Can we measure the value of a goal?

Publish date: 2024-06-08

All goals are worth the same — one. Or are they?

Imagine the scenario. You have Player A, who scores 20 goals in a season, with each one embellishing their team’s two, three, or four-nil victory.

Then there’s Player B, who also gets 20 that season. However, each of their goals helps to change the course of the game concerned for their team, equalising in the second half of a draw, say, or even getting a last-minute winner.

Both players have scored the same number of goals, but have those goals contributed the same value? No.

So could we find a way to quantify how much a player contributes to their team’s outcome when they score a goal — especially in those crucial moments of a match?

Several American sports have already found ways to explore this. In basketball, the NBA has a stat called Crunch-Time Offensive Rating, which focuses on the final five minutes of games that are decided by five points or fewer.

In American football, the NFL has Fourth-Quarter Passer Rating, for the time when the game is on the line, and Red Zone Passer Rating, for when the ball is closest to the end zone.

Association football/soccer has no such metric yet.

American sports have also provided the concept of the well-established “clutch” player — those who will step up and hit the winning shot in the dying moments of a game.

The phenomenon is as interesting as it is difficult to quantify. The debate rumbles on over what it is, or whether it even exists.

In 2019, The Athletic’s Seth Parnow explored ‘hero-shots’ in the NBA, noting that scoring percentages went down significantly in crunch time (Parnow uses the term for games with a scoreline margin of three or fewer points at some time in the last two minutes). He put this down to more predictability in the game situation — if you are losing by three points, the defending team can cover the obvious need to score a three-point shot more easily.

For him, the concept of clutch is close to a “coin flip”. But as much as “clutchness” is made up of tangible, on-field outcomes, it is also a product of mentality.

Peter Keating, writing for ESPN eight years ago, argued that “clutch is, in part, the absence of anxiety”. It is not that great players elevate their play to an unsustainable level when the lights are at their brightest. It is that they are not blinded by that brightness, and can still execute their core skills.

Who might such players be in football?

In the modern game, the obvious candidates of Cristiano Ronaldo and Lionel Messi will be up there, or even Liverpool cult hero Divock Origi. Historically, the likes of super-sub Ole Gunnar Solskjaer or more recently Javier Hernandez will be fondly remembered by Manchester United fans for their contributions in the latter minutes when the game was on the line.

(Photo: Matthew Ashton – PA Images via Getty Images)

But when compared with higher-scoring sports such as basketball, American football and baseball, quantifying these “clutch” moments is far more difficult.

One method considered by The Athletic was to look at which players outperform their xG in the final 10 minutes of a match when attempting to score a game state-changing goal. However, this method came with its issues, not least that it provided a sample size that would be simply too small in the aggregate.

Happily, there were other avenues available.

First, we can simply look at the players in the last five seasons with the highest share of “game state-changing” goals out of their total tally scored — irrespective of the outcome of the game. For example, those who scored an equaliser when their team were losing, or put them ahead when drawing.

While the raw number of “game state-changing” goals is understandably reserved for the likes of Harry Kane, Mohamed Salah and Jamie Vardy — as players who simply score a lot of goals, regardless of game state — the players with the highest proportion of such goals is interesting.

When filtering for a healthy sample of players who have scored 30-plus Premier League goals overall since 2016-17 and through the previous round of fixtures, the list is led by Richarlison, now of Everton, with 82 per cent of his total tally having changed the course of the game since signing for Watford in the summer of 2017.

You need to look no further than the 1-1 draw with Leicester City at Goodison Park on Wednesday as an example of the Brazilian’s influence, as he popped up with a 92nd-minute equaliser to earn Everton an important point in their fight to avoid relegation.

Second, third and fourth are Wolves favourite Raul Jimenez, Christian Benteke of Crystal Palace and Chris Wood, now at Newcastle United after his January move from Burnley — all central strikers whose remit is very much to be in the right place at the right time.

This data is interesting in itself, but it doesn’t account for some key factors.

For example, how can we distinguish Richarlison’s opening goal against Liverpool after two minutes of a 2-0 victory at Anfield last season from his equaliser against Arsenal in December with 10 minutes to go in a match Everton pushed on to win 2-1?

Did the goal change the state of the game in the first minute or last minute? And surely, a goal to put your team ahead should have more value than an equaliser?

Put simply, we want to measure how many points a player’s goal earns — or was set to earn — at the time they scored it.

Intent is key here, as a player might score to put their team 2-1 ahead in the 89th minute, only for them to then concede two in stoppage time and lose. The actions of a player should not be penalised because of the outcome of the game.

Therefore, inspired by the work of others, we can create a simple formula that allows us to adjust the value of a goal depending on the context within which it has been scored. This is based on these two key factors:

The percentage of time elapsed within the game
The type of game state-changing goal scored — equalising or putting their team ahead.

To answer this question, let’s go back to the 2010-11 season and take a closer look at the highest contributors.

Put simply, if you score the winner in the last minute of a game every week, your goal value will be closer to two — indicated as the additional number of points you have earned your team from a one-point draw to a three-point win.

An equaliser just after half-time will give you a value closer to 0.5, as there is still plenty of time for the scoreline to change within the game.

If you score the final goal of a 4-0, however, that value is getting a zero. Consider the applause of a buoyant crowd reward enough.

On to the results.

First, we can look at the highest total value of goals accrued by Premier League players across the decade since. Understandably, it is skewed towards players who have simply scored more goals, or at least been in the division long enough to rack up a healthy total.

Nevertheless, there are some interesting wrinkles in the top 20. (As stated above, the figures included below do not cover Saturday’s matches.)

Simply looking at the raw number of goals would suggest that Sergio Aguero should be top of the pile — scoring 184 times since 2010-11. However, the value of those goals is attenuated by the context within which he scored them.

Aguero’s goal contribution was essentially enough to earn Manchester City 55.7 points at the time he scored them — good enough for third on our list.

Kane has scored six times fewer than Aguero in this period, but his goals earned a higher 69.5 points for Tottenham at the time he scored them.

Why might this difference be? Put simply, the wider sample suggests that Kane’s goals are weighted to be more decisive ones that change the course of a match, and in the later moments of them, over our sample period.

Let us not forget, that “Agueroooooooo!” goal in May 2012 will go down as one of the best moments in the Premier League era — and was arguably the highest value goal in City’s history. However, based on our formula you can see that the Argentinian’s overall goal contribution is a little dampened by a healthy number of goals early on in games or finishes that simply added gloss to a convincing scoreline.

Aguero’s team-mate Raheem Sterling suffers a similar fate.

His 106 goals, mostly scored for a dominant City team after his move from Liverpool, have only been responsible for 28.6 points.

Contrast that to fellow winger Sadio Mane, effectively Sterling’s replacement at Anfield, whose 109 goals for Liverpool and previous club Southampton are responsible for 47.3 points — meaning he has contributed nearly double the value to his team’s outcome despite a near-identical goal tally.

Given the skew towards high-scoring players in the graphic above, it is worth looking at those who contribute the highest average value with the goals they have scored over our sample period.

This means that players who might not play for dominant teams — but perhaps have ice flowing through their veins — are still recognised despite their lower goal outputs.

The results are equally interesting.

Recently retired Jermain Defoe tops the list, with his goals for Tottenham, Sunderland and Bournemouth holding the most weight in their importance towards his team’s scoreline — contributing 0.6 points per goal scored. Defoe also has the latest average goal time (62 minutes) of any player to score 50-plus goals in this period, with 26 of his 65 goals putting his team ahead in the game.

For those interested, the player in the same group with the earliest average goal time? Kevin De Bruyne of Manchester City on 41 minutes.

Other names within the top 20 include the archetypal super-sub role, with the likes of Hernandez, Olivier Giroud and Andy Carroll all fulfilling their remit of delivering goals later on in the game — with all three players’ average goal time coming in the second half.

Other players who make up the top 20 list are those whose goalscoring importance is swollen for their respective teams. For example, Wilfried Zaha, Wood (in his time at Burnley), and Vardy have very much been the focal points of their side, tasked with most often being the one to grab the goal in the important moments.

Finally, a high frequency of attacking midfielders feature, with Juan Mata and Christian Eriksen right at the top of the list, and Dele Alli featuring lower down.

This is an interesting wrinkle, especially with Mata and Eriksen typically thought of as players who provide the pass for a crucial late goal, rather than being the finisher.

Their position might indicate their role on the pitch mimics that of the clutch point guard in the NBA — an elite decision-maker who can either pick a pass to a well-positioned team-mate or step back and drain the shot themselves.

Now, we know what you’re thinking.

It is useful to consider the contribution of each goal at the time it was scored, to ensure that a player’s goal value is not skewed by the overall outcome of the game. But, the ultimate value of those goals might be futile if their team went on to lose.

So wouldn’t it also be fun to see who has actually earned their team the most points with decisive goals that influence the final scoreline?

Using the same methodology as above, we can dig further into goals that decided the final outcome, similarly weighted more strongly to goals that put a player’s team in the lead rather than equalise, plus those that are scored later on in the game.

For example, Bruno Fernandes’ penalty scored in the 100th minute after a VAR check against Brighton in 2020-21 comes out as having the maximum goal value in the list — adding a decisive two points to Manchester United’s outcome that September day.

Looking back over the decade-plus we’re concerned with, Kane retains his place at the top of the pile as the player whose goals have added the most value to his team’s point haul — 26.8 in total when adjusted for the time within which the goal was scored.

It is also interesting to see Benteke remain so high on the list, having scored decisive goals for Aston Villa, Liverpool, and now Palace.

Meanwhile, Robin van Persie’s influence cannot be understated, as the Dutchman almost single-handedly dragged Manchester United to the title in his first season at Old Trafford, 2012-13, scoring late winners against Manchester City and Southampton along the way.

Similarly, we can look at the average points that a player’s goals have been worth in the same period.

Here, we see Kane’s former Spurs team-mate Eriksen topping the bill, with 10 of his 51 goals for the north Londoners being winners. In his time in the Premier League, Eriksen’s goals have earned his side 0.35 points on average, which is the most decisive of any player on the list — just in case current employers Brentford needed any further evidence to try to keep the 30-year-old around for next season.

Meanwhile, a reminder of the value of super-subs like Hernandez, Carroll and Danny Welbeck cannot be understated, and the numbers in the graphic above simply serve to back that up.

Overall, this whole exercise is largely using some napkin maths, but the value of scoring those important goals speaks to an interesting, wider point on an elite player’s ability to perform during high mental pressure.

As researchers from KU Leuven University in Belgium and SciSports have shown recently, the role of the psychological component of the game is undervalued.

Quantifying the performance of players during moments of higher mental pressure can be useful in helping clubs with their recruitment, training methods and decision-making within a game — for example, choosing who might be the most appropriate player to bring on as a substitute during a certain game-state or moment within the match.

It is well established that physical and mental fatigue influences cognitive performance in any condition — elite sport is no different. Knowing which players are most likely to execute key actions in those decisive moments can be crucial.

Adjusting a player’s goal tally for the overall contribution they make to their team’s outcomes is worthy of consideration — at the very least, it helps to separate the flat-track bullies from the decisive scorers.

(Photo: Catherine Ivill/Getty Images)

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Can we measure the value of a goal?