World Cup

Write a program to run simulations of the FIFA World Cup.

In the soccer World Cup, the knockout round consists of 16 teams. In each round, each team plays another team and the losing teams are eliminated. When only two teams remain, the winner of the final match is the champion.

Soccer teams are assigned FIFA Ratings, which are numerical values representing each team’s relative skill level. A higher FIFA rating indicates better previous game results, and given two teams’ FIFA ratings, it’s possible to estimate the probability that either team wins a game based on their current ratings. The FIFA Ratings from just before two previous World Cups are available:

• May 2018 Men’s FIFA Ratings
• March 2019 Women’s FIFA Ratings

Using this information, we can simulate the entire tournament by repeatedly simulating rounds until we’re left with just one team. And if we want to estimate how likely it is that any given team wins the tournament, we might simulate the tournament many times (>1000 simulations) and count how many times each team wins a simulated tournament.

What’s provided

Start by looking at the 2018m.csv file. This file contains the 16 teams in the knockout round of the 2018 Men’s World Cup and the ratings for each team. Notice that the CSV file has two columns, one called team (representing the team’s country name) and one called rating (representing the team’s rating).

The order in which the teams are listed determines which teams will play each other in each round (in the first round, for example, Uruguay will play Portugal and France will play Argentina; in the next round, the winner of the Uruguay-Portugal match will play the winner of the France-Argentina match). Do not edit the order in which teams appear in this file!

In Python, we can represent each team as a dictionary that contains two values: the team name and the rating. Uruguay, for example, would appear as {"team": "Uruguay", "rating": 976}.

Next, see 2019w.csv, which contains data formatted the same way for the 2019 Women’s World Cup.

Now, open tournament.py, where some code has already been written for you. The variable N at the top represents how many World Cup simulations to run: in this case, 1000.

The simulate_tournament() function accepts a list of teams (in a variable called teams) as input, and repeatedly calls simulate_round() to simulate a round of play until only one team remains.

In the main function

is a list called teams (which will eventually be a list of teams) and a dictionary called counts (which will associate team names with the number of times that team won a simulated tournament). Right now they’re both empty, so populating them is left up to you.

Finally, at the end of main(), we sort the teams in descending order of how many times they won simulations (according to counts) and print the estimated probability that each team wins the World Cup.

Populating teams and counts and writing the simulate_round() and simulate_game() functions are left up to you.

Implementation Details

Complete tournament.py.

First, in main(), read the team data from the CSV file and add each team to the list teams.

• You can open a file with open(filename), where filename is a variable storing the name of the file.
• Once you have a file f, you can use csv.DictReader(f) to give you a “reader”: an object in Python that you can loop over to read the file one row at a time, treating each row as a dictionary.
• By default, all values read from the file will be strings. So be sure to first convert the team’s rating to an int.
• Append each team’s dictionary to teams.
• Remember that each team should be a dictionary with a team name and a rating.

Next, implement the simulate_game() function. This function should accept as input two teams and return True if team 1 wins, and False otherwise.

• team1 and team2 are dictionaries from the teams list.
• The probability of team1 beating team2 based on each team’s rating can be found with this formula:

probability = 1 / (1 + 10 ** ((rating2 - rating1) / 600))

• You can get a random number between 0 and 1 with random.random().

Next, implement the simulate_round() function. This function simulates one round of play. It takes as input a list of teams that are playing in the round, and returns a list of the winners.

• Remember that the returned list of winners will always be half the size of the list of teams that are playing in the round!

Finally, back in the main() function, run N tournament simulations, and keep track of how many times each team wins in the counts dictionary.

• For example, if Uruguay won 2 tournaments and Portugal won 3, then your counts dictionary should be {"Uruguay": 2, "Portugal": 3}.
• You should call simulate_tournament() to simulate each tournament and determine the winner.
• You can use the in keyword in Python to check if a dictionary has a particular key already. For example, if "Portugal" in counts: would check to see if "Portugal" already has a value in the counts dictionary.

Testing

Your program should behave as below. Since simulations involve randomness, your output may not match these examples exactly.

Belgium: 20.9% chance of winning
Brazil: 20.3% chance of winning
Portugal: 14.5% chance of winning
Spain: 13.6% chance of winning
Switzerland: 10.5% chance of winning
Argentina: 6.5% chance of winning
England: 3.7% chance of winning
France: 3.3% chance of winning
Denmark: 2.2% chance of winning
Croatia: 2.0% chance of winning
Colombia: 1.8% chance of winning
Sweden: 0.5% chance of winning
Uruguay: 0.1% chance of winning
Mexico: 0.1% chance of winning

In case you’re wondering, here’s what actually happened at the actual tournaments:

• In the 2018 Men’s World Cup, France won, defeating Croatia in the final. Belgium defeated England for third place.
• In the 2019 Women’s World Cup, the United States beat the Netherlands in the final. England defeated Sweden to finish third.