One of the recurring themes of this blog is an attempt to illustrate that the kind of stats that are usually used to quantify how good or bad a team or individual is are almost always an imperfect snapshot of their true abilities. In this guest post I used as large a sample size as is currently available of shots saved by team keepers to distinguish between teams which habitually signed excellent keepers and teams which did not.

We can use a similar approach to investigate the shooting abilities of Premiership sides over the last ten completed seasons. The number of goals scored by teams has obviously varied over that period. But title contending sides invariably have scored more goals than perennial strugglers or yo yo sides who have regularly swapped Premiership football for a less demanding existence in the Championship. The likely reasons for these differing goal tallies include more successful teams creating more chances and then being more proficient at converting them than are lesser teams. One current debate surrounds the extent or indeed the very existence of the latter cause. In short, is the goalscoring talent distribution so narrow in the Premiership that there is little or not difference between the conversion abilities of individual strikers and by extension the teams they play for.

Natural random variation will exist even in trials where we know with absolute certainty the expected success rate. A simulated, fair coin toss won't always produce 1,000 heads from 2,000 trials, but will bunch around that average. I've just run a mere 20 such trials and have seen a low of 949 heads and a high of 1046. Therefore, if we compare a football team's strike rate from a large number of goal attempts, we should expect to see such variation, even if the strike rate of each team is identical.

The average conversion rate for teams which attempted at least 2,000 shots at goal in the EPL since 2002 was 11.3% or roughly one goal every nine attempts. 19 teams have passed this milestone of 2,000 attempts, with Manchester United topping the attempts table at nearly 6,000 shots and Birmingham creeping in at the bottom with a few hundred more than 2,000.

From a purely visual stand point, we can simulate a typical spread of conversion rates for each of the 19 teams, if we assume that each has an identical true converting talent of 11.3%. As expected even in this state of absolute parity, some teams appear more efficient than others simply because of random variation. One team, Spurs, in this single simulation required an average of 10 shots to score once and WBA and Birmingham were apparently the league's most lethal finishers, needing just over 8 shots to score.

If we compare this idealized, egalitarian fantasy with the reality of the last ten EPL seasons, we find that Arsenal, Manchester United and Chelsea are the three most efficient converters of chances and Wigan, Sunderland and WBA are the least proficient. Just as importantly, the spread of shots required to score once is wider than our single simulation. Ranging from 7 shots per goal for the very best to over 11.5 for Wigan.

The identity of the best and worst teams, along with the wider spread of shots required to score once goes part of the way to implicating other causes in addition to mere random chance being present when deciding the actually observed conversion rates seen in the EPL over a decade. Arsenal for example have scored 153 more goals than expected compared to a side converting at the league average from their 5271 shots

We can more formally calculate the size of these other "skill" factors that appear to be present in the real life EPL and use the answers to regress towards the mean each side's conversion rate to obtain a better estimate of their true conversion rates. And the difference persists. The top sides do continually buy players who can convert chances at higher rates than their counterparts in less successful sides. The difference in the number of shots needed to score once ranges from 7 for the best to 11 or more for the worst, even among relatively successful and regular members of the elite flight. If we include the likes of Derby the skill gap widens even more, although the shrinking sample size increases the likely variation in shot quality.

If we regress the simulated trial by the amount required by the distribution of randomly generated conversion rates, we find each "team" in a league decided entirely by luck needs a virtually identical 9 shots to score once. In short, the reality of the EPL over ten years is much more consistent with scoring being part skill, part random variation.

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