Tomorrow is Labor Day here in the United States. So naturally, I've been thinking about how we measure work performance in football. It's also a long weekend, with most people off from work for three days. If they spend it catching up on the Premier League season so far, they could be forgiven for scratching their heads upon finding out that last year's top scorers in the Premier League Dimitar Berbatov and Carlos Tevez have yet to start a singe match this season. Why would teams handicap themselves by having these prolific scorers come to work but then leaving these potent weapons on the bench?
|(c) Gordon Flood|
Relative metrics are useful because they shed light on performance in relation to some standard (what proportion of all events fall into a particular category), or they communicate something about the connection of events on the pitch (how much of x produced how much of y?). Both can tell us something about the productivity and efficiency of a player or team. The Oxford dictionaries define “efficient” as the characteristic of a system or machine “achieving maximum productivity with minimum wasted effort or expense” or as “preventing the wasteful use of a particular resource.” Defining it as minimal waste in production, we can think of it as the ratio of inputs to outputs. So it helps us to think about performance in a way that connects attempts with failures or successes (again, think pass completion or goals/shots).
Of course, the better teams (in an absolute sense) will score more goals than the not so good ones. But efficiency measures take into account what players or teams are able to do, given the resources they have, not simply whether they do a lot or a little. An example may help. Let’s think of a team’s productivity in terms of its ability to score goals. A team is more efficient if it achieves goals with less effort or expense. The effort or expenses that matter are things like possessions, passes, and shots – things teams do before they ultimately score. So if we want to know how efficiently teams produce goals, we want to know how many inputs they use to produce the output we care about.
A straightforward way to measure this is to calculate the ratio of goals to shots. Take a look at last season's efficiency statistics for the Premier League (by club) in the graph below.
We see some expected but also some surprising patterns.
While we may not be surprised to see Manchester United top this table or find Manchester City in third place, the data also show that the very best teams in the league do not necessarily cluster at or near the top in efficiency. The teams that needed to take fewer shots to produce a goal also included Blackburn, West Brom, Birmingham, and Blackpool. In fact, we see that these teams were more efficient than Chelsea and Arsenal. So in terms of offensive production, some mid-table and even relegated clubs were very efficient.
Their problem may have been that they did not produce enough shots - but when they did, they did well. At the bottom, we see that Wigan and West Ham were the most profligate. Even when they did get a chance to score - which wasn't all that often - they managed to waste their chances. We also see that clubs like Tottenham and Chelsea performed worse than they should have, given their aspirations. They had to take too many shots to score.
So what do we see when we put the absolute and relative scoring metrics together? Below is a graph of the average number of shots by goal scoring efficiency, along with a quadratic (curvilinear) best fit regression line superimposed.
The data show that the relationship between shots and efficiency is not linear. Teams that shoot more do not necessarily score more efficiently. In fact, there's a great variety in absolute shot production even among the most efficient teams. Compare Birmingham City and Manchester United, for example. Both were very efficient last season - but United managed to win the league by producing, on average, about six more shots per match. So City's problem wasn't a failure to take their chances, it was not creating chances in the first place. The same can be said of Wolves and Rovers. A curious case is West Brom: they almost matched Manchester United on shot production and goal efficiency (and obviously didn't win the league last time I checked); here, it would be interesting to see what the differences were by types of matches or before and after Roy Hodgson took over.
Finally, take a look at Tottenham, Arsenal, and perhaps especially Chelsea. While the London clubs managed to create lots of shots, they were only average in efficiency. In contrast, United created the fourth most shots but they were also the most efficient offensive team in the league. So efficiency seems to have been a key ingredient in winning the league last year, while profligacy was punished. So when you keep tabs on your favorite club this season, ask what they do with the assets they have - do they use them productively or waste them?