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.

Stat Series: Corner Kicks

This is the first in what is hopefully a several part series on stats that are out there and what they say about a match.

Conventional wisdom on corners.

A team is awarded a corner kick when the ball goes over the goal line outside of the goal and it is last played by the defense. In almost all cases this happens because the team winning the corner was in a dangerous position. Therefore, if A has a lot of corners and B just a few or none at all then A is dominating B and is surely the better team on the day. The number of corner kicks is a decent indicator of how the match went.

What does the data say?

To examine the significance of corner stats, I looked at all matches from the previous five seasons in the English Premier League, French Ligue 1, German Bundesliga, Italian Serie A and Spanish Primera Division. I was surprised by the results.

Again the main tool I used was the correlation coefficient. First I looked at the correlation between goals for the home team and their number of corners in the match as well as the same for the away team. I was quite surprised that not only was value very small but it was negative! For the home team there is a correlation of -0.046 and -0.031 for the away team. In other words, while the relationship is extremely weak, the fewer corners a team has the more goals they tend to score. Because the sample size is large, 5432 matches total, these numbers are statistically significant at the standard 5% level. Having said that, they are clearly not actually significant. In other words, the data suggests that the number of corners really doesn't indicate much of anything about the number of goals a team will score but to the very small extent that it does there is a negative relationship.

Next I did the same thing, but for the opposing team's corners; I compared the number of goals scored by the home team with the number of corners won by the away team and vice-versa. This turned out to be positive, but very small. For the home team and away corners the correlation is 0.0195. For away goals and home corners it is 0.0265. So again, the numbers indicate that there is basically no relationship (these numbers are not statistically significantly different than 0), but there is, if anything, a slight relationship between the number of goals a team scores and the number of corners they concede.

Still wondering what was going on, I divided the matches into those where the home team won, those that were draws and those where the away team won. I then broke those into matches where the home team got more corners than the away team, they got the same number and those where the away team got more corners. Again I was surprised by the result. Home teams that won the match got more corners 55% of the time, the same number of 10% of the time and fewer corners 35% of the time. That seems to make sense and contradict the previous findings. The story doesn't end there, however. In matches that were draws, the home team got more corners 60% of the time, the away team 30% of the time and 10% of the time they got the same number. Finally, when the away team won the match, the home team got more corners 63% of the time, the away team 28% and they got the same number 9%.

In other words, the home team won the corner battle a majority of the time no matter the outcome of the match. However, in matches that were draws they got more corners with higher frequency than those that they won. In losses for the home side they won the corner battle even more often. So again we have an indication that teams winning tend to get fewer corners than teams losing, though the difference isn't all that large.

Finally, I looked at the connection between margin of victory and corner difference in an individual match. Starting with correlation, it again was small and negative: -0.058. Looking into it further, I took the average corner differential for each different scoreline. Here is the chart:

Goal Difference : Corner Difference (sample size)
-3 : 1.36 (163)
-2 : 1.84 (423)
-1 : 1.84 (821)
0 : 1.64 (1445)
+1 : 0.98 (1261)
+2 : 0.65 (758)
+3 : 1.00 (349)

In words, in matches where the home team lost by 3 goals they averaged 1.36 corners more than the away team. As you can see the story continues. The home team on average wins more corners than the away team in all types of matches. However, this margin is larger for matches that the home team loses. than those they win. Again we have a negative relationship.

What is going on here?

The "correlation does not imply causation" cliche applies here. A team obviously can't improve their chances of scoring a goal by playing it back and kicking it out to give the other team a corner. It's just a theory, but here's what I think is going on.

At the start of this article, I stated what I feel is the conventional wisdom that due to the usually dangerous circumstances that create a corner, dominating a match will lead to more corners. I think this needs to be changed. It's not dominance that leads to most corners but sustained pressure. Corners are more likely to occur when both teams are in around the area. For example, a team with a corner kick or other set piece around the goal often gets a corner when the ball is headed out by a defender or a shot is deflected wide off a defender or the goalkeeper. These situations are more likely to develop when a team is behind and pressing. If a team is ahead then they don't need to press forward as much, and usually won't because they would then be susceptible to a counterattack and a goal scored is less good for them than a goal conceded would be bad. On the other hand, a team that is behind is more likely to press forward since they are desperate for a goal. In a sense I'm saying that scoring a goal to go ahead will cause a team to later give up more corners.

The only evidence I can offer of this is that I think the same applies to home teams, which is why they average more corners than the away team. There isn't data on "pressing forward" but it certainly seems like a team will tend to push guys forward more when they are at home than away. Perhaps players are just the slightest bit more tentative when playing away and that makes a difference. Maybe this is the reason that there is a home-ground advantage even though teams are playing on the same pitch under the same rules.

Keep in mind that the explanation I'm offering is why the very small relationship is in the direction it is. There is a lot of randomness when it comes to corners. Sometimes a team will win a corner just about every trip into the attacking third. Other times their attacks will just so happen to end in throw ins, goal kicks, clearances or goals instead of corner kicks. In my opinion, the main thing to take away from all this is that corners alone don't say much about which team was better in a match. It's possible that a stat like "corners while the score is tied" would indicate which team is better, but I have never seen that sort of thing published.

What do you think of my theory? Do you have a different explanation for why teams that win more corners tend to score just a tiny bit less than those getting fewer? Were you surprised that there is pretty much no relationship at all between them? I'm very curious what you think.