I think in football, and sports in general, it’s very easy to get by without questioning the conventional wisdom and intuition that tends to be ingrained in punditry and commentary. However, this does not mean that we should not question these ideas; it is important to challenge and analyse the status quo, even if the questions you ask initially appear simple, obvious and even stupid.
So in this post, I’ll be looking a little at fouls and the factors that influence them. All data used is from the Championship seasons 04/05 to 13/14.
1. Teams that foul more get fouled more
This is a plot of seasonal totals of fouls committed (x axis) and fouls committed by opponents. The data here suggests that 41% of the variation in fouls committed against your team over the course of a season can be explained by variation in fouls committed by your team over the same period. There is a clear correlation between the two variables, which is probably unsurprising, but nice to see nonetheless. As for the reasons, I would suggest it’s perhaps a conscious choice of teams playing these “rougher” opponents to foul more in return.
Interestingly, although again unsurprisingly, the same effect is not nearly as visible on a game-by-game basis:
2. Away teams foul more…
This plot shows the Foul ratio (Fouls committed as a fraction of total fouls) of home and away teams in the Championship on a game-by-game basis. We can see that the FR for away teams is slightly higher than that of home teams (i.e. the away team tends to commit a larger number of fouls than the home team). However, this effect is pretty small. Although it falls within the bounds of statistical significance and we can be pretty confident that there is an effect here, it takes a very large sample to be apparent (10 seasons worth of games). Furthermore, the mean of each group are incredibly close to each other: Home = 0.496, Away = 0.504. However, though the effect is small it could point towards a slight bias in refereeing against away teams (amongst myriad other explanations), which brings me on to…
3. … and appear to get punished more harshly.
Were, referee bias to be a real effect, we would probably expect away teams to not only get called up more frequently (which we do), but we would also expect to see away teams punished more harshly for those fouls which they do commit. As you can see from the plot above (Yellow Ratio = Yellows/Fouls), any effect is likely to be very small. In fact, the raw data above, suggests there is no significant difference in yellow ratio between home teams and away teams ( p = 0.16). However, when we take into account an additional bit of information latent in the data – namely that we would expect away teams to be punished more harshly than the home team in the same game – a large amount of noise is removed. Consequently, the effect becomes far more statistically significant (p = 0.0019). As with the fouls, though, the effect remains very small. This suggests to us that as well as being judged to have fouled more, away teams receive more yellow cards than home sides per foul committed.
It is at this point I feel obliged to note a couple of things. Firstly, I am aware that I have written in a way that perhaps implies that the higher incidence of fouls and yellow cards in away sides is a consequence of referee bias. This is an easy and intuitive explanation, but there is no evidence here linking referee bias to this effect; the data only shows that there is an effect. Secondly, this effect is very small and even if it is due to referee bias, I would suggest that said bias is unlikely to significantly affect games in favour of the home team on a regular basis due to other, far more important factors.
4. Everybody fouls
As we can see from this plot of seasonal Total Shots Ratio (a decent, if imprecise proxy for team quality), there is no correlation between good teams and bad teams fouling more or less than one another.
Furthermore, we don’t see an effect in teams that are dominated on a game-by-game basis either:
It appears that teams getting outshot by their opponents don’t foul significantly more than their opponents. This could have helped explain the home/away bias were there a correlation; however it now seems unlikely. If I had the data to hand, I would like to see Foul ratio as a function of Game State (i.e. do teams foul more/less when winning/drawing/losing?).
So there we have it: there’s karmic balance in the distribution of seasonal fouls, referees could be a little biased, but it probably doesn’t matter, and bad teams aren’t necessarily dirtier. If I have the time, I may look at this topic again to see if average attendance has an effect on game fouls, as well as geographic proximity between teams. Anyway, thanks for reading.