Football fans love forecasting their favorite teams' probability of winning, especially in a competitive division such as the 2024-2025 Premier League. In this paper, I introduce the approach through which I approximated every team's probability of winning using a binomial probability model. This approach allows us to make an approximation of the probability of a team winning its seen number of games based on historical performance.
Data Collection
To start, I gathered win stats for all Premier League teams from a sports card that gave them their wins for the season. Below is a brief rundown of some key teams and their wins:
•Liverpool: 25 wins
•Manchester City: 21 wins
•Arsenal: 20 wins
•Chelsea: 20 wins
•Newcastle United: 20 wins
•Aston Villa: 19 wins
•Nottingham Forest: 19 wins
•Brent Ford: 16 wins
•Brighton: 16 wins
•Bournemouth: 15 wins
•Fulham: 15 wins
•Crystal Palace: 13 wins
•Wolverhampton Wanderers: 12 wins
•Everton: 11 wins
•Manchester United: 11 wins
•Tottenham Hotspur: 11 wins
•West Ham United: 11 wins
•Leicester City: 6 wins
•Ipswich Town: 4 wins
•Southampton: 2 wins
Since both teams have played 38 games, the win rate (number of wins divided by games played) came in handy when making our calculations.
Methodology: Binomial Probability Model
To estimate probabilities of wins, I employed a binomial probability model. It is particularly suitable for use in determining the probability of obtaining a specified number of successes (wins) in a fixed number of trials (games). The most critical formula to apply when one is estimating the probability of acquiring exactly kk wins is:
P(X=k) =(nk)⋅pk⋅(1−p) n−k
P(X=k) =(kn)⋅pk⋅(1−p) n−k
Where:
•n refers to the number of games (38 for the Premier League).
•k refers to the number of wins each team achieved.
•p is the rate of winning, which is equal to the number of wins divided by 38.
This model allows us to determine the probability of each team achieving its specific number of wins based on its historical record.
Results
After doing the math, I compiled the win probabilities for all Premier League teams. Below are some important results:
•Southampton: 27.81% chance of achieving their win total
•Ipswich: 20.65%
•Leicester: 17.50%
•Everton: 14.15%
•Manchester United: 14.15%
•Tottenham: 14.15%
•West Ham: 14.15%
•Wolves: 13.81%
• Crystal Palace: 13.54%
• Liverpool: 13.54%
These probabilities indicate how probable each team was to achieve its recorded number of wins for the season.
Visualization
For better comprehension, I have created a horizontal bar chart with the probability of winning for each of the teams. Through this visualization, we can quickly observe which teams were most probable to achieve their win totals.
Conclusion
This decomposition shows one easy but practical method of calculating Premier League teams' win probabilities using a binomial probability model. Based on historical win data, we now have a sense of what to anticipate from each squad this season.
Having these probabilities not only adds an analytical spin to our love of football but also enhances the excitement of cheering for our favorite teams.
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