gets 3 points, and a loss gets a team 0 points.

Here’s an example of the output I’m looking for with a league of 8 teams over 11 seasons. It’s based off an attempt I made but isn’t completely correct because it’s not allocating point across the winner and loser correctly.

columns = season,
rows = team,
observations are the points tally.

1	2	3	4	5	6	7	8	9	10	11
1	57	51	66	54	60	51	57	54	45	72
2	51	51	42	51	66	60	63	60	81	63
3	51	69	51	48	36	48	57	54	48	60
4	54	57	66	54	75	60	60	66	69	42
5	72	57	63	57	60	54	48	66	54	42
6	54	45	54	45	60	57	51	60	66	51
7	51	63	72	63	63	54	60	63	54	66
8	66	57	42	57	51	57	51	75	72	60

>Solution :

Here is one approach. This simulates each season independently. For each season and pair of teams, we simulate two outcomes for two games, assuming each team has a 50% chance at victory.

import numpy as np
import pandas as pd
from itertools import combinations

def simulate_naive(n_teams):
  'Simulate a single season'
  scores = np.zeros(n_teams, dtype=int)
  for i, j in combinations(range(n_teams), 2):
      # each pair of teams play twice, each time with 50/50 chance of 
      # either team winning; the winning team gets three points
      scores[i if np.random.rand() < 0.5 else j] += 3
      scores[i if np.random.rand() < 0.5 else j] += 3
      
  return scores

n_teams = 8
n_seasons = 10
df = pd.DataFrame({season: simulate_naive(n_teams) for season in range(n_seasons)})
print(df)
#     0   1   2   3   4   5   6   7   8   9
# 0  15  30  21  12  24  24   9  21  18  33
# 1  21  18  24  24  15  21  12  30  18  21
# 2  21  27  21  18  21  27  27  15  12  24
# 3  27  12   9  36  18  12  30  15  24  21
# 4  24  24  27  24  18  18  33  18  30  15
# 5  18  15  21  15  15  27  15  24  24  15
# 6  18  18  30  21  33  21  24  27  18  21
# 7  24  24  15  18  24  18  18  18  24  18

I wonder if there is a nicer statistical approach that avoids simulating each game.