Weighted Goal Average

Most football (a.k.a soccer) leagues award the player who scored the most goals during a season the Golden Boot award: Erling Haarland in England’s Premier League, Harry Kane in Germany’s Bundesliga, Artem Dovbyk in Spain’s La Liga. It doesn’t matter whether the goal was scored in open play, from a free kick, or a penalty, they’re all equal.

Question: Should all goals be equally valued?

The Premier League’s Sheffield United allowed 104 goals and had only one clean sheet across 38 English Premier League matches: Brentford should be embarrassed in their 1-0 loss, as Sheffield was blown out many times (Sheffield 0-6 Arsenal and Sheffield 0-8 Newcastle among the worse, multiple five goal losses). Everyone scored against Sheffield, so much so that the playground taunt My grandmother could score against Sheffield! was never more true, especially if grandma played striker against Sheffield United.

[FYI: My grandmother does not play striker.]

Answer: No, all goals should not be equally valued.

On the other end of the spectrum from Sheffield, goals scored against top teams should be more valued more because top teams are – unsurprisingly – really, really good! During the 2023-24 season, Son (Tottenham) scored three against Arsenal, Hwang (Wolves) and Mateta (Crystal Palace) scored two against Man City. Those two clubs had the best Goals Against for the season, so scoring goals against them – especially multiple goals – should be commended.

So is there a better way of evaluating a season’s best scorer than just raw goal count?

Defining Weighted Goal Average

Weighted Goal Average (WGA) is an attempt to apply an objective value to each goal scored based on its quality. My quality metric is the opponent against which the goal was scored.

Multiplier

A multiplier is assigned to each club based on their final table standing, where the multiplier is the inverse of table position: in a 20-club league, the champion’s multiplier is 20, the runner-up is 19, and so on. For those mathematically-inclined:

multiplier = (# of clubs in league) - (club's final table placement)

Weighted Goals

The weighted goals (WG) total is determined by multiplying the goals scored by a player with the opponents multiplier, and adding the value across all opponents.

Cole Palmer (Chelsea) scored four goals against both Manchester United and Everton. While considered equally when determining the Golden Boot, the weight goals are 42 and 20 as Manchester United finished eight positions higher in the final table.

weighted-goals = 
   ((goals-scored against #1) * 20) +
   ((goals-scored against #2) * 19) +
   ((goals-scored against #3) * 18) +
   .
   .
   .
   ((goals-scored against #19) * 3) +
   ((goals-scored against #19) * 2) +
   ((goals-scored against #20) * 1)

As an example, Gordon (Newcastle) scored 11 goals against 10 different opponents. His weighted goals would be calculated as:

• 1 v Manchester City = 20 wg
• 1 v Arsenal = 19 wg
• 1 v Liverpool = 18 wg
• 1 v Tottenham = 16 wg
• 1 v Chelsea = 15 vg
• 2 v Manchester United = 26 wg
• 1 v Crystal Palace = 11 wg
• 1 v Bournemouth = 9 wg
• 1 v Wolves = 7 wg
• 1 v Sheffield United = 1 wg

for a total of 142 weight goals.

Weighted Goal Average

The weight goal average (WGA) is calculated by dividing the weighted goals by the number of goals.

weighted-goal-average = weighted-goals / goals-scored

In our example, Gordon’s WGA is 12.91, the highest of any of the top 30 goal scorers in the Premier League in 2023-24.

In Real Life

I calculated the Weighted Goals Average for each of the top-thirty Premier League scores in 2023-24, each of whom scored at least ten goals.

The weight goals ranged from 73 WG (Fernades) to 237 WG (Haarland). Only four players had totals over 200: Haarland (27 goals), Isak (21 goals, 211 WG), Foden (19 goals, 201 WG), and Mateta (16 goals, 200 WG). As these four were among the top goal scorers for the season, their WG is not surprising.

The weighted goals average is where things get interesting. Gordon (12.90 WGA) and Mateta (12.5 WGA) have the highest WGA by almost a complete point, with Son (17 goals, 11.6471 WGA), Hwang (12 goals/11.3333 WGA) and Adebayo (10 goals/11.0 WGA) in the neighborhood.

Eight of Gordon’s eleven goals came against the top half of the table, one each against the top three, giving him a major boost.

And Haarland? Despite winning the Golden Boot, his 8.778 WGA was only 20th best among the top-thirty goal scorers, aligning with the narrative that he isn’t the same threat when the bright lights shine. Alvarez, whom I thought may be called to the main striker if Haarland decides to leave, had a 6.8182 WAG, worst of all players analyzed. Ouch.

Conclusions

I always believed that statistics alone don’t necessarily tell the more nuanced story when context is provided, and baseball, in particular, has shown the way with the advanced analytics/metrics that have become more accepted in the last fifteen to twenty years. Football has its advanced analytics/metrics – which I’m not very knowledgable of – and think this post shows a possible way to think differently about goal scorers.

That said, I believe the multiplier could be enhanced to bring other variables into the equation: home v. away goals; match outcome, win v. draw v. loss; goals scored in-play v. free kicks v. penalties; games played; days rest between matches; points separation v. placement in table. There are definitely different ways to slice/dice the data.

My main focus was to start the discussion about actual value of goals, and I believe I have a good starting point. Gordon’s high WGA was a surprise until I looked against whom he scored, and then it became apparent: while he didn’t score the most goals, he did score well against the top teams. And with that, I believe, shows potential in furthering this discussion.

Supporting Data

Feel free to download the spreadsheet to play around or find my errors.

Image Credits

• “Soccer” by ViNull is licensed under CC BY 2.0.
• “Erling Haaland 2023 (cropped)” by Jacek Stanislawek is licensed under CC BY-SA 4.0.