Monday, November 2, 2009

More on Corners (Stats Series)

In my previous article I looked at corner kicks. I was surprised to find that there was little to no correlation between the difference between the number of corners for the home and away side in a match and the goal difference in the match. In fact, there was some evidence that there might even be a reverse effect because in matches where the home side won, they got fewer corners on average.

A lesson in variance

Looking into it deeper, there was a problem with some of the results in the previous article: I was not careful enough when looking at variance. I assumed that with those sample sizes the standard deviations would be pretty low so things would look statistically different. That didn't turn out to be the case for one of the results. The reason for this is that the standard deviation for corners is much higher than goals. If you think about it, this makes sense. Some matches your favorite team will get no corners and they might get well over 10 the next time out. Goals are much tighter - 0 to 3 for most matches with the odd 5 or 6-goal performance thrown in there.

As a result of this, the table near the bottom (just above "What is going on here?") is effectively meaningless. There is no statistical difference between the corner differential when the home team wins by 2 as when they win by 1. In other words, while the averages indicate that teams get fewer corners in the more goals they win by, there is a too strong a chance that this just happened in the sample due to randomness so we can't say that the relationship holds.

Having said that, other surprising results are valid. Firstly, the home team on average gets more corners than the away team in any type of match (home win, draw, away win). Furthermore, in matches where the home teams win, the difference in corners is smaller than it is in matches where there is either a draw or the home team loses. So from this we can conclude that when the home side wins, they tend to get fewer corners compared to their opponent. The difference is roughly three quarters of one corner. One claim that can't be verified without getting more data is that the home side gets significantly more corners compared to the away side in matches that end in a draw than those that end in an away win.

In summary, while the other results do not meet the statistical significance test, we can conclude that home teams tend to get more corners than away teams no matter the result of the match and that the difference in home and away corners is smaller in matches where the home team wins than those where the away side gets a result.

Comparing Teams

I decided to look further into it by taking a look at how different teams do when it comes to corners. I would not have found the results surprising before writing the first article. The short of it is that conventional wisdom seems to hold and good teams get more corners over a season than bad teams.

The data is from the last four seasons in the English, Spanish and Italian top flight. For each team I calculated their final tallies in wins, draws, losses, goals for, goals against, goal differential, corners for, corners against and corner differential. I also calculated the average number of corners for and against in matches where the given team won, drew or lost.

I'll start with overall correlations. Looking at goal differential and corner differential, the correlation between the two is 0.58; there is a strong, positive, correlation. In other words, teams that won more corners than their opponents over the course of the season tended to also score more goals than they conceded. The correlations for goals scored and goals conceded and their corresponding corner stats are similar. Both are right around 0.45. So we have what we would expect - teams that get more corners tend to get more goals and those giving away more corners also tend to concede more goals.

Here's a scatter plot with corner differential and goal differential along with the linear regression line.

As you can see, there is definitely a positive relationship. It's not as strong as goal differential and points, but it's certainly there. There are two decent outliers. The one in the upper left is Real Madrid two seasons ago. The Madridistas won the Spanish league and had the league's best goal differential with 48 more goals scored than allowed. Despite that, they won 164 corners and gave up 237. The one on the bottom is Derby County from that same season. The Rams finished with an "impressive" record of 1 win, 8 draws and 29 losses. They scored 20 goals and conceded 89 for a goal differential of -69. Despite that, they "only" allowed 79 more corners than they got. For comparison, Manchester City that season gave up 88 more corners than they got and had a goal differential of -8.

Looking at the graph, it seems to curve up toward the end as far more observations are above the regression line than below. To improve the fit, I ran a regression including a term that is the square of corner differential and got a much better fit as you can see:

Using these results, it depends on where a team is, but an extra corner is worth about an extra quarter of a goal. For better teams it's even more valuable. This is because teams that score more goals get fewer corners per goal. Here's a plot of that:

I find this interesting. It's far from perfect, but corners are a decent representation of attacking chances. Thought of in that way, I would argue that this relationship suggests that teams that score a lot of goals do so not only because they get more attacking opportunities, but that they also convert a higher percentage of those chances. That's not too surprising, strikers certainly get paid to both create and convert on goal-scoring opportunities. I think it's interesting though that the data supports the idea that good attacking teams are more efficient at taking advantage of chances and that it's not simply getting more that leads to more goals.

What about defense? I won't post the scatter plot, but it is essentially the same for goals conceded; teams that concede a lot of goals give up more goals per corner conceded. I would argue that this suggests that teams that are bad defensively not only allow more chances, but they also allow chances that are better on average.

Again, corners aren't a perfect representation of scoring chances. Something like "times with the ball in the attacking third" would be better but it isn't recorded. Sometimes "scoring chances" is given on air during a match, but as far as I know it's never listed as a stat. A problem with scoring chances in general is that it's subjective. The use of the term "half chance" is common and one guy's chance is another guy's half chance and vice-versa. In my view, corner kicks are the best objective method available to measure this.

Viewed thusly, the stats suggest a nice synergy between defense, midfield and attacking players. Team strength is usually pretty similar in all areas. If you'll forgive me for simplifying, midfielders are responsible for both creating attacking opportunities for the team and preventing them for their opponents. Forwards are responsible for converting those chances and defenders for keeping their opponents from doing the same. Good teams tend to have midfielders that create a lot of opportunities for their forwards. These chances will tend to be better than those created by worse teams as well and as a double whammy the forwards on these good teams are better at putting them away. Similarly, good defensive teams have strong midfielders that don't allow a lot of opportunities to score and the defenders take care of business by allowing just a small percentage of these opportunities to be put in.

What about the previous article?

The previous article suggested that there was little to no relationship between the scoreline of a match and the number of corners for each team. This article suggests that good teams get more corners than bad teams. How can that be so? I think the reason gets back to variance. In a single match, anything can happen. That's true for results, I don't need to list big upsets. For corners the variance is even larger. So from one match we can't really conclude much of anything from corner kicks, but over a season there is enough time for things to even out.

As far as home losses leading to more home corners compared to away corners than other results my best guess is that it's selection. Home wins and draws are going to have a lot more cases where an inferior team is ahead or tied and playing 11 men behind the ball against a superior opponent. That situation probably leads to more corners than any other. As long as the better team keeps getting unlucky they're likely to tally a lot of them making the corner difference very small. That is the only explanation I have come up with, I'd love to hear your idea if you have another. Please leave a comment.

Conclusion and Future Work

In my previous work on goal differential, I made the case that conventional wisdom is wrong - there is no evidence that performance in close matches is itself a skill apart from the ability to score and prevent goals and some evidence that it all comes down to luck. In this case though, using full-season data for each team I'm arguing for the common view that good teams are not only better at scoring and defending but more efficient in doing so as they convert a higher percentage of their opportunities and concede on a lower percentage of opportunities they allow their opponents to have.

In the future I may try to use this idea of corners as a proxy for chances to assess goalkeepers and forwards. It's one data point, but I think the Real Madrid outlier above is evidence for the fantastic play of Iker Casillas. I certainly don't think it's the be-all-end-all of stats but corners/goal scored or conceded serve as some measure of how well a team's forwards or defenders and goalkeeper played.


  1. Jared,
    Good post, makes sense.
    Do you plan to preview EPL (Chelsea vs Man Utd)?
    Can you also post your predictions for every EPL
    game this weekend and/or future weeks (just results not long explanations)?
    Thanks you,

  2. Thanks!

    I definitely will write a preview for Chelsea - Man U. The other match I'll likely write about is the Madrid derby in la Liga. Tonight I'm going to post some rankings for other leagues, probably with little text, and work on those previews. I'll post both previews either tonight or tomorrow night.

    I can give the model predictions for the other matches if you like.


  3. Indeed, is the data available somewhere?