Europe's Hottest Prospects Going Into the New Year

With the final whistle of 2015's last match having been blown and the opening of the winter mercato being imminent, an excellent moment has come to re-assess the goal-scoring performances of Europe’s top scorers. In previous posts, I developed a multi-measure analysis, considering top scorers’ performance according to four meaningful dimensions, in addition to the simple number of goals scored: efficacy, efficiency, relative efficacy and importance of goals scored. No less than four different top scorers top one of these five rankings, underlining the value of the multi-measure approach. 

In the below analysis, as before, I will be taking into account appearances and goals scored in the five main domestic leagues in Europe as well as in the UEFA Champions and Europa leagues. To be considered a top scorer at this stage of the season, I require a player to have scored ten goals or more, a condition satisfied by 25 players, coming from 20 teams –FC Barcelona, Real Madrid, Bayern Munich, PSG and… Leicester City have two each.

The top 10 of simple top scorers as of 01/01/2016 is being headed by Cristiano Ronaldo:

·      “Simple” goals, or the number of goals scored:

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

Observation 1: Only one of this happy bunch (of 25) has a contract due to expire mid 2016 and can thus be snatched up without a transfer fee: Zlatan Ibrahimovic.

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

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

Observation 2: After making the proposed adjustment for penalties (i.e. valued at 0.5x), Lewandowski retains his top spot in the efficacy ranking, let it be shared with Cristiano – with Lewa having needed less time on the field to score his 22.

Observation 3: Bayern are the only team with two players in the penalty-adjusted top ten. Lewandowski-Müller thus remains the most efficacious duo in Europe.

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

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

Observation 4: While Lewandowski is still Europe’s most efficacious top scorer, he no longer is the most efficient one. Furthermore, Lewa-Müller is no longer the most efficient duo. Benzema-Cristiano is the only couple in European football that, combined, scored more than two(!) (penalty-adjusted) goals on average per 90 minutes on the field.

Observation 5: In addition to the most efficient Benzema and Lewandowski, Aubameyang and Higuaín are the only other top scorers to have scored more than one (penalty-adjusted) goal on average per 90 mins on the pitch – indeed quite a feat, halfway down the season. Both Luis Suárez and Cristiano being not far off either.

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

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

Observation 6: Agirretxe and Ighalo continue to spearhead their respective team’s attack: both top scorers’ respective goals accounted for no less than 67% and 64% of Real Sociedad’s and Watford’s (penalty-adjusted) total, respectively. Indeed, it would be hard to overestimate the reliance of both teams on their top scorer’s goals.

Observation 7: Lukaku’s emergence, with a 44%-share of Everton’s (penalty-adjusted) goal tally, is well-worth pointing out.
 

Observation 8: Betis’ Castro and Rayo Vallecano’s Guerra both (temporarily) dropped out of the rel. efficacy ranking. Although each accounted for well over 50% of his respective team’s goal total, neither managed to put in double-digit goals and is thus, at this point, considered a top scorer.

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

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

Observation 9: The prophecy at the end of the previous post has become reality: Jamie Vardy has become the most important top scorer on European fields. What is more, no tandem in Europe has gained more points for their team than the duo Vardy-Mahrez did for Leicester. All the more remarkable considering that Leicester does not play in the Europa - let alone Champions - League and thus both stars-on-the-rise had relatively fewer games to win points for their team. And that they play their games in the Premiership, Europe’s most competitive domestic league. And that Leicester is a club of relatively modest means – as evidenced by both top scorers original acquisition prices (£1m for Vardy; £350k for Mahrez)...

Source: theguardian.com

Observation 10: Did you notice the only player to feature in the top ranking according to all five dimensions? Hint 1: It’s one of the many considered not good enough by Louis van Gaal for his struggling Man. United squad. Hint 2: Little pea J

That’s right, it’s Chicharito. Quite an achievement considering the Mexican sniper arrived in a new – and quite a different – country and league only in September!

Source: telesurtv.net

Batman & Robin, Europe's Most Efficient Duo. But One.

The mid-November international break marks a point of reflection for many a club manager. Some so far performed better than expected, whereas for others it is quite the opposite. Irrespectively, however, most have set their sights on players, especially forwards, they feel could make all the difference in their team. Wenger, allegedly, is thinking of landing Bayer Leverkusen’s Bellarabi. Mourinho is rumoured to have a keen eye on Bellarabi’s teammate Chicharito as well as on Higuaín and Griezmann. Meanwhile, Benítez is believed to be eager to add Lewandowski to his merengue squad. Some of these names seem more obvious than others. In this post, I will shed light on Europe’s five top leagues’ top scorers’ performance following the multi-measure method developed earlier.

As explained in the previous post, I consider goals scored both in the domestic league and in the UEFA Champions and Europa Leagues. To qualify as a top scorer at this stage of the competition, a player must have scored 7 or more goals. Now let’s have a look at those rankings!

·      “Simple” goals, or the number of goals scored:

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

Observation 1: Lewandowski, Aubameyang and Müller - all playing in the Bundesliga(!) - aready made up the top three at the end of September, at the time of the previous post. All three of them managed to hold on to their exceptional form.

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

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

Observation 2: Counting any converted penalties for half a field goal, Lewandowski distances himself from Aubameyang. The difference between both, on the one hand, and the rest, headed by Müller, on the other, becomes more pronounced.

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

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

Observation 3: The two most efficacious top scorers also turn out to be the most efficient ones. Lewandowski and Aubameyang, on average, score well over one (penalty-adjusted) goal per game.

Observation 4: Of the four top scorers who managed to put in more than one (penalty-adjusted) goal per game, two play for Borussia Dortmund! Fielding both Aubameyang and Reus for 90 minutes so far implied the team would score at least two goals, on average - quite a luxury. Still, Bayern Munich's combination of Lewandowski and Müller yielded even more (penalty-adjusted) goals on average per 90 minutes.

Source: futturk.com

Observation 5: We see two relatively unknown top scorers pop up, both from lesser La Liga teams. Real Sociedad's Agirretxe and Rayo Vallecano's Guerra have, respectively, been good for slightly more and slightly less than one field goal per 90 minutes played.

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

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

Observation 6: And here they are again!: Agirretxe and Guerra turn out both not only to have scored around one goal per game on average, but also to have accounted for 2/3^rds of all the goals scored by their respective teams.

Observation 7: They are joined at the top of this ranking by Odion Ighalo, already Europe's most relatively efficacious scorer at the end of September. The Nigerian striker continues to make the difference for his team.

Observation 8: As opposed to the top four, who, in part, are heading this ranking because of a failure of their teammates to score goals (e.g. all four teams rank in the right-hand side column in their respective national leagues), Jamie Vardy is managing a huge chunk of his team's goals with the whole team cruising through the league.

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

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

Observation 9: So far in my analysis, he remained largely unnoticed, but Luis Suárez is the top scorer whose goals resulted in most points for his team. Also well worth pointing out is that his teammate Neymar - who, before any adjustment, scored more goals than the Uruguayan - collected less than half of the points for Barça with his goals so far (5.25).

Observation 10: Eye on Vardy. Without his team playing in Europe, as the only player to make it to this ranking's top five, he has managed to earn his team 11 points with his goals already - all within the Premier League, the most competitive national league. Indeed, the Englishman's goal spell is no stranger to Leicester City's extraordinary league position.

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.

Money and Football: Big Spenders Take All?

It’s Transfer Deadline: D-Day for many managers and club Presidents across Europe to scramble together their winning team for the months to come. One of the main insights stemming from a “soccernomics” approach is that transfer-fee spending does not lead to positive results on the pitch, but that wage spending does. This relationship was proposed some years ago by sports economist Stefan Szymanski and sports journalist Simon Kuper in their bestseller Soccernomics and, meanwhile, has influenced some of the most powerful people on the business side of sports, such as Ferran Soriano, CEO of the highest-spending sports club worldwide, Manchester City, as evidenced in his book Goal: The Ball Doesn’t Go In by Chance. In an earlier post, I pointed out that a causal relationship going from wage spending to success is very unlikely to exist. Interestingly, in his new book Money and Football: A Soccernomics Guide, Professor Szymanski formally reiterates his stands on the matter, although he actually gives away that it is wrong... I’ll explain very succinctly.

Prof. Szymanski states that there is a very high correlation between wage spending of football clubs and their league position. He now acknowledges that correlation (i.e. two things occurring at the same time) does not automatically imply causation (i.e. one causing the other). However, he points out that, “now there are some statistical tests that one can implement in order to get a better idea about whether a relationship is causal. Some (but) not all of these studies support the view that causation runs from wage spending to league success” – without any indication of what “some (but) not all” concretely means (e.g. two out of ten?, nine out of ten?; which ones yes and which ones no?) He further mentions – and here I certainly do follow – that, “it’s also important to have a theoretical model in mind" and he goes on by suggesting that, "it’s very hard to develop an argument to explain the data that does not entail causality from wages to performance.” Don’t mind if I at least gave it a try:

Wage and talent, or quality, of a player tend to be very highly correlated – including for reasons mentioned by Prof. Szymanski, i.e. that players are operating in a competitive market, with lots of information being available on players and their performance. As a result, a team made up of highly-paid players often reaps success. But the causal driver is the talent, not the wage. In other words, if a same quality player would earn less (within reasonable bounds), performance would be very likely to be the same. For example, do we really expect Kevin De Bruyne to start playing so much better even now than last season just because his wage just nearly doubled? Ridiculous. The driver of – player and team – performance is the quality of the player(s). The wage a player earns is an indicator of that quality, but it does not drive that quality.

Source: mcfc.co.uk

Prof. Szymanski actually confirms exactly that with his “revised formulation” of the pay–performance relationship in his new book. He mentions that money is the key to success, not because by paying donkeys very high wages you will become successful, but because a big checkbook gives you access to superstars (i.e. very high-quality players). It doesn't take a PhD to realize that, if you put two and two together, what this in fact means is that quality, or talent, not wage, drives success. And that quality or talent tends to be highly correlated with wages, due to supply and demand dynamics of the market for players. Prof. Szymanski actually concludes that his "pay-performance line works because there is a market–...the market prices the relationship...between talent and success"! (emphasis added)

For those who love statistics, my conjecture corresponds to a strong suspicion that Prof. Szymanski's results demonstrate what is known in the jargon as omitted-variable bias. According to Wikipedia, "in statistics, omitted-variable bias occurs when a model is created which incorrectly leaves out one or more important causal factors. The "bias" is created when the model compensates for the missing factor by over- or underestimating the effect of one of the other factors." Leaving out an actual variable for talent, or quality, while including a variable that is highly correlated with quality (such as wage) may thus lead to showing a very strong direct relationship between wage and success - but only because talent as such has erroneously been omitted. A look at the original 2002 Journal of Sports Economics paper by Hall, Szymanski and Zimbalist confirms omission of a talent variable in both the regressions and the causality tests.

The main lesson for sports managers out there? Look out for talent, not just to spend your money! Something the likes of Swansea’s Garry Monk realized quite some time ago – partly out of necessity – and something Louis van Gaal still doesn’t – partly for lack thereof. Fortunately for mad King Louis, he seems blessed with Maecenases who don’t seem to either.

Source: BBC's Match of the Day (30/08/15)

How Barça’s Treble Will Change the History of Football Tactics

Before turning the page on the 2014/2015 season, let’s have a look at the learning and implications for football tactics of Barça’s treble. At least as significant as the move away from tiki-taka is the adoption of a three-forward format, Barça’s so-called trident (with both moves obviously not being unrelated). In this post, I seek to highlight why, from an evolutionary perspective, the importance of FC Barcelona having managed to win everything with such a system can hardly be overestimated.

Source: financialexpress.com

In what is widely considered the most authoritative book on the history of football formations, in Inverting the Pyramid, Jonathan Wilson brilliantly describes the history of formations as a process in which the pyramid became inverted, i.e. a move from an all-out attacking 2-3-5 in the game's early days to a much more cautious sole-striker formation. In particular following FC Barcelona’s tiki-taka success under Guardiola and Spain’s victory at Euro 2012, some observers as well as coaches, notably Carlos Alberto Parreira, prophesied the winning formation of the future even to be the 4-6-0 – perhaps a final evolutionary step.

Did Luis Enrique, with his trident, then defy the laws of football tactics’ natural evolution? The answer is no. In an attempt to make sense of their environment, people naturally tend to look for patterns and cause-and-effect relationships, also where none exist. As football is a social undertaking, made by men’s thinking and acting, there is no “natural" evolution of which the future can easily be predicted or inferred from what came before. Most analysis is thus ex-post sense-making and assuming current tendencies will amplify in the future. Matthew Whitehouse’s recent book Universality: The Blueprint for Soccer’s New Era reads as a prime example hereof: enlightening in explaining the past; very unlikely to have any predictive power. Luis Enrique did not escape from any inevitable evolutionary path but, rather, realized that – as in any human endeavor – there was an active choice to be made.

For signs of just how powerful and self-fulfilling a formation’s success can be, we need not look far: with Cristiano Ronaldo, Bale and Benzema, Real Madrid have a trident of their own. Furthermore, the most promising formation for Atlético, notorious for their defensive pressing through a 4-4-2, in the upcoming season, seems to combine Jackson Martínez (center), Griezmann and Ferreira Carrasco (both wide) – and it probably won’t take Simeone long to figure out just that.

Source: laacib.net

So, apart from there not being any pre-defined, inescapable evolution in football formations, what is the take-away of Barça’s treble this time? Get three excellent forwards and success will take care of itself? Not quite.

1. There’s no one formation that beats the others (which is obviously not the same as saying that all formations are equally good or that formations don’t matter). A team’s best formation depends on the players you have at your disposal. In case you don’t have three – relative – star attackers, there’s as little point in playing with a “trident” as there is in not fielding all three when you have got them.
2. Provided you have the quality forwards, attacking in numbers can be very effective, especially when playing against a team with a non-adaptive system that does not account for facing numerous attackers. Belgium – Argentina, to which I dedicated the first post in this blog, being a case in point. As much as people like to analyze and philosophize about the beautiful game, you get three points only when you score more goals than the opponent, so scoring goals is a prerequisite to winning.

Whether the “trident” will take the rest of Europe by storm remains to be seen. What already seems certain is that Barça’s recent treble success on the back of its trident has silenced prophesies of there being no more room for strikers in the football of the future. We may now also better understand why it makes little sense to believe in some kind of determinism when it comes to the future of football tactics. In Whitehouse’s words,

Football’s future will be defined thanks to the visionaries and risk takers who seek to try new things and experiment with the game. This is how anything evolves, change through trial and error.

Copa América: An Unfair Tournament by Design?

Much of Latin America is currently in the grips of the Copa América, a very exciting tournament indeed. Yet I take great issue with two aspects relating to its format. As I will explain, the tournament’s particular format makes that some countries are awarded an unfair advantage relative to others, just because of the group they were drawn into and/or the timing of their games.

Source: quepasa.cl

The first issue is a straightforward one. In all major tournaments (e.g. FIFA World Cup) as well as national leagues, the final games in the group stage of any particular group or league are scheduled at the same time. The purpose is that no team has an undeserved advantage of knowing what its competitors did and thus of being able to know what result it would need – whereas the competitors who had to play before didn’t. 

A real-life instance that made the involved unfairness all too obvious in practice and which is part of our collective football memory occurred at the 1982 FIFA World Cup. Both West Germany and Austria were to proceed to the next round if, in their final group game, West Germany were to beat Austria 1-0. After ten minutes, the West Germans scored and both teams ran down the clock for the remaining eighty. The Disgrace of Gijón incited FIFA, in future world cups, to have the final games of each group scheduled at the same time. At the Copa América, anno 2015, CONMEBOL still seems content awarding half of the teams the potential advantage of knowing what result they will need from their final group game.

The first issue can very easily be fixed. This is quite different for the second, which is more structural and relates to the two (out of three) “best thirds” qualifying. Naturally, this implies that what happens in other groups also affects what happens in any given group. Again, the teams that will play later will have the advantage of superior information about the result they need: at the time of the final games of group A, the final games in groups B and C are still left to be played, implying uncertainty of outcome, whereas at the time of the final games in group C, the final ranking of groups B and C is already known.

So the teams in later groups know better what result they need to progress. But does this actually affect how likely they are to get it? For those who prefer numbers over reason, let’s have a look at the nine editions of the Copa América where the current “best-thirds” rule was used (i.e. since 1993) and see if there’s any differences. In case better information does not affect who progresses, we would expect, on average, to see three times the best third of each group not to have made it through. The actual results, however, show the following:

Each bar indicates for the respective groups how many (on Y-axis) out of nine times the
third of that group did not progress to the knock-out stage, due to being the "worst third"

In six out of nine editions, it was the third of group A which happened to be the worst third and thus the one not to progress. Interestingly, also, the one time the third of group C did not manage to qualify, in 2007, this was a mathematical certainty already ahead of the last matchday of group C.

So now that we are clear on what the problem is, how do we solve it? By making sure that the same number of teams from each group is to progress, so that what happens in one group does not affect how many are to progress in another (alternatively, the final games of all the groups could be scheduled at the same time, but this can be considered too much of a drawback for TV audiences). Let’s assume that Copa América wants to hold on to twelve countries playing the group stage and eight progressing, to the quarters. We could have four groups of three, with the two best of each group making it through. Downside here would be that the number of teams per group is uneven, so that in each group one team would be free on the last match day and thus continues to have more complete information. The solution would be to make two groups of six, with the best four of each group qualifying for the next stage. The first of group A would then play the fourth of group B and vice versa and the second of group A against the third of group B and vice versa. The teams that would make it to the final will have competed in eight games, one more than in the case of the World Cup. If this is considered too many, one could immediately move from the group stage to the semis instead, with only the top two qualifying, which would make even more sense. 

Is the problem of an undesirable format confined to the Copa América and CONMEBOL? Interestingly, UEFA has decided to import a similar system for the Euro Cup, starting from next year’s edition, when the number of teams participating will increase with a staggering 50%. In light of the above, it is curious that a federation that is becoming adamant about creating a level playing field through Financial Fair Play, more or less at the same time decides to start assigning arbitrary (dis)advantages to some of the teams competing in its main tournament, i.e. with now “best thirds” qualifying; with some group winners meeting teams that became second, others that ended up third; some teams that were second meeting group winners and others other seconds. Again, the solution may be simple: four groups of six teams, with either only the winner or the best two of each group progressing to the knock-out stage. That’s what I would call fair play.

Which Premier League Top Scorer Would You Like in Your Team?

As national leagues across Europe draw to a close, it is a favoured time to produce lists of top scorers. With the Premiership being the toughest and most advanced domestic league - as José Mourinho likes to remind his colleagues - the top scorers of this competition are of particular attention. Sergio Agüero inherits the golden boot from Luis Suárez, having scored 26 goals, 5 more than first contender and season revelation Harry Kane. Premiership debutants Diego Costa (20), Charlie Austin (18) and Alexis Sánchez (16) complete the top 5.

Source: dailymail.co.uk

But do these single scores tell us all we need to know? For instance, how do Agüero’s 26 goals for vice-champion Man. City compare to the 18 Charlie Austin managed to put in for bottom-of-the-table and relegated QPR? Impossible to say? Let’s give it our best shot! In this post, I will argue that if we are to choose the most useful top scorer based on a single number, the simple count measure, by which penalties count as much as field goals, calls for an adjustment. Furthermore, while people like to take single-number mental shortcuts, considering several informative “stats” in conjunction is likely to yield a much more accurate and nuanced view of top scorers’ relative performances and utility to their teams.

Why is an adjustment in light of penalties due? First and foremost, whereas scoring a field goal tends to involve a unique skill, in the case of a penalty, the reduction of a team’s conversion rate by having the second best kicker shoot the team’s penalties tends to be negligible. Having Yaya Touré as designated penalty shooter instead of Agüero is highly unlikely to make a real difference for Man. City, for instance. Second, while a field goal requires finishing as well as positioning/preparation, a penalty only involves the finishing aspect. Third, it is not uncommon for a team to "award" its best scorer and/or striker with the task of taking the spot kicks exactly to provide him with the chance to up his goal tally.

An accurate efficacy measure for scorers, so I argue, ought to take into account the above qualifying features of scoring penalties. At the same time, however, spot kicks tend to involve enhanced pressure as – in contrast to most field situations – the “norm” is for the player to score. To reflect the above particularity, then, I propose for a penalty to count half of a field goal. This year's top 5 rank would remain unchanged, though the differences become smaller – e.g. as Agüero scored 5 times from the spot kick, whereas Sánchez none.

While efficacy is key, efficiency, i.e. one’s output (i.e. goals) compared to input (i.e. time played) is also crucial. For instance, say one striker scores 20 goals over the 38 league games, playing all of them, and another striker totals 20 goals appearing in only 20 games. The latter is obviously preferable, i.e. more efficient, as he needed less playing time to score the same number of goals. This implies one could be fielding someone else in the 18 remaining games, who may again score goals. Efficiency measures come with a note of caution, though: the numbers involved have to be large enough so as not to be sensitive to small changes. In case of the Premiership top scorers, however, all scored more than 15 goals and were fielded over 2,000 minutes, implying the efficiency stat is meaningful.

The efficiency ranking, i.e. the adjusted goals (efficacy) divided by the number of minutes played over the season, multiplied by 90, leads to the following ranking of average number of penalty-adjusted goals scored per game:

Adjusted goals/90 mins represents the number of goals scored on average during 90 minutes
given the player's actual scoring rate when fielded (with converted penalties counting for half)

The efficiency numbers show important additional information: when playing, Diego Costa was the highest scorer of the lot – the difference with Agüero being less than meaningful. 

Source: dailystar.co.uk

But perhaps a lot of the credit should go to Chelsea and Man. City, respectively, for being the two highest scoring teams in the league? To see how these top scorers performed relative to their teammates, let’s indeed look at their relative efficacy, i.e. the number of adjusted goals they scored relative to the number of adjusted goals scored by their team overall. Charlie Austin then turns out to be the undisputed champion, scoring 41% of QPR’s adjusted goals, followed by Kane with 35% of Spurs’ and Agüero with 30% of the Citizens’.

Do efficacy and efficiency capture everything we’d like to know about our top scorers? The answer is "no" as scoring essentially is a means to the end goal of the team winning points. So we also want to know how many points these players’ goals actually won for their team, i.e. valuing the goals they scored by their importance. To measure importance, I propose a measure that is the average of two numbers: the first is the increment in the number of virtual points resulting from the goal. For instance, if you score the 1-0, your team’s virtual points from the game go from 1 to 3, so +2 as a direct result of the goal. The second number is the end-of-game increment in points resulting from a player’s goal(s). For instance, if you scored the 1-0 and the game finishes in 2-2, then, without your goal, your team would have had 0 points instead of 1, so the increment is 1. The overall importance of such a goal would thus be (2+1)/2 = 1.5. The maximum number of points a player can contribute in a single game is limited to 3 and penalties again count as half a field goal.

The beauty of this importance measure is twofold: First, it relates goals to points, which is what matters in the end, e.g. if you score 5 goals, it makes a big difference for your team whether you scored all in a 5-0 victory or, instead, put your team up 1-0 on five different occasions. Second, both being part of a successful (e.g. Chelsea) and a less successful (e.g. QPR) team has its advantages and disadvantages, allowing for a more levelled comparison of players’ individual contributions, irrespective of the quality of their team: as part of an unsuccessful team, it is harder to put in the goals, but when you do, it is more likely to be one that matters. The importance measure yields a clear “winner”:

Note that efficacy is expressed as number of goals;
importance as number of points won (both on Y-axis)

Harry Kane’s goals won Tottenham Hotspur a clean 24 points, no less than 7 more than did Aguëro’s goals for City. The goals of Diego Costa, our most efficient player, turn out not to have resulted in that many additional points for Chelsea: out of the 16 games he got himself on the score sheet, in 8 of those his goal(s) made a difference of less than a point. The average point contribution of Kane’s goals is 1.2, nearly double that of Diego Costa’s. After re-scaling the importance measure to account for time played - meaning allowing all top scorers as many minutes as the one who collected most, viz. Austin - Diego Costa jumps Austin and Sánchez, but Kane remains far ahead of both Diego Costa and Agüero: the PFA's Young Player of the Year's goals then yield 28.5 points; Agüero’s 20 and Diego Costa’s 18.

Will those who scored more/less important goals repeat this again next year? That, luckily, is impossible to predict. We'll have to tune in again to the Premier League next season!

Who would you choose for your team if you could only pick one? J