Leicester City’s meteoric rise

A look at the 2015-2016 Premier League season through Elo ratings.

A few weeks ago, the 2015-2016 Barclays Premier League season wrapped up and what a season it has been. The Leicester City Foxes captured the crown on May 2nd overcoming a 5000/1 odd at the beginning of the season. This means that if I put down a $5 bet on Leicester to win the Premier League title back in August 2015, I would have collected a cool $2.5K return on May 2nd. Perhaps what makes this an even more outlandish and unimaginable story is the fact that only a year ago, Leicester was on the verge of being relegated to a lower division. With seven games remaining in the 2014-2015 BPL season, Leicester was dead last but remarkably managed to narrowly escape being relegated.

While looking at betting odds for English soccer, I found the 2015-2016 Premier League match results and stats data from Football-Data.co.uk. I thought it would be an interesting exercise to apply the Elo rating system to this data and visualize the progression of Leicester City’s fairytale run in terms of Elo ratings. But first, let’s delve into the mechanics of the Elo rating system and look at some of the assumptions behind it.

The Elo rating system was developed by Arpad Elo originally to estimate the strength of chess players. Each player’s Elo rating is based on their prior results. When two chess players enter a match, the system can calculate the expected outcome using each player’s Elo rating and then update each player’s rating once the match has concluded. The rating system was then adapted for international football by Bob Runyan in 1997.

In the World Football Elo Ratings, the k factor is a constant that reflects the importance of the match and thus changes depending on the tournament in which the match is in. As an example, the k factor would be higher if Argentina played Germany in the World Cup finals compared to if they played each other in a friendly.

In our exercise, we are only looking at the domestic league games during the Premier League season, so every match should be equally weighted by some k factor. But still we need to figure out what our k factor should be.

In this blog post, the author found the “optimal” k factor that would minimize the error of the predicted outcome (a probability) against the actual outcome of the match. For our exercise, we will apply the same idea to find our “optimal” k factor and we will use mean squared error as our metric for evaluation. After going through 40 iterations, we see that the k value that minimizes mean squared error is k = 8.

Graph1

Another key modification made to the original Elo rating system is to consider goal differences in a match. For this, we will simply follow how it is implemented in the World Football Elo ratings.

Finally, every team will start the season with an Elo rating of 1500. We could have gone back and dug out every Premier League season’s match results since the league’s inception but it would be a lot more complicated given that at the conclusion of each season, the bottom three teams are relegated to a lower division and three new teams are promoted to the Premier League. Furthermore, we would have to figure out how much of a team’s Elo rating to carry over from the conclusion of one season to the beginning of the next season.

Below is a time series plot of the the top ten teams based on their Elo ratings throughout the 38 weeks of the season. I added a few anecdotes to the plot that I thought were major headlines during the season.

Graph2

A few notes/thoughts:

  • Manchester City were the early favourites to win the title coming out of the gate by winning their first five games while withholding their opponents from scoring. This is clear just by looking at the sizable gap in Elo rating between Manchester City and the other teams in week 5. Then things started falling apart. A key stat that most soccer pundants like to highlight is Manchester City’s disappointing performance against the top three teams (Leicester City, Arsenal, and Tottenham): 0 wins, 2 draws, 4 losses.
  • Coming off a championship season in which they held the top of the table for all 38 weeks, Chelsea did not come close to resembling their dominant form in 2015. Their Elo rating dipped to the lowest in week 16 when their manager José Mourinho was fired. Since then,  Chelsea went undefeated for 15 consecutive weeks, but it was too little too late.
  • For much of the season, the focus was on Leicester City’s cinderella story. But Tottenham had certainly thrived in Leicester’s shadow. From our time series plot, the second half of the season looked like a two-horse race and at times Tottenham looked like the stronger team relative to Leicester (despite never eclipsing Leicester for the top spot in the PL table). It’s interesting to point out when Leicester was eventually crowned as the champion in week 35, Tottenham had the higher Elo rating.

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