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