With the pressure and excitement of each and every week's matches, it's sometimes easy to lose the overall plot of how a season has evolved in the league as a whole. Since we are just past the halfway point of the season, I thought I'd take a look at a couple of trends in teams' output in the Premier League this season.
The data show the average goal and shot production over the course of the season for each week of play with data for the first 20 weeks of the season. In addition, I superimposed the best-fitting trend lines.
First things first: let's look at goals. After we saw an increase in goals from slightly over 1 per team and match in the first few weeks of the season, goal production increased markedly through Week 10 to around and even above 1.5 per team and match. However, since Week 10, we have also witnessed a decline to lower levels. Statistical tests reveal that this pattern in the data is best approximated by a quadratic function, suggesting that goal production in the Premiership has followed an inverted U this year.
The data show the average goal and shot production over the course of the season for each week of play with data for the first 20 weeks of the season. In addition, I superimposed the best-fitting trend lines.
First things first: let's look at goals. After we saw an increase in goals from slightly over 1 per team and match in the first few weeks of the season, goal production increased markedly through Week 10 to around and even above 1.5 per team and match. However, since Week 10, we have also witnessed a decline to lower levels. Statistical tests reveal that this pattern in the data is best approximated by a quadratic function, suggesting that goal production in the Premiership has followed an inverted U this year.
One natural question is "why"? Did teams start taking and allowing fewer shots on goal in Weeks 11-20, or did strikers forget how to find the net? Let's take a look. The next graphs show the average number of shots per team and week as well as the goals to shots ratio - how efficiently teams converted shots to goals.
As the graph of shots per match reveals, there were no noticeable trends in shot production over the first twenty weeks of the season. If anything, there was a slight downward trend, but this trend was very shallow, and the pattern very much looks like random variation around the league mean of around 13 shots per team and match.
But what about efficiency? As it turns out, that's what seems to explain the inverted U we have seen in goal production above. As the next graph shows, efficiency increased significantly over the first 10 weeks, only to decline again afterwards. So slightly fewer shots coupled with significantly lower efficiency translated into a decline in goals after the first ten weeks of play this season.
The interesting question, of course, is why. Why do we see an increase in goals and efficiency in the first two and a half months of the season, followed by a decrease in production and efficiency? The answer is far from obvious. Of course, we can imagine that teams improve their performance over time - but this should be true both on the offensive and defensive ends of the pitch. That is, improved offensive performance brought on by better coordination, fitness, whatever, should be counterbalanced by better defensive performance, with the net result being a flat line rather than a curve of some kind. Or we can imagine that newly promoted clubs or players from abroad learn to play in the Premiership and get used to the level and style of competition. But again, it is not altogether clear how this should translate into strong trends in league-level outcomes.
Without having done any serious analysis of the underlying causes, my suspicion is that, perhaps, what we see in the graphs is simply variation around the average level of performance in the league, and that the inverted U will therefore soon enough give rise to yet more efficient (looking) play and a slightly larger number of goals. This would mean that, when we look back on the season after Week 38 in a few months, the picture for the season as a whole will probably be one of random variation around a relatively stable long-run level of performance for the league.
But to find out, we'll have to keep watching (and counting).
