In the wake of yet another contentious penalty decision given against Arsenal, I thought it would be interesting to dive into the numbers to see whether Premier League referees do actually discriminate against Arsenal at either end of the pitch.
This is by no means going to be a comprehensive analysis of each individual decision and whether they were right or wrong. Rather, I'll be attempting to look into the number of penalties awarded and conceded over time, and seeing how they compare to other clubs, and against what we'd expect for a team of Arsenal's style and stature. This is partly to open our eyes to the potential influence of footballing reasons, and partly because looking at the refereeing errors affecting one club in isolation doesn't tell us anything about bias - ALL clubs suffer from bad decisions to some degree and ALL fans complain about decisions that go against them; looking at one club alone couldn't possibly tell you anything about whether they receive different treatment to other clubs.
This first part will focus on penalties awarded. In order to be thorough, data from the 10 seasons between 2007/2008 and 2016/2017 will be used, from the 22 teams that have featured most frequently in that time.
All statistics are sourced from OPTA, via Statbunker and Whoscored.
The most basic stat to start off with is the actual number of penalties awarded per season. In the following table you can see that Leicester surprisingly top this list, thanks in part to their haul of 13 awarded penalties in their title-winning 15/16 season. The top of the table is otherwise dominated by the league's strongest teams, with the exception of Arsenal all the way down in 9th place, and Blackburn and Crystal Palace way up in 6th and 7th.
Now penalties in isolation don't tell you much. To get a better idea of whether a team is winning too few penalties, we need to look at their general attacking threat. Well non-penalty goals is a good gauge of how potent a team's attacking threat is (and is independent of potentially biased penalties). Arsenal top this list over the last 10 years, which produces quite an odd contrast with their lowly penalty figures. Definitive proof of refereeing bias right?
But Arsenal are not the only team who are under-represented. Swansea and Southampton would also have legitimate claims to be the victims of refereeing bias if we were to use this simple logic. And the likes of Leicester, Crystal Palace and Blackburn would appear to be enjoying the favour of referees.
To get a better idea of the discrepancy between a team's rank in the penalties awarded category and the non-penalty goals category, we can express the former as a percentage of the latter. This gives us a very nice spectrum as shown in the following table, with the likes of Crystal Palace and Leicester sitting at the top, winning penalties at more than double the rate (relative to their attacking level) of Arsenal, who sit at the very bottom.
Now, far from reinforcing the idea that referees are biased in favour of or against certain teams, this table actually goes a long way to explaining the footballing reasons behind this disparity. The top of the table is dominated by teams that could broadly be described as playing direct football, be it Leicester's lightning quick counter-attacks, Palace's tricky winger-based system, or Stoke and Blackburn's physical, aerial game. At the other end of the spectrum you have Arsenal and Swansea, two teams renowned for playing short-passing, possession football. And then in the middle you have the traditional big teams - minus Arsenal of course. These teams tend to dominate possession perhaps by virtue of their quality rather than by design, and they are not necessarily wedded to a slow, intricate approach.
On the face of it this contrast would make sense - penalties are often won during transitions, when tricky, pacy attackers can take advantage of opposition disorganisation, isolating defenders and drawing them into desperate fouls in the box. Teams that move the ball quickly from back to front are likely to win more penalties at any given level.
So the next table looks at a team's "directness", measured as the percentage ratio of long passes to short passes. Directness also correlates incredibly well with average possession, as you'd expect.
From this table we can see that there's a pretty clear trend of penalty % increasing as directness % increases. It's not a perfect trend of course, as Wigan seem to win more penalties than you'd expect for a team of their style, and Bolton have won far less than you'd expect with their direct approach, to name just 2 outliers.
So what does this data tell us? That there's a pretty good correlation between a team's directness, and the likelihood of them winning penalties at their particular quality level. The following graph demonstrates this better:
But this doesn't explain everything. Why, for example, do Man City win so many penalties for such an indirect team, while Arsenal win so few? Why are Arsenal awarded penalties at the rate of a mid-table team while their rivals at the top all earn considerably more despite not being that much more direct than Arsenal?
You would of course expect good dribblers at top clubs to also win penalties in crowded boxes, so directness cannot FULLY account for the penalty rates. Hence why the top clubs such as Man Utd, Chelsea, Liverpool and Man City hover around midtable for the penalty award rate, despite being at the bottom of the table of directness. Arsenal don't seem to benefit from this effect.
To illustrate this point one final time, let's compare average points per season to the penalty % rate below. You can see that the top 7 cluster all win significantly more penalties relative to NPG than Arsenal.
What can we conclude from these numbers? Firstly, this DOES NOT prove that referees are biased against Arsenal. This analysis is nowhere near exhaustive enough to be able to confirm that point of view. As we've seen, just a quick dive into the possession/directness figures has already uncovered one significant factor that affects how often different clubs are awarded penalties. There's no reason to think that a more detailed analysis of other metrics wouldn't uncover any more insights.
With that being said, there is room within the data for potential refereeing bias. This doesn't necessarily have to be an intentional bias, or the result of a conspiracy among referees. It could be something as simple as a sub-conscious stereotype of Arsenal as a 'soft' team who go down too easily under challenges. Again, the data above doesn't prove this, but doesn't rule it out either.
Part 2 will focus on penalties conceded, which should give us another angle to approach the issue from, and more data to add to the playing style vs refereeing debate.
