Lab 6: World Cup
Labs are practice problems which, time permitting, may be started or completed in your section, and are assessed on correctness only. You are encouraged to collaborate with classmates on this lab, though each member in a group collaborating is expected to contribute equally to the lab.
Write a program to run simulations of the FIFA World Cup.
$ python tournament.py 2018m.csv
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
Background
In soccer’s 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.
In soccer, teams are given FIFA Ratings, which are numerical values representing each team’s relative skill level. Higher FIFA ratings indicate 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 two previous World Cups are available as the May 2018 Men’s FIFA Ratings and 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 (e.g. 1000 simulations) and count how many times each team wins a simulated tournament. 1000 simulations might seem like many, but with today’s computing power we can accomplish those simulations in a matter of milliseconds. At the end of this lab, we’ll experiment with how worthwhile it might be to increase the number of simulations we run, given the tradeoff of runtime.
Your task in this lab is to do all this using Python!
Getting Started
Open VS Code.
Start by clicking inside your terminal window, then execute cd
by itself. You should find that its “prompt” resembles the below.
$
Click inside of that terminal window and then execute
wget https://cdn.cs50.net/2022/fall/labs/6/worldcup.zip
followed by Enter in order to download a ZIP called worldcup.zip
in your codespace. Take care not to overlook the space between wget
and the following URL, or any other character for that matter!
Now execute
unzip worldcup.zip
to create a folder called worldcup
. You no longer need the ZIP file, so you can execute
rm worldcup.zip
and respond with “y” followed by Enter at the prompt to remove the ZIP file you downloaded.
Now type
cd worldcup
followed by Enter to move yourself into (i.e., open) that directory. Your prompt should now resemble the below.
worldcup/ $
If all was successful, you should execute
ls
and you should see the following files:
answers.txt 2018m.csv 2019w.csv tournament.py
If you run into any trouble, follow these same steps again and see if you can determine where you went wrong!
Understanding
Start by taking a look 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 UruguayPortugal match will play the winner of the FranceArgentina match). So be sure not to edit the order in which teams appear in this file!
Ultimately, in Python, we can represent each team as a dictionary that contains two values: the team name and the rating. Uruguay, for example, we would want to represent in Python as {"team": "Uruguay", "rating": 976}
.
Next, take a look at 2019w.csv
, which contains data formatted the same way for the 2019 Women’s World Cup.
Now, open tournament.py
and see that we’ve already written some code for you. The variable N
at the top represents how many World Cup simulations to run: in this case, 1000.
The simulate_game
function accepts two teams as inputs (recall that each team is a dictionary containing the team name and the team’s rating), and simulates a game between them. If the first team wins, the function returns True
; otherwise, the function returns False
.
The simulate_round
function accepts a list of teams (in a variable called teams
) as input, and simulates games between each pair of teams. The function then returns a list of all of the teams that won the round.
In the main
function, notice that we first ensure that len(sys.argv)
(the number of commandline arguments) is 2. We’ll use commandline arguments to tell Python which team CSV file to use to run the tournament simulation. We’ve then defined 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_tournament
function are left up to you!
Implementation Details
Complete the implementation of tournament.py
, such that it simulates a number of tournaments and outputs each team’s probability of winning.
First, in main
, read the team data from the CSV file into your program’s memory, and add each team to the list teams
.
 The file to use will be provided as a commandline argument. You can access the name of the file, then, with
sys.argv[1]
.  Recall that you can open a file with
open(filename)
, wherefilename
is a variable storing the name of the file.  Once you have a file
f
, you can usecsv.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 anint
(you can use theint
function in Python to do this).  Ultimately, append each team’s dictionary to
teams
. The function callteams.append(x)
will appendx
to the listteams
.  Recall that each team should be a dictionary with a
team
name and arating
.
Next, implement the simulate_tournament
function. This function should accept as input a list of teams and should repeatedly simulate rounds until you’re left with one team. The function should the return the name of that team.
 You can call the
simulate_round
function, which simulates a single round, accepting a list of teams as input and returning a list of all of the winners.  Recall that if
x
is a list, you can uselen(x)
to determine the length of the list.  You should not assume the number of teams in the tournament, but you may assume it will be a power of 2.
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 tournaments, then your
counts
dictionary should be{"Uruguay": 2, "Portugal": 3}
.  You should use your
simulate_tournament
to simulate each tournament and determine the winner.  Recall that if
counts
is a dictionary, then syntax likecounts[team_name] = x
will associate the key stored inteam_name
with the value stored inx
.  You can use the
in
keyword in Python to check if a dictionary has a particular key already. For example,if "Portugal" in counts:
will check to see if"Portugal"
already has an existing value in thecounts
dictionary.
Walkthrough
This video was recorded when the course was still using CS50 IDE for writing code. Though the interface may look different from your codespace, the behavior of the two environments should be largely similar!
Hints

When reading in the file, you may find this syntax helpful, with
filename
as the name of your file andfile
as a variable.with open(filename) as file: reader = csv.DictReader(file)

In Python, to append to the end of a list, use the
.append()
function.
Not sure how to solve?
Testing
Your program should behave per the examples below. Since simulations have randomness within each, your output will likely not perfectly match the examples below.
$ python tournament.py 2018m.csv
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
$ python tournament.py 2019w.csv
Germany: 17.1% chance of winning
United States: 14.8% chance of winning
England: 14.0% chance of winning
France: 9.2% chance of winning
Canada: 8.5% chance of winning
Japan: 7.1% chance of winning
Australia: 6.8% chance of winning
Netherlands: 5.4% chance of winning
Sweden: 3.9% chance of winning
Italy: 3.0% chance of winning
Norway: 2.9% chance of winning
Brazil: 2.9% chance of winning
Spain: 2.2% chance of winning
China PR: 2.1% chance of winning
Nigeria: 0.1% chance of winning
 You might be wondering what actually happened at the 2018 and 2019 World Cups! For Men’s, France won, defeating Croatia in the final. Belgium defeated England for the third place position. For Women’s, the United States won, defeating the Netherlands in the final. England defeated Sweden for the third place position.
Number of Simulations
Once you’re sure your code is correct, let’s tinker with the value of N
, the constant at the top of our file, to adjust the number of times we simulate the tournament. More tournament simulations will give us more accurate predictions (why?), at the cost of time.
We can time programs by prepending their execution at the commandline with time
. For example, with N
set to 1000 (the default) execute
time python tournament.py 2018m.csv
or
time python tournament.py 2019w.csv
which should output something like
real 0m0.037s
user 0m0.028s
sys 0m0.008s
though your own times might vary.
Pay attention to the real metric, which is the time, in total, it took tournament.py
to run. And notice that you’re given time in minutes and seconds, with accuracy to thousandths of a second.
In answers.txt
, keep track of how long it takes tournament.py
to simulate…
 10 (ten) tournaments
 100 (one hundred) tournaments
 1000 (one thousand) tournaments
 10000 (ten thousand) tournaments
 100000 (one hundred thousand) tournaments
 1000000 (one million) tournaments
Each time you adjust N
, record the real time in the appropriate TODO in answers.txt
by using the same 0m0.000s
format. After timing each scenario, answer the two followup questions by overwriting the given TODO:
 Which predictions, if any, proved incorrect as you increased the number of simulations?
 Suppose you’re charged a fee for each second of compute time your program uses. After how many simulations would you call the predictions “good enough”?
See a correctly formatted answers.txt
Times:
10 simulations: 0m0.028s
100 simulations: 0m0.030s
1000 simulations: 0m0.041s
10000 simulations: 0m0.139s
100000 simulations: 0m1.031s
1000000 simulations: 0m11.961s
Questions:
Which predictions, if any, proved incorrect as you increased the number of simulations?:
With a small number of simulations...
Suppose you're charged a fee for each second of compute time your program uses.
After how many simulations would you call the predictions "good enough"?:
It seems like the predictions stabilized after about...
How to Test Your Code
Execute the below to evaluate the correctness of your code using check50
. But be sure to compile and test it yourself as well!
check50 cs50/labs/2022/fall/worldcup
Execute the below to evaluate the style of your code using style50
.
style50 tournament.py
How to Submit
 Download your
tournament.py
andanswers.txt
files by controlclicking or rightclicking on the files in your codespace’s file browser and choosing Download.  Go to CS50’s Gradescope page.
 Click “Lab 6: World Cup”.
 Drag and drop your
tournament.py
andanswers.txt
files to the area that says “Drag & Drop”. Be sure it has those exact filenames! If you upload a file with a different name, the autograder likely will fail when trying to run it, and ensuring you have uploaded files with the correct filename is your responsibility!  Click “Upload”.
You should see a message that says “Lab 6: World Cup submitted successfully!”
Per Step 4 above, after you submit, be sure to check your autograder results. If you see SUBMISSION ERROR: missing files (0.0/1.0)
, it means your file was not named exactly as prescribed (or you uploaded it to the wrong problem).
Correctness in submissions entails everything from reading the specification, writing code that is compliant with it, and submitting files with the correct name. If you see this error, you should resubmit right away, making sure your submission is fully compliant with the specification. The staff will not adjust your filenames for you after the fact!
Want to see the staff's solution?
# Simulate a sports tournament
import csv
import sys
import random
# Number of simluations to run
N = 1000
def main():
# Ensure correct usage
if len(sys.argv) != 2:
sys.exit("Usage: python tournament.py FILENAME")
# Read teams into memory
teams = []
filename = sys.argv[1]
with open(filename) as f:
reader = csv.DictReader(f)
for team in reader:
team["rating"] = int(team["rating"])
teams.append(team)
# Keep track of number of wins for each team
counts = {}
for i in range(N):
winner = simulate_tournament(teams)
if winner in counts:
counts[winner] += 1
else:
counts[winner] = 1
# Print each team's chances of winning, according to simulation
for team in sorted(counts, key=lambda team: counts[team], reverse=True):
print(f"{team}: {counts[team] * 100 / N:.1f}% chance of winning")
def simulate_game(team1, team2):
"""Simulate a game. Return True if team1 wins, False otherwise."""
rating1 = team1["rating"]
rating2 = team2["rating"]
probability = 1 / (1 + 10 ** ((rating2  rating1) / 600))
return random.random() < probability
def simulate_round(teams):
"""Simulate a round. Return a list of winning teams."""
winners = []
# Simulate games for all pairs of teams
for i in range(0, len(teams), 2):
if simulate_game(teams[i], teams[i + 1]):
winners.append(teams[i])
else:
winners.append(teams[i + 1])
return winners
def simulate_tournament(teams):
"""Simulate a tournament. Return name of winning team."""
while len(teams) > 1:
teams = simulate_round(teams)
return teams[0]["team"]
if __name__ == "__main__":
main()