I split the sample between shots inside the box and shots from everywhere else (including shots and goals scored from you own box.....Tim Howard, take a bow), in an attempt to maintain a decent sample size, but to also smooth out any positional shooting preferences among the teams.
The method sees if the distribution of goals scored by each side, given their relative shot totals, is substantially different from the range you may expect if every side is equally talented at converting similar types of chances.
I deliberately left in penalty kicks for shots from inside the box, because I wanted to see how the conclusions changed as certain types of readily identifiable and unevenly distributed shots were removed from the sample.
So the first run included every goal attempt from inside the box. The distribution of goals scored by the twenty sides did appear to differ markedly from the spread you might expect to see if Manchester City had had 450+ attempts and Stoke had 230+ with every other team contained somewhere between those shooting extremes, but all sides had striking talent that was equally adept at converting the chances that fell to them.
Next, I took out penalties, which tend over time to be given to those that do the most attacking and present a significantly higher chance of scoring that other, open play opportunities from inside the box.
Virtually the same result.
Compared to the sample with penalties, we do edge very slightly closer to a distribution of actual goals in 2011/12 that better resembles a random draw from an equally talented 20 team strike force being presented with varying numbers of opportunities. But we still can very safely say that our actual spread of goals from 2011/12 doesn't resemble a lucky dip with a universal strike rate. About 2% of teams manged at least 60 goals from the distribution of shots actually attempted by teams during 2011/12 in simulations using a universal, average conversion rate. In reality during 2011/12, three teams out of 20 managed to surpass this target.
So I then took out headers.
Overall, headers present a poorer likelihood of success compared to shots and in 2011/12 headers comprised a heft chunk of the total goalmouth attempts for some teams, (no prizes for guessing Stoke).
With headers culled from the data, the difference between the actual distribution and the range you might expect from one drawn from a group of equally lethal strikes, plummeted to within touching distance of each other.
It is just one season, but once you take out penalties and headers, then the number of goals scored by all other means inside the box, still differs from what might expect to occur by random chance where there is no difference in the finishing talents of each forward line, but the gap is small....Very small.
Here's the regressed conversion rates for shots (with the feet) inside the box for sides from 2011/12 suggested by the above analysis.
|EPL Side from 2011/12.||Regressed Conversion Rate for Foot Shots Inside the Box %.|
To put these figures into perspective, the difference in conversion rates between top and bottom, given an average number of shots from inside the box (240) accounts for 4 extra goals and that represents about three league points.
If we ignore Newcastle at the top and Liverpool at the bottom, both of whom broke most statistical models during 2011/12, the actual top five from 2011/12 are to be found in the top seven for converting shots inside the box. And relegated Bolton and Blackburn are at least in the bottom half. So the ranking is fairly consistent with league position in May.
By attempting to produce a reasonably sized, homogeneous sample size, the gap between the degree by which real life conversion rates fall, at first slightly and then precipitously towards a random draw is seen. There's still evidence for a talent divide at the very top, but it is narrowing, throwing the importance of shot volume into the spotlight.
Ten years worth of shot data would be nice to see which side of the line shot conversion rates finally settle on!