Odds of Winning the League: The Final Day | Probability Analysis

Odds of Winning the League: The Final Day | Probability Analysis

Wow. What a day. In what was the most exciting finish to the English Premier League season ever, Manchester City secured the title with 2 stoppage time goals to beat out Manchester United on mere goal differential.

Kompany and Aguero Celebrate

Instead of trying to sum up the craziness that was this final day in words, I thought it would be better to quantify all the swings that happened. City went from being confident of winning the title before the game, to even more confident after the Zabaleta goal, to sheer anguish after the Mackie goal (even tears), to desperate hope after the Dzeko goal, to absolute elation after the Aguero goal. But how did the actual probabilities of winning the title change throughout the games?

To do this, I used the Outcome Probability Calculator on my blog to quantify United and City’s probability of winning, drawing, and losing their final game. There were essentially 9 scenarios that could happen, 6 of which would result in City securing the title and 3 of which would result in United winning. If City won and United won, drew or lost, City would win the title. If City drew and United drew or lost City would win the title. If City lost and United lost, City would win the title. If United won and City drew or lost, United would win the title. If United drew and City lost, United would win the title. Based on each club’s probability of winning the game using the outcome probability calculator, I was able to calculate each club’s chance of winning the league throughout the games. I was also helped by the fact that the games occurred at the exact same time.

After all of this, I graphed the results. The graph is shown below, and each goal is labeled on the graph.

 

It’s pretty easy to see how insane the day really was. Throughout the entire game the odds of winning the title for each time fluctuated up and down. The two clubs had a 50-50 chance of winning the league around the 59th minute where the two lines on the graph intersect. The most drastic switch, of course, comes in the 94th minute, after Aguero’s goal. City’s chance of winning the title literally went from essentially 0%, to essentially 100%. Unbelievable.