Offensive Contribution in La Liga: Usual Suspects and One Ugly Duckling

In this post, we look forward to the new season of La Liga by looking back to the previous one. More specifically, we’ll zoom in on the offensive contribution of those forwards who put in stellar performances on this front. A player’s offensive contribution is typically determined "quick and dirty" by considering goals and assists, often by simply adding the two. Naturally, there are much more sophisticated – and accurate – ways to gauge the offensive contribution a player represents to his team. One such method that I will employ here has been proposed by Thomas Severini, Professor of statistics at Northwestern University, and concerns a regression model with multiple predictor variables.

The intuition and rationale behind the statistical model are as follows: For all teams in the Primera División, over the last seasons, we know how many goals they scored and a bunch of other statistics, including how many shots on goal, how many attempts at goal from outside the box, from inside the box, how many dribbles, passes, etc. they executed. What we are interested in to find out, is what are the variables that actually relate (most) to the number of goals scored by a given team. To this extent, in our model, we consider each team’s performance over the last five seasons, leading to 100 (i.e. 5 times 20 teams) observations. The statistical model allows for filtering out those variables that yield important additional information about the dependent variable (here: goals scored).

A concise model that allows us to explain no less than 85 percent (i.e. the R²) of the goals scored in the past five seasons of La Liga turns out to be the following:

– 13.7 – 0.10112*shots_outside_of_box + 0.41682*shots_on_target + 0.0132*successful_passes

Most important when interpreting this model – rather than the actual number, which is hard to interpret – are the variables included and their respective signs: Shots on target has a positive sign, implying that more shots on target tend to coincide with more goals. The sign of the variable shots outside of box is negative as it negatively adjusts the impact of shots on target attempted from outside the box in terms of their success probability. Successful passes turn out to constitute another important aspect of the offensive contribution, whereas, for example, successful dribbles, do not. Also noteworthy is the relative difference between the respective coefficients of variable shots on target and of successful passes: A shot on target will have an impact on the offensive contribution over thirtyfold (i.e. 0.41682/0.0132) the one of a successful pass. In case I would have data on the area of the pitch where the passes took place (e.g. final third), the model could be made even more accurate and I could also include non-forwards.

Following Severini's Analytic Methods in Sports (2015), to apply to above team-level model at the level of the individual player, we merely need to divide the intercept by 10 (because of the ten field players). Thus, for an individual player,

Offensive Contribution = – 1.37 – 0.10112*shots_outside_of_box + 0.41682*shots_on_target + 0.0132*successful_passes

The top 10 of offensive contributors for the 2015-2016 La Liga season is as follows:

Figure 1: Top 10 offensive contributors, La Liga 2015-2016

Naturally, some players received more playing time than others, e.g. due to injury. For comparative purposes, therefore, it is also helpful to consider offensive contribution assuming all players would have played all matches – at the level of their offensive contribution when they were actually fielded:

Figure 2: Top 10 offensive contributors, La Liga 2015-2016,
assuming all players would have played all of their team's games

Key observations:

1.     The number 1 in terms of offensive contribution is Lionel Messi.

2.     Although Cristiano Ronaldo came closest to Messi in terms of offensive contribution, Neymar would have jumped Cristiano, had they both had the same playing time.

3.     All members of MSN as well as of BBC are included in the top ten, assuming all players played the same number of games.

4.     MSN’s combined offensive contribution is larger than BBC’s.

5.     There is one “ugly duckling” in the top 7 (8), otherwise made up entirely of “usual suspect” stars: Jonathan Viera of Las Palmas. The 26-year-old Canary Islander tends to remain under the radar of more traditional measures of offensive contribution.

6.     The top 10 is completed by club topscorers who had an exceptionally prolific season: Depor’s Lucas Pérez, Betis’ Rubén Castro, Bilbao’s Aduriz and Real Sociedad’s Agirretxe – who missed over half the season due to injury.

7.     Relative differences are quite substantial, e.g. Messi's offensive contribution is almost double the rankings' number 10.

While it is difficult to perform even better in the season following an exceptionally good one – among others, due to a principle known in statistics as “regression to the mean” – I particularly look forward to finding out whether Las Palmas’ Viera can really make a name for himself this season and whether Messi and Cristiano Ronaldo can remain at the very top, or whether youngster Neymar will make a move towards absolute supremacy.

Note that by means of our regression model, we are measuring correlations, not causation. This concretely means that, over the past five seasons, the selected variables were accurate predictors of offensive contribution in La Liga. However, it does not imply that a player’s future offensive contribution will move accordingly. Especially if players were to “act upon” the above model, e.g. by dribbling less and shooting or passing more instead, the included predictor variables may (or may not) lose part of their positive correlation with the dependent variable.

Let the new season commence! J

The Birth of the Aging Striker?

During the Champions League round-of-16 first legs, one thing worth noticing was that the ones to open the score for the all-star teams of Real Madrid and PSG were “old-timers” and club top scorers Cristiano Ronaldo (31) and Zlatan Ibrahimovic (34), respectively. What is more, Zlatan has now scored in each of his last nine(!) appearances for PSG, including Champions League, Ligue 1 and French Cup. In the only one of their last ten encounters PSG did not manage to score, the Swedish veteran was not fielded. 

Source: telegraaf.nl

Meanwhile, Jamie Vardy, aged 29, is leading the Premier-League’s "pichichi". An unlikely feat, particularly given that, at the age of 24 – generally considered already quite “old” for a striker – Vardy seemed to have reached his terminal in the fifth tier of English football. During the 2014 FIFA World Cup, the BBC published an article claiming that, in accordance with popular wisdom, a football player peaks at the age of 27.5. Naturally, goalkeepers are expected to peak above and strikers below this average. Are Vardy, Zlatan and others defying logic then? Or could it be the logic rather than these players that is dated? 

As you probably rightfully noticed, all of the above examples I carefully cherry-picked. For instance, there was no mention of the opening goals by youngsters Dybala and Draxler, both 22 years of age. In order to see if something of interest may actually be going on, let’s be slightly more scientific. As of currently, the top-10 scorers active in the five main European leagues, including any goals they may have scored in the Champions or Europa Leagues and with penalties counting for half a field goal, are, in order: Cristiano Ronaldo, Suárez, Lewandowski, Higuaín, Aubameyang, Ibrahimovic, Benzema, Müller, Aduriz and Messi. Their average age is slightly above 29 years and 6 months (median age: 28.44). For strikers – moreover, the top ones in Europe at this very moment – that seems pretty old. It begs the question, “are top strikers – as is the general population – actually getting older?”

Source: marca.com

In order to investigate this question, I turn to the “Golden Shoe” (or "Golden Boot"), an annual trophy awarded to the most prolific scorer in any national league within Europe (since 1997, adjusted by a coefficient depending on the strength of the league). The Golden Shoe is being awarded since the 1967-1968 season, when Eusébio was the first to try it on. For each year since, I computed the average age of the scorers that made it to the podium (top-3). Importantly, the winner of this award is not elected but rather results from having scored most goals. Hence, any changes that may appear over time won’t resemble changing preferences but rather an evolution of the game and/or scorers as such. For the running season, I include the current top-3 in the Golden-Shoe ranking: Barça’s 29-year-old Suárez, Napoli’s 28-year-old Higuaín and Benfica’s 31-year-old Jonas. The below chart indicates the average age of each season’s top-3.

Figure 1: Average age of "Golden Shoe" award top-3 (years on X-axis; age on Y-axis)

At first sight, there is no trend clearly emerging and what mainly grabs the eye are the many fluctuations. I next include a linear trend-line, hinting to some general trend. The important thing to note is the trend-line's upward slope, indicative of an increase in average age over time.

Figure 2: Average age of "Golden Shoe" award top-3 (years on X-axis; age on Y-axis).
Actual data in blue; linear trend-line in red.

The next graph depicts the non-linear trend-line that is closest to the data and which is readily supported by Excel. This trend-line starts off at slightly below 25 years of age and increases - let it be not monotonically - to nearly 29 years. 

Figure 3: Average age of "Golden Shoe" award top-3 (years on X-axis; age on Y-axis).
Actual data in blue; non-linear trend-line in red.

For those readers who know about statistics, the R²-values neither of the linear nor of the non-linear trend-line are high. However, the Spearman rank coefficient of season and age is 0.29 and significantly different from 0, suggesting that there is indeed an upward trend in topscorers' age over time. Even if from a strictly scientific viewpoint the evidence is limited, I could draw a parallel with global warming: the possibility of a few years difference over a less-than-50-year period may still be worth some consideration, wouldn’t you think? Here's what Aritz Aduriz (35) has to say about that.

Which of Europe's Best Scorers Are On Fire, Really?: A Multi-Measure Analysis

With the new football season now well underway, some of Europe’s top strikers have already found their best form while others struggle to regain it. Considering performances in Europe’s five major domestic leagues (Premier League, La Liga, Bundesliga, Serie A and Ligue 1) as well as its main international team competitions (UEFA Champions and Europa Leagues) the “happy few” scorers with already six or more goals to their tally, as of 29/09/15 (morning), are as follows:

Tabel 1. Simple ranking: Europe's top scorers by number of goals scored 

In my May’s post, “Which Premier League Top Scorer Would You Like in Your Team?,” I proposed an evaluation method for top scorers based on multiple measures that would allow for deeper insight into what lies beyond a simple ranking. In this post, I will evaluate Europe’s current top scorers by means of this method. A multi-measure analysis will bear out several critical insights and nuances about Europe’s on-fire scorers.

·      “Efficacy”, or the number of penalty-adjusted goals scored:

For reasons explained in the May post, I adjust the ranking so that converted penalties account for half a field goal. Those with an efficacy rating higher than five are as follows:

Tabel 2. Efficacy ranking: Converted penalties count for half a (field) goal

Observation 1: Making the recommended adjustment for penalties converted, the difference between Lewandowski’s ten goals and first contenders Aubameyang, Müller and Cristiano Ronaldo (all having converted three penalties) becomes clearer. Indeed, Lewandowski so far managed to score as many field goals as both Müller and Ronaldo together.

Observation 2: The penalty adjustment also allows for a better appreciation of the difference between Real Madrid teammates Cristiano Ronaldo’s eight and Benzema’s six goals: If Benítez appointed Benzema rather than Ronaldo as penalty taker, Benzema would have overtaken Ronaldo as the club’s top scorer as Ronaldo would then have scored max. five and Benzema min. six times.

·      “Efficiency”, or the average number of penalty-adjusted goals scored per 90 minutes on the pitch:

The rationale behind the efficiency measure, I explained in the May post. Efficiency, which reflects a scorer’s average performance during a ninety-minute (i.e full-game) period, is all the more relevant when comparing across leagues: not all leagues have the same number of match days and some teams additionally compete in Europe whereas others don’t.

Five of Europe’s top scorers so far have managed to score on average one or more goals during every ninety minutes on the pitch:

Tabel 3. Efficiency ranking: Avg. number of penalty-adjusted goals scored during 90 minutes

Observation 3: To put Lewandowski’s exceptional form in context, not only is he the only one who managed to almost put two field goals in per ninety minutes, but also has he been well over three times as efficient as Manchester United’s sensational signing Anthony Martial (efficiency: 0.54; including three games at Monaco) so far has been this season, for example.

Source: sueddeutsche.de

Observation 4: Karim Benzema so far has also been extraordinarily efficient, scoring more than twice as much as Martial, when on the field, as well comfortably outperforming his teammate Cristiano Ronaldo (efficiency: 0.93).

·      “Relative efficacy”, or the percentage of penalty-adjusted goals scored relative to the team:

As explained in the May post, relative efficacy accounts for the fact that it may well be more complicated to put goals in if you’re a forward at, say, Watford rather than Bayern Munich or Real Madrid.

Tabel 4. Relative efficacy ranking: Percentage of team's penalty-adjusted goals scored by top scorer

Observation 5: Note that the relatively most efficacious scorer in Europe, Watford’s Odion Ighalo, did not even show up in the simple goal top scorer ranking. In fact, none of these scorers featured in any of the above rankings and it is noteworthy that they play their football at relatively smaller teams, which partly accounts for why they managed to score half or more of their team’s (penalty-adjusted) goals.

Observation 6: It is important to note I only consider actual top scorers for these rankings, e.g. only one Premier League player scored more goals than Bournemouth’s Callum Wilson. Málaga, for instance, have not managed to score a single goal yet, so whoever will score their first will attain a 100% relative efficacy (i.e. will have scored 100% of the team’s goals at that point) – but he wouldn’t be anywhere near a league top scorer and thus should and would not enter in this ranking. A similar argument applies to the above efficiency ranking.

·      “Importance”, or the average of the virtual and eventual incremental points won by the player’s team because of a player's goals:

The notion of the importance of a goal in terms of additional points won for the team is critical and is also further detailed in the May post. Arguably, from a team perspective, it is the single most relevant measure as the team's objective is to maximize points rather than goals. Those top scorers whose goals already earned their team more than five points are:

Tabel 5. Importance ranking: Avg. of virtual and eventual incremental points won by team because of top scorer's goals

Observation 7: Lewandowski and Benzema have not only been putting in lots of goals, but also goals that led their respective teams to win more points, notably as opposed to Cristiano Ronaldo whose eight goals so far amounted to a total one-point importance only, according to the measure’s definition.

Observation 8: Ighalo’s ranking as Europe’s joint second team scorer in terms of most important goals for his club demonstrates that his topping the relative efficacy ranking is not just an oddity, but rather demonstrative of something highly meaningful.

Source: theguardian.com

Concluding observations from the multi-measure analysis:

Observation 9: Robert Lewandowski is clearly on fire: not only is he currently Europe’s most effective as well as efficient scorer, but also is he the scorer whose goals so far delivered most points to his team.

Observation 10: Some scorers who so far have been instrumental to their team’s successes, e.g. Griezmann and Ighalo, in a simple ranking of goals scored, would remain largely unnoticed, whereas the impact of others' goals, e.g. Cristiano Ronaldo's, may be overstated.

Observation 11: It is not any single measure, but the combination of several which results in a much deeper and nuanced insight into the meaning of the game’s top scorers.