Variance in Expected Goals
The idea for this article comes from a recent discussion on Twitter on the astonishing case of Brighton Hove Albion this season. The team has accumulated a goal difference of -7 and an xG difference of 12.3 (as of 28.2.2020). This is an underperformance of -0.74 per game.
Consequently, the central question of this article is the following: how probable is under- or overperforming Expected Goals over the course of a season by a certain magnitude?
Setup and data scope
For the analysis I use xG data from understat.com for the top 5 leagues from six seasons, namely 2014/15–2019/2020. The data of the 2019/20 season from Ligue 1 was ignored because the season wasn’t finished.
In principle, the analysis could be extended with some theoretical estimations if single shot data is available (unfortunately, I don’t have it). I wrote about this for single players:
Analysis
The approach is very simple. For every team we calculate the difference between the Expected Goals difference and the actual goal difference for each game. We then average this over the season. Hence, we have a sample size of (4*6 -1)*20 + 6*18 = 568 (Bundesliga has only 18 teams). The variable of interest is the following:
diff = (Goals scored - Goals conceded) - (xG -xG conceded)
We now plot the same information in a slightly different way. We calculate empirical probabilities of a certain under-/overperformance, in other words quantiles. The result is below:
How to interpret this chart? Empirically, the worst underperformance observed was -0.7 xG difference per game and the best +0.91 (over the course of a season). Hence, Brighton so far are on the way of setting a new underperformance record. Side note: the best overperformance so far was AS Monaco 2016/17, the worst underperformance by Deportivo La Coruña in 2017/18.
Naturally, with probability 1/2 a team over- or underperforms its xG value (because this is a zero sum game). An underperformance of -0.25 per game or worse appears with a probability of roughly 16%.
More importantly, the interval around 0 covering 50% of probability is [-0.196, 0.16]. Hence, an under-/overperformance within this interval shouldn’t be considered extraordinary. Surprisingly, this interval is not symmetric, there are more teams having large under- than outperformances (but I do not have an explanantion for this effect).
Another question of interest is whether xG outperformance happens more likely for stronger teams. The standard argument is here that better players have better finishing technique and thus will outperform their xG. Side note: on the defensive side this argument could also be made for goalkeepers.
From the plot below we see that xG difference is a factor for explaining xG outperformance, though there seems to be a lot of unexplained variance still.
Conclusion
This article is (at best) only a partial answer to the underlying question in the case of Brighton: we still don’t know whether their performance is due to extreme bad luck or has a fundamental root cause.
However, the above plots allow to estimate roughly how probable such an event would be. It also helps to get a feeling for the natural variance of Expected Goals.
Only specific analysis can show whether Brighton’s underperformance is due to bad decision making, finishing technique or other reasons (xG model issues could also come into play).
However, the variance in xG should be explored better. For example, under the hypothesis that good/bad finishing has a psychological impact on a team, one could test whether xG outperformance is auto-correlated over time. Moreover, these analyses could be done — in contrast to the above — separately for offense and defense.
