I just got one of the data sets from the Manchester City analytics initiative, so of course I started dipping my toe in it. The set gives information aggregated by player and match for the 2011-2012 Premier League, in the form of a number of counters (e.g. time played, goals, headers, blocked shots, etc); it's not the really interesting data set Manchester City is about to release (with, e.g., high-resolution position information for each player), but that doesn't mean there aren't interesting things to be gleaned from it.
The first issue I wanted to look at is probably not the most significant in terms of optimizing the performance of a team, but it's certainly one of the most emotional ones. Attackers: Who's the best? Who's underused? Who sucks?
If you look at total goals scored, the answer is easy: the best attackers are van Persie (30 goals), Rooney (27 goals), and Agüero (23 goals). Controlling by total time played, though, Berbatov and both Cissés have been quite more efficient in goals scored by minute played. They are also, not coincidentally, the most efficient scorers in terms of goals per shoot (both on and off target). The 30 goals of van Persie, for example, are more understandable when you see that he shot 141 times for a goal, versus Berbatov's 15.
To see how shooting efficiency and shooting volume (number of shoots) interact with each other, I made this scatterplot of goals per shoot versus shoots per minute, restricted to players who regularly shoot to avoid low-frequency outliers (click to expand).
You can see that most players are more or less uniformly distributed in the lower-left quadrant of low shooting volume and low shooting efficiency — people who are regular shooters, so they don't try too often or too seldom. But there are outliers, people who shoot a lot, or who shoot really well (or aren't as closely shadowed by defenders)... and they aren't the same. This suggests a question: Who should shoot less and pass more? And who should shoot more often and/or get more passes?
To answer that question (to a very sketchy first degree approximation), I used the data to estimate a lost goals score that indicates how many more goals per minute could be expected if the player made a successful pass to an average player instead of shooting for a goal (I know, the model is naive, there are game (heh) theoretic considerations, etc; bear with me). Looking at the players through this lens, this is a list of players who definitely should try to pass a bit more often: Andy Carroll, Simon Cox, and Shaun Wright-Phillips.
Players who should be receiving more passes and making more shots? Why, Berbatov and both Cissés. Even Wayne Rooney, the league's second most prolific shooter, is good enough turning attempts into goals that he should be fed the ball more often, rather than less.
The second-order question, and the interesting one for intra-game analysis, is how teams react to each other. To say that Manchester United should get the ball to Rooney inside strike distance more often, and that opposing teams should try to prevent this, is as close to a triviality as can be asserted. But whether or not an specific change to a tactical scheme to guard Rooney more closely will be a net positive or, by opening other spaces, backfire... that will require more data and a vastly less superficial analysis.
And that's going to be so much fun!