Spanish Liga Update and Rankings

Unfortunately I managed to miss last week with the Spanish league update. Last week was more interesting than this week with Barcelona held to a draw against Osasuna. All went to plan this week. I still think the league looks a lot like last season, but it's looking more open than before. Last season at this point Barcelona had 25 points, Real Madrid 23 and Sevilla 20. Currently Barcelona sit top with 26, Real Madrid have 25 and Sevilla 22. So it's a bit closer. Depor and Valencia continue to look very good as well. A team continuing to not look good is Atletico de Madrid. Atleti find themselves in the relegation zone and already eliminated from the Champions League with two matchdays to go. Their losses in the derbi and the week before in Bilbao did little to inspire confidence and bring calm to the chaos.

Here are the rankings, using my new ranking system:


O Rank - rank by goal-scoring strength
D Rank - rank by goal-conceding strength
EGD - expected goal difference if they played a full season at the level the results so far indicate

Barcelona rates about five goals better than Real Madrid when it comes to scoring and about half a goal behind Sevilla defensively. In other words the results so far indicate that they are as dominant as ever. Real Madrid to their credit are looking better than usual defensively. Looking closer to the bottom, Atletico de Madrid are looking awful with an expected goal differential under -24. These numbers indicate that Villarreal and Malaga have been running below expectation in luck since their places in the table are significantly lower than what I have here.

EPL Rankings and Update - 9 November

Chelsea picked up a gritty win at home against Manchester United to go five clear, though Arsenal still have a match in hand. Earlier today Liverpool only managed a draw at Anfield against Birmingham. I am going to claim defeat in my prediction that the big four would stay in the race through the end of the year. I was a full two months off as Liverpool are now 11 points back and out of it already. Man City also got a disappointing result with a 3-3 draw at home against Burnley, the Clarets first points away from home this season. Villa and Spurs both picked up expected wins to continue their fight for a spot in Europe.

Here are the rankings, using my new averages model:



The Poisson rankings have a few differences. In offensive ranking, the Poisson model flips Liverpool and Chelsea. Defensively it flips Arsenal and Man City, leaving Spurs in between. Overall the Poisson model puts Man City one spot below Tottenham instead of above. Nearer the bottom of the list, the Poisson model has Burnley 15th, Blackburn 16th, Portsmouth 17th and Bolton 18th. Otherwise they are the same in terms of ordering.

New Rankings and Predictions System

I've been working on a new model which I think helps with some of the problems the Poisson model has. It is based on work done at Smart Football Rankings, an effort to develop a rankings and prediction system for college (American) football. I'll call this the averages model.

The idea is this: instead of making assumptions about the distribution of goals, let's just look at how well each team does at scoring and conceding goals compared to their opponents. There are two stages. In the first, I calculate a scoring and defensive factor by taking the difference between a team's goals for (also goals against but I'll just talk about the scoring half for this) in each match and how many goals on average were conceded by the opponent in their matches against other teams. To account for home-ground advantage, I adjust the average up or down for the match based on whether the team is at home or away. The adjustment is simply the difference between the league average goals and the average goals scored by home teams only. For example, Manchester United had given up 1 goal per match before facing Chelsea. Home teams on average score roughly 0.29 more goals per match than away teams. Chelsea scored one goal so their goals-for score from their match with Manchester United is 1 - (1 + 0.29) = -0.29. For Manchester United, Chelsea had conceded 8 goals in 11 matches for an average of 0.727 goals per match. Since United were playing away and failed to score, they would get 0 - (0.727 - 0.29) = 0.437. For the first step, this would be done for every team in each match. A team's scoring factor is then the average of these for each match played.

The second step adds a level. The first step compares your team's scoring to that of the average opponent of your opponent. If the teams you play have played an easy schedule themselves then your extra goals look less impressive. A way to control for this is instead of using average goals against use the scores calculated from step one along with the average goals for and against for the league as a whole. Getting back to the Chelsea - Manchester United example, Manchester United's defensive score from the first step is -0.689. In other words, they've given up about 2/3 of a goal per match less on average compared to what their opponents have scored against other opponents. The league average for the league as a whole is 1.52 goals per match, and home teams 1.80. Chelsea scored 1 goal against United so they get 1 - (-0.689 + 1.80) = -0.111. Chelsea's defensive score from step 1 is -0.83 and away teams average 1.23 goals per match so Manchester United got 0 - (-0.83 + 1.23) = -0.4. Each team's scoring and defensive factor is the average of of these for all matches played.

There are two reasons I like this system better than the Poisson. The first is that it has gotten better results in some testing. I've done something very similar to the PLM where I use ordered logit on the expected goals for each team according to the model and its predictions have been better. If there is interest I'll post more detailed work there but I used two different scoring systems. One just looks at squared difference between predicted probabilities and what actually happened, assigning 1 if the outcome (home win, away win, draw) happened. The other was a betting system where I looked at how much would be made by the PLM using odds given by the estimates of the averages model and the other way around. The averages model outperformed the PLM in both of these tests. Beyond just these things, I think the rankings make more sense when I look at where it rates teams.

The second reason I like the averages model better is that it I think using sums is more accurate than using products. In the Poisson model, home-ground advantage is given by multiplying the expected goals for home team by a number between 1.1 and 1.5 for most competitions. Similarly, the expected goals in a match for a team is their scoring factor times the opponent's defensive factor. A result of that is that high-scoring teams are more sensitive to the quality of their opponents and playing at home than low-scoring teams. This doesn't seem to be reflected in reality. I'll write more on this later, but for better teams playing at home tends to be a bit less important. The averages model assumes it equally important for all teams so that's an improvement. Note that other than including home-ground advantage, a major difference between mine and the methodology used by Smart Football Rankings is that they actually use products instead of sums.

For at least the next few weeks I'll include both Poisson/PLM and the averages model when giving rankings and predictions. Because I believe the averages model, and its logit, to be superior I'm using it as my main model until I work out a better one.

Other EPL Predictions

Here are the numbers for the other matches. Keep in mind that the model does not take into account injuries and only uses goals so these numbers are just a rough guide. As I've said several times, I think the model overrates Arsenal particularly as they've been running white hot when it comes to scoring goals.

Aston Villa - Bolton
Villa - 66%
Draw - 22%
Bolton - 12%

Blackburn - Portsmouth
Blackburn - 48%
Draw - 29%
Portsmouth - 23%

Man City - Burnley
Man City - 74%
Draw - 18%
Burnley - 8%

Tottenham Hotspur - Sunderland
Spurs - 63%
Draw - 22%
Sunderland - 15%

Wolverhampton - Arsenal
Wolves - 11%
Draw - 20%
Arsenal - 69%

Hull City - Stoke City
Hull - 34%
Draw - 31%
Stoke - 35%

West Ham - Everton
West Ham - 57%
Draw - 25%
Everton - 18%

Wigan - Fulham
Wigan - 38%
Draw - 30%
Fulham - 32%

Liverpool - Birmingham
Liverpool - 62%
Draw - 24%
Birmingham - 14%

Weekend Preview: Chelsea - Manchester United

The match between the top two teams in the Premiership kicks off at 16:00 local. For the Americans, it can be found at 11 AM Eastern on the Fox Soccer Channel.

History

These two teams have won the last 5 English Premier League titles. In the last six seasons both have been in the top 3 and three of those times they finished in first and second. While Arsenal and to a lesser extent Liverpool and Man City are thought to be contenders this season, the champion this year will most likely be one of these two clubs.

Looking at their head-to-head results, going further back is even more pointless than usual due to the recent influx of quality at Chelsea when Abramovich took over. I'll give it to you anyway: in league play Chelsea have beaten Manchester United 37 times, Man U have bettered Chelsea 56 times and 41 times they played to a draw. Since Abramovich took over in the summer of 2003, Chelsea have 5 wins, 4 draws and 3 losses against Manchester United in league play. At Stamford Bridge United have not won since the Abramovich takeover; Chelsea have 4 wins and 2 draws in league matches, throw on an extra win and a draw if you want to include cup play. The last time United won at Stamford Bridge was the 2001-2002 season.

Form

Usually when these two clubs play it's a given that they've won 4 or 5 of their last 5 matches but that's not the case this week. Chelsea are 3-0-2 in their last 5 and Manchester United are 3-1-1. Chelsea's losses were 3-1 at Wigan and 2-1 at Aston Villa. You don't expect any team to win them all, but Chelsea fans are surely disappointed with those results. The loss to Villa isn't so bad, they'd probably feel ok with a draw there, but losing by two goals to a team that figures to be midtable at best and probably in the relegation fight is. If you think that Manchester United's loss was 2-0 at Anfield and their draw was 2-2 at home against Sunderland. There they equalized in extra time on an own goal.

An interesting thing is that there is a big divide between home and away form for these teams. Chelsea have won all 5 of their home matches so far this season. After edging out Hull 2-1 in their opener, they have been on fire beating Burnley then Spurs by 3 goals, Liverpool by 2 and then Blackburn 5-0. They have scored 15 goals and only conceded 1 in their 5 home games. Away from home Chelsea have 4 wins and those 2 losses mentioned above. Similarly, Manchester United are 4-1-0 at home with the only blemish that 2-2 draw versus Sunderland. On the road they are a less impressive 3-0-2 with losses to Liverpool and Burnley. We're talking about quite small samples of 5 and 6 matches, but if home and away form mean anything it points to an edge for Chelsea.

Injuries

Chelsea are relatively free of injury. Mikel and Zhirkov are expected to play but have ankle and knee injuries respectively. Bosingwa is the only player likely to be unavailable. The same cannot be said for Manchester United who have several players that either can't play or won't be fully fit. In the first column, it appears that Rio Ferdinand will not play due to a nagging calf injury. Park Ji-Sung and Hargreaves are also likely to miss out. Someone we know won't play is Gary Neville due to suspension. On the brighter side, Vidic is expected to be able to play. Fletcher still has an ankle injury but says he can play with an injection.

Model Rankings

In my rankings Chelsea are second and Manchester United third. Despite being in positions next to each other, the model actually has them a fair bit apart at nearly 22 goals of goal differential. Most of that difference is at the attacking end. Not to the same extent as Arsenal, but Chelsea seem to have been running hot at scoring so far. They are on pace for 96 goals, the model says they would score about 91 at this pace because they've played a slightly easier than average schedule. Last season they only scored 68. I think that Manchester United have also been running above their scoring expectation as the model says they'll average around 76 goals playing at this level and they also only scored 68 last year. I think both will cool off and it's too early to say for sure, but Chelsea have certainly looked better in attack than Manchester United. This shouldn't be a huge surprise given the sale of their best attacking player over the summer.

On the defensive side of things, the model puts Chelsea on pace to concede 28 and Manchester United 35. Last year they both conceded 24. Manchester United have had some surprising defensive lapses this season. I've said repeatedly that over the last couple years I think they have had the best defense in football but they've not looked like it this year. Something I wonder is how much of it has to do with losing Ronaldo. Ronaldo didn't defend much, but his ability to go after the other team certainly made it more risky to attack the United goal. That doesn't cause things like Rio Ferdinand handing Man City an equalizer in the 90th minute, but I think it does play some role.

Predictions

Like before, I'm using the PLM to give the result prediction and the Poisson model to say the most likely scoreline. The models give Chelsea a surprisingly big edge, especially when you consider that they don't take injury into account. They say the Blues win just over 55% of the time, United 18% of the time with the remaining 27% being a draw. The most likely scoreline is 1-0 with a 13.5% chance. Next is 2-0 (11.9%), 1-1 (10.8%) and 2-1 (9.6%). I think the injuries become too much to overcome and Chelsea win 2-0. We'll see if I get the exact scoreline for the first time.

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.

Premier League Rankings - 2 November

I'm going to go quite short this week and mainly just post the rankings. I'm working on a follow-up article on corners and I want to focus on that.



Not a lot of changes this week as the outcomes weren't far off from the expectations of the model. Liverpool dropped a spot while Fulham moved up 2 when Fulham got the 3-1 win at Craven Cottage. Liverpool are certainly looking like the favorite to throw off my prediction that the big four would all be in the race at the new-year break. At the other end of the table, the biggest mover was Portsmouth moving up 5 spots and 15 expected goals in goal difference due to stuffing Wigan 4-0. The (wait, do Portsmouth have a nickname?) are now just 3 points from getting out of the relegation zone and that battle looks like it could be good this year. With Portsmouth's attack moving out of the cellar, Hull have a stranglehold on the bottom position in the rankings as they rate the worst both scoring and defending. It's pretty telling that Burnley moved down in the rankings after beating them 2-0. In fairness, that's due to other results since Burnley's expected goal differential actually went up slightly.