Following up on my post about shot creation versus shot conversion as measures of offensive production (see also the On Football post), here's a quick and dirty analysis of Premier League teams' ability to degrade opponents' shot frequency (measured by shots allowed) and shot accuracy (the ratio of shots on target to shots allowed).
We can think of these as two dimensions that aren't necessarily related. Teams can allow the other team lots of shots without letting them make accurate shots; or they can degrade their opponents' ability to create lots of chances while allowing a high level of accuracy on their opponents' part (say, allowing them to hit 3 of 4 shots). If it's the former, they may need to focus on improving midfielders' defensive capabilities to degrade the other side's ball delivery into good striking positions; if it's the latter, they may need to focus on defenders' ability to degrade chances that crop up.
Using data from the 2009/10 season gives you the following picture (calculating each team's average over the course of the season).
Two things are noticeable about the pattern we see.
First, there seems to be a moderate positive relationship between opposing team frequency and accuracy; that is, teams that allow more shots are also more likely to allow accurate shots overall. However, there is considerable variation around this relationship, mainly allowing us to say that some teams are just weaker defensively (or stronger, depending on how you look at it). The teams that excelled defensively in 2009/10 were Chelsea and Liverpool (located he lower left hand corner): they allowed the fewest shots overall, and they had the best overall frequency/accuracy combination. In contrast, Burnley allowed their opponents to take lots of shots and were unable to prevent opposing teams from making them accurate.
Second, we can see that the upper left hand corner of the graph is mostly empty; this means that there are really no teams that allow opponents to take lots of shots but manage to degrade their accuracy significantly. Instead, we see teams that excel at degrading both frequency and accuracy of shots (Chelsea and Liverpool, and to some extent Man United). Then there are teams that allow relatively few shots but also allow opponents to shoot with higher levels of accuracy (Arsenal, and to some extent Wigan and Tottenham - I know this is debatable). And then there's everyone else clustered in the middle, allowing between 10 to 14 shots, and decent accuracy around .54.
Before we start taking these numbers from one season and one league too literally, it's clear that, in 2009/10, the best Premier League teams clustered in the lower left hand quadrant, suggesting that good defense paid nice dividends last year.
