A few days ago, I wrote about different ways of measuring a team's performance - either in absolute or relative terms. Relative metrics are useful if we are interested in drilling a little deeper into what players or teams are able to do, given the resources they have or in relation to some other event on the pitch, not simply whether they do a lot or a little (like scoring or possessing the ball). In those analyses, I looked at a team’s offensive productivity in terms of its ability to score goals efficiently. A team is more efficient offensively if it achieves goals with less effort or expense - in that particular case measured as the ratio of goals to shots taken.
The logic of efficiency should also apply to teams' defensive performance. We can investigate how well teams defend by examining their ability to prevent shots from finding the back of the net - that is, by calculating the ratio of goals to shots conceded in each match. Take a look at last season's defensive efficiency figures for the Premier League (by club) in the graph below.
As in the case of offensive efficiency, some of the best teams are found at or near the top.
Of course, Birmingham's problem may have been that they simply allowed too many shots in the first place. So what do we see when we put the absolute and relative defensive metrics together? Below is a graph of the average number of shots conceded by defensive efficiency, along with a quadratic (curvilinear) best fit regression line superimposed.
As with offensive performance, the data show that the relationship between shots conceded and defensive efficiency is not necessarily linear. This means that teams that allow more shots per match do not necessarily defend less efficiently. Compare the following four teams, for example: Manchester City, Blackpool, Arsenal, and West Brom. They have very different defensive profiles. Manchester City didn't allow all that many shots, and they were hugely successful in preventing those shots from being converted into goals. In contrast, Arsenal allowed even fewer shots on goal, but they were almost 50% less efficient than City defensively. In fact, the big difference between Arsenal's and Blackpool's defense was not defensive efficiency - the clubs were roughly the same on that score. So for them, the difference in goals conceded was that Blackpool allowed lots of shots - the most in the league - and Arsenal didn't. Finally, West Brom matched Manchester City on the number of shots they allowed, but as we saw above, the Baggies' defense was more of a sieve than a proper defense.