Best Defenses

In my previous post, I talked about offense and defensive ratings of Chelsea. In this post, I'd like to explain how these are computed (in rough terms) and use the same scores for other teams to give a list of the best defenses.

Offense and Defense Ratings

As described before, each team gets two numbers, their offense and their defense. The number of goals scored by a team are assumed to be given by a Poisson distribution with parameter offense (that team) - defense (their opposition). For each game, there are two numbers of goals, one from each team, to explain. We choose offense and defense numbers for each time so as to make all of these outcomes as likely as possible. (This is called "maximum likelihood estimation".)

Top 5 Defenses in the EPL

Applying this to all the matches in the English Premier League, we get the following scores:

1. Manchester City — 0.517
   
2. Chelsea — 0.501
   
3. Sunderland — 0.382
   
4. Manchester United — 0.348
   
5. Arsenal 0.318
   
6. Honorable mention: Fulham — 0.257
   

There is one surprise on this list (to my mind, anyway): Manchester United has slipped. Earlier in the season, their defense was about the same as Manchester City. Their performance against Blackpool (conceding two goals) can't have helped. It will be interesting to see if move back up over the coming weeks.

Top 5 Defenses in the World

If we do the same to teams in the Champion's League competition, and then extrapolate to the rest of the teams in each league, we get the following scores:

1. Barcelona — 0.52
   
2. Borussia Dortmund — 0.61
   
3. Chelsea — 0.64
   
4. Manchester United — 0.76
   
5. Sunderland — 0.77
   

(Note that these numbers are from slightly earlier this season, which is why Manchester City does not appear here.)

Hopefully, no one is surprised to see Barcelona at the top of this list. Negative Football has talked at length about Barcelona's great defense before. They are without doubt the best defense in the world.