Luis Suarez and Regression to the Mean

Luis Suarez had an interesting season. While he finished the season with 25 goals and 18 assists in La Liga, he was at times frustrating and often had fans shaking their heads. Throughout the season, people speculated that Suarez may have been injured, that Suarez had lost confidence, and that Suarez was just downright past his peak, and done as an elite player. To justify these speculations (especially the argument that he was past his peak), people started pointing to the stats tables for things like number of times caught offside – ignoring that Luis Suarez also led the league in number of times caught offside in his last three full seasons (2013/14 with Liverpool and 2015/16 and 2016/17 with Barcelona).

Along with the questions of injury and age, fans also began to bemoan the lack of consistency from Suarez. Fans started complaining about his poor touch, his misplaced passes, and his inability to hit what seemed to be easy shots. Those all seemed like fair criticisms, so I dug deeper into the numbers that would indicate if any of those assessments were true. I looked at whether he had more unsuccessful touches, whether he was dispossessed more, and whether he was actually misplacing passes more consistently. To my surprise, the answer to all was no – at least not significantly:

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As you can see from the graph above, there are a few more unsuccessful touches – but not so much so that someone would notice. Over the course of a full 38-match season (3,420 minutes), Suarez was on pace for an extra five unsuccessful touches – or about one every 7.6 matches. You can also see the number of successful dribbles has declined slightly compared to the recent past, but his completion rate was nearly identical – 38.6% from 2013/14 to 2016/17 vs 38.9% in 2017/18. The difference wasn’t ability, just in the number of dribbles attempted. Finally, in his pass figures, if he was really displacing more passes, it would show up in his pass completion rate. While passing percentage isn’t perfect, by any means (Ted Knutson covers why here), they do – at the very least – tell us whether someone is completing passes less frequently. Again, Suarez seems to be the same as in the past – 75.1% in the past vs 76.9%, now. He could still have been misplacing simple passes more frequently, which would cause frustration with fans – especially Barcelona fans – so I dug into whether he was misplacing shorter passes. Once more, there wasn’t any luck on that front.

So what was it about Suarez’s game that had changed, and was driving fans so crazy? Obviously there was something different, but I still couldn’t find what it was. I began to wonder whether it was about the consistency of his performances. Maybe his individual performances were inconsistent, and that was giving the perception that he had declined and wasn’t producing as well. To do this, I decided to look into his expected output on a five match rolling average. This average would show us how he’d looked over the past season, while helping to remove some of the extreme outliers. While we are, in part, looking for matches significantly different than the rest, we’re mostly looking for groups of matches. Every player has had a bad or great match, but the fans won’t be upset for a one-off match where Suarez looked dull. The rolling average will show us what fans will be upset about – runs of poor matches. To start, I looked at his rolling averages for the stats listed above – unsuccessful touches, times dispossessed, successful dribbles, and times caught offside. All of the averages are based off per 90 figures, to account for matches in which he was subbed on or off:

For the most part, the number of times his unsuccessful touches were consistent, ranging basically from two to three per 90. The number of times he was dispossessed was a little bit less consistent, but certainly nothing wild – and nothing worth complaining about. Outside of about a month and a half, he was also between about 0.5 and 1.5 for the season. Looking towards his dribbling and times caught offside, he was inconsistent on that front, but his performances in both areas got better as the season went on. This indicates that fans would’ve been happier about his performance, if the concern was actually about consistency. In terms of the quantity of his contribution to final attack (xG and xA) and the quality of that contribution (xG/shot and xA/KP), there is some variability in the averages, but it’s almost all positive. His expected goal (xG) averages is above the 95th percentile (0.6 per 90) and his expected assist (xA) average is similarly elite (0.31 per 90).

It’s not until we see any sort of significant inconsistency until we look at the quality of his efforts. There are some peaks and values in terms of both the shots he took (xG/shot) and the shots he set up (xA/KP). Still, both figures are consistently at high levels. While the inconsistency is there, we’re looking at a player bouncing between (at worst) being very good and being out of this world elite. That’s hardly something fans would complain about. The deeper I dug, the more it seems that there’s not really any sort of inconsistency on efforts Suarez could control. His touch hadn’t become worse, he wasn’t dribbling worse, he wasn’t misplacing more passes, he wasn’t taking poor shots, he wasn’t avoiding creating shots for others – he was consistently doing everything he could control. That’s where we get into the problem Suarez faced.

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Looking at the graph above, we can see there’s a period in the season where Suarez’s actual output (“G Cumulative”) is lower than his expected output (“xG Cumulative”). By the end of the season, however, we see Suarez’s expected output matched his actual output almost perfectly. While most fans would be quick to point out that this shows an inconsistency in finishing ability, it should be noted that finishing is very rarely a consistent skill – and not one that can often be attributed to player skill (and Suarez has been a notoriously inconsistent finisher for his entire career, anyway).

What Suarez experienced is a simple regression toward the mean. Regression toward the mean is a statistically principle that basically says that any time output is different than average, or would be expected, it’s likely to come back to the average. Soccer Data Analyst Ted Knutson has referred to cases similar to Suarez’s as the “Law of Ibrahimovic” – saying that players whose actual output significantly differs from their expected output will move towards their expected figures. That’s all Suarez experienced, this season. As we have seen from the graphs above, his production caught up to his expected production, and the Law of Ibrahimovic rang true.

That’s not to say Luis Suarez hasn’t declined or that father time isn’t catching up with him. It’s simply to say that Suarez’s poor season wasn’t as bad as people make it out to be. By the end of the season, he had compiled a season of elite offensive expectations (he was the only forward above the 95th percentile in xG per 90 minutes, xA per 90 minutes, xG/shot, and xA/KP) without any significant variance to the things he could control, and by the end of the season his actual output matched his expected almost perfectly.

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