Brendan Sudol
April 2015

Soccer outcome probabilities

I’m a big fan of English Premier League football. Manchester United is my team. Why? Because this girl I dated back in high school really liked them. We’ve since gone on and got married and now I think I like the Red Devils more than she does. :)

As I watch more and more games, I find myself wondering a bunch of data related questions, like how important is home field advantage, is this a common final score, when do goals tend to be scored, do they come in bunches, how comfortable is a 2 goal lead with 30 minutes to go, how do all of these things differ across teams and seasons, and on and on.

I decided to get some data and explore. It turned out to be surprisingly hard to get my hands on a good dataset. This is an awesome resource but it only has halftime and final scores – I wanted more info on when goals were scored during a match. I eventually resorted to scraping the season summary pages on soccerbot (example). See this github repo if you’d like to see what I did / reproduce (it turned out to be trickier than it should have been due to the site’s fairly crazy client side data loading and rendering). Then I imported the dataset into an IPython notebook to analyze and slice & dice. Here’s my notebook if you’re curious.

For this post, I’ll focus on just one question from above to kick things off: How comfortable is a two goal lead? Or to make it more general and interesting, what is the likelihood of a particular outcome (win/lose/draw) based on the goal margin, location (home or away), and how much time is remaining. A soccer blog called Soccer Statistically looked into this problem a couple years ago and the Wall Street Journal even wrote a small blog post about it, but it seems like their ‘calculator’ is no longer maintained or working, so I’m happy to pick up the baton and explore the question using my data tools of choice, python and D3.js.

How can we answer this question? Since we know when all goals were scored with our newly created (and well earned) dataset, we can back out what the score was at every minute for each game. So we can look at all matches where the home team was leading by 2 goals at the 60 minute mark and then see how often that team went on to win. And we can do this for other goal differentials and at each minute of the game - for example, how likely is a draw when teams are tied (0 goal diff) in the 80th minute. Results are below (please adjust the inputs to see how things change!), and the javascript that powers it is here.

Hover over chart to see outcome probabilities at different times.
Goal differential: 0
Win: -
Draw: -
Lose: -
Games: -

Note: The data that powers the chart above includes ~4.5k Premier League games since 2000. At each minute, you can see the win/draw/lose probabilities above the graph (as well as the number of games that go into that calculation). To make the trend lines less noisy, only scenarios that occurred in at least 5 different games are plotted (e.g., there were not 5 games when the home team had a 3 goal advantage within the first 17 minutes).

A few observations:

  • If the score is tied and your team is playing at home, you may want to start lowering your expectations for a victory around the 70 minute mark - this is when a draw becomes more likely than a win.
  • How comfortable is a one goal advantage at home? Pretty comfortable actually - teams go on to win over 70% of the time even if that lead came in the 2nd minute. That said, the win likelihood doesn’t cross 80% until the 70th minute and it doesn’t hit 90% until the 85th minute.
  • A one goal lead is not nearly as cushy when you’re away - a 70% win rate doesn’t happen until the 68th minute for away sides that go up by one.
  • What about a two goal advantage? Home or away, a two advantage in the second half leads to a victory over 90% of the time.
  • It’s interesting to see some of the rare and crazy comebacks that happened over the years, like the home team that was down by 3 in the 80th minute and went on to secure a draw (this was West Brom (h) vs. Man U (a) in 2013, summary here).

Feel free to play around with the inputs and hover over the chart to explore the scenarios you’re curious about, or maybe the one your team happens to be facing during a match.

Oh, and in case you missed the Manchester derby earlier today, enjoy :)