Is it a given that the top goalscorer is also the best goalscorer?

They are big questions: who is the ‘Top’ and who is the ‘Best’ Goalscorer. Big questions that matter and it is therefore vital we fully understand and challenge the metrics employed when awarding such an accolade.

Who were the Premier League’s Top Goalscorers in 2018-19 season?

• Mohammed Salah
• Sadio Mané
• Pierre-Emerick Aubameyang

Who was the Premier League’s Best Goalscorer in 2018-19 season?

• Sergio Agüero. He was by far the best Premier League striker last year. Agüero scored at a much superior rate than any of the Top Scorers (Mohammed Salah, Sadio Mané and Pierre-Emerick Aubameyang), including scoring a far greater number of goals against the Big Six.

How much is a goal worth?

• Is a goal worth more when it is a match-winning goal?
• Is a match-winning goal worth more when it is scored late on in the game?
• Is a late match-winning goal worth more when it is scored against top-of-the-table?

Are goals worth the same? You may answer Yes or No depending on your view point.

Let’s look at an example: Player A scores to make it 5-0 against bottom-of-the-table. Player B scores a match-winning goal in the 88^th minute to beat top-of-the-table. Over the course of the season both Player A and Player B score 18 goals. All Player A’s goals are scored against bottom-half clubs with none of his/her goals affecting the points won/gained. All Player B’s goals are scored against the top half of the clubs and many of his/her goals are match-defining goals, i.e., rescuing a point or winning all three points for their team. Now assuming that everything else is equal, e.g., number of chances, minutes played etc., then who is the better striker?

If your answer is Player B, then you agree that goals can be ‘worth’ more than others. Whilst the above example is fairly extreme, it does highlight further dimensions to the goal metric. This article will explain how weighting could be introduced in order to better compare players using sporting metrics.

How is the weighting calculated?

1. Opposition Strength

There are two ways opposition weighting could have been carried out: final table position OR goals against/conceded. The latter was chosen for two reasons. First, as the table illustrates below, a team’s final position does not correlate perfectly with team’s defensive record (goals against). For example, Manchester United finished 6^th but conceded the 10^th most goals. Second, it allows for relative weighting. In other words, it notes that the difference between Liverpool (best defence) and Manchester City (2^nd best defence) is not the same as the difference between Manchester City (2^nd best defence) and Chelsea (3^rd best defence).

Opposition weighting is calculated for a team by dividing the bottom (Fulham) team’s goals against by the goals against for that team. For example, to calculate the weighting for Manchester United, the calculation is 81/54 = 1.5. The illustration below shows Fulham’s 81 goals against can be split into 3 boxes of 27 goals. Manchester United’s 54 goals against can be split into 2 boxes of 27 goals. We can then compare the boxes of Fulham to Manchester United as 3 boxes to 2 boxes, which can be written as a ratio of 3/2 and has a value of 1.5.

Now, you may have noticed from the table above that Cardiff City conceded 69 goals last season whereas Manchester City conceded only 23 goals, meaning Manchester City conceded 3 times less than Cardiff City. From the illustration below, it shows Cardiff City’s 69 goals against can be split into 3 boxes of 23 goals. Again we can compare the boxes of Cardiff City to Manchester City as 3 boxes to 1 box, which can be written as a ratio of 3/1 and has a value of 3.

2. Importance (Points Gained)

A match-winning goal is ‘worth’ more than a goal that just increases the winning margin or simply a consolation goal. Now, these weightings are arbitrary and thus open to scrutiny. However, it must be pointed out that opposition weighting accounted for a significant majority (over 90%) of the weighting for all of the players. In other words, the other two weightings for importance (points gained and timing) contributed less than 10% to the overall weighting.

A-not-so familiar metric is sometimes used to demonstrate the importance of a goal scored by reporting the total number of points that a player’s goals has earned their team. In other words, if a player scores a match-winning goal, the metric credits them with 3 points. However, it must be pointed out that several permutations could lead to a player be credited with 3 points. For example, a player scoring to put their team 4-0 up and the game ends 4-3. On the other hand, a player could score in the same minute as before to put their team 4-0 up but the match ends 4-0 and the player is not rewarded with 3 points, yet at the time of the goal, everything else was equal (including opposition).

Below is the table of weightings for importance goals scored.

3. Importance – Timing of Goal

A match-winning goal scored in the 86^th minute should be ‘worth’ more than a match-winning goal in the 12^th minute. Not much, but a little. Again, this weighting is arbitrary and open for debate. To note, the timing of goal weightings are very small. It must be noted that to gain this weighting the goal itself must be important in the context of the game (there are some exceptions – see example below). In other words, if a player scores in the 89^th minute to make it 5-0, they will not be awarded the timing of goal as it is deemed unimportant on the matches outcome.

Examples of the weighting system

Example 1: No importance weighting added

Aubameyang doubled the lead in the 59^th minute. The goal he scored was worth 1.76 (1.76 x 1 x 1). Everton had the 6^th best defence record.

Example 2: Points gained weighting added

Agüero scored the only goal of the game in the 63^rd minute. His goal ended up as a match-winning goal. The goal was worth 1.79 (1.19 x 1.5 x 1).

Example 3: Timing but no points gained weighting (exception)

Salah scored in the 80^th minute to make it 2-1 and had the game finished 2-1 he would have earned 1.5 weighting for points gained. However, his teammate scored in 86^th minute to make it 3-1 and the game ended 3-1. So, whilst Salah did not receive any weighting for points gained, my view is that he should keep his timing weighting as he did score an important goal late on in the game. It just happened to not be the deciding goal. The goal was worth 1.50 (1.25 x 1 x 1.2).

Overview of Goals and Weighting

Summary Table

The table below gives an overview of a number of metrics to help better inform us of the best striker. All calculations are done with exact numbers and the answers are rounded.

The full season goals metric shows how many goals the player would have scored if they had played every minute of the season scoring at the rate they did. It helps quantify the difference between 0.73 goals per 90 and 0.77 goals per 90 in terms of goals scored. As shown in the table above, this difference in goals per 90 is equivalent to 1.78 more goals when each player plays every minute of every game. In other words, if both played every minute of the season, Agüero would be expected to score 1.78 more goals than Aubameyang (due to having a better scoring rate).

The weighted goals metric shows that despite scoring one less goal than the Golden Boot winners, Aguero’s 21 goals were ‘worth’ 34.41 goals which was an increase of 63.85%. This indicates that Agüero’s 21 goals, on average, were scored against tougher opposition. As stated earlier, the opposition weighting accounted for the majority of the total weighted goals metric: 92.90% (Salah), 93.40% (Mane), 91.71% (Aubameyang) and 93.82% (Agüero). The full season weighted goals metric shows how much the goals are ‘worth’ if they had played every minute of the season. Agüero’s lead is extended as he played the fewest minutes.

Despite Harry Kane scoring 17 goals last season in 2427 minutes, the table below shows that his metrics were not on the same level as Agüero’s.

There are, of course, other dimensions that could have been weighted: penalties, home and away goals, derby matches etc.

Returning to the question: Who was the Premier League’s Best Goalscorer in 2018-19 season?

In order to use metrics to help compare strikers in a particular league, weighted goals metric should be used. The metric is more accurately measuring a striker’s performance by:

1. Weighting chances relatively to value the difficulty of scoring against a better defence [better measurement].
2. Valuing important goals scored late on in the game [better measurement].

Even better if a player’s number of minutes are factored into the final metric. This allows for a fairer comparison between player’s performances. The full season weighted goals metric allows this whilst also accounting for the weightings of the goals.

The Stat Squabbler concludes:

1. That goals should be weighted on two criteria: opposition strength and importance, which is further broken down to points gained and timing.
2. Arbitrary weighting can, and will, always divide opinion as who decides what to weight and how much to weight it.

Do you agree with The Stat Squabbler? Was Agüero the best striker in the Premier League last season (2018/19)? Comment below.