Wednesday, October 21, 2009

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.

4 comments:

  1. Jared,
    I've been reading your blog for at least a month and like it a lot. Great job! Regarding correlation between corners and goals.
    I quite surprised by your results regarding corners.
    Have you tried to compute correlations separately for every football league (English Premier League, Spanish La Liga, Bundesliga, etc)? Given that these leagues use very different style of play (long ball in England vs short passing in Spain) it may produce different results. Another thing, it maybe not linear relationship between corners and goals.
    Have you tried to create graphs, similar to the first graph on Wikipadia page about "correlation_coefficient"? You may see some patterns there even with the small corellation.
    Thank you again for the great blog,

    Igor

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  2. Thanks for the comment. I was quite surprised myself. I thought it would be small but statistically significant, maybe something like .15 or something like that.

    The league thing is interesting, I'll definitely look into it as I have the data. I don't think it'll matter but it would be interesting to see if maybe it's different in different leagues. I also plan to look at individual teams.

    I did make some graphs. The problem there is because the number of goals is usually 0,1,2 or 3 the graphs don't look nice like those on the wikipedia page. Everything kind of bunches up. You can't really see a pattern, which makes sense given that there is almost no correlation. To the extent that you can it looks like what the numbers came out - there seems to be a small shift downward as you move up in corners. It certainly doesn't look like a non-linear relationship exists that is positive, like a U shape or something where it goes down and up. It just kind of moves down.

    Another thought just occurred to me that I'll look at next article. I should have also sorted the matches by number of corners like I did by goal margin. That might be interesting. With the teams, leagues and that I'll definitely be writing a follow-up article. Next up in the series I'm going to talk about fouls, probably Sunday or Monday I'll post that. Then maybe I'll get back to corners.

    Thanks again for your comment.

    Jared

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  3. Very interesting!!
    ARe the data available is some form?
    Is it possible t have them?
    Reagrds
    Dimitris

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  4. Did you look at what percentage of corner kicks are converted into a goal? Arsenal today had a ton of corners and only cashed in on one and we're trying to figure out if Arsenal sucks at set pieces or if corners mater at all?

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