What is wrong with using Goals minus Expected Goals (G-xG) to measure finishing ability?

Goals minus Expected Goals (G-xG) has two fundamental flaws: it ignores sample size and gives a false sense of precision. A player with one lucky goal can appear as good as someone who consistently overperforms over hundreds of shots. It also provides a single number without showing how confident we should be in that assessment, making it impossible to distinguish between repeatable skill and random luck.

How does a Bayesian hierarchical model improve finishing analysis?

A Bayesian hierarchical model improves finishing analysis in two key ways: 1) 'Borrowing strength' and shrinkage - it analyzes all players simultaneously and shrinks estimates toward the league average for players with little data, preventing outliers from topping leaderboards by luck alone. 2) Quantifying uncertainty - instead of a single number, it provides a full range of plausible skill levels (credible intervals) showing how confident we can be in each assessment.

Who are the top finishers according to the Bayesian model?

According to the Bayesian analysis of hundreds of thousands of non-penalty shots from Europe's top leagues, Son Heung-Min ranks as the top finisher with a mean skill of 0.354, followed by Lionel Messi (0.292), Antoine Griezmann (0.305), James Rodríguez (0.324), and Harry Kane (0.247). The model is 100% certain that both Son Heung-Min and Messi are above-average finishers.

What do the HDI percentages mean in the rankings?

HDI (Highest Density Interval) percentages represent the confidence range for a player's true finishing skill. The HDI 3% and HDI 97% values mean we can be 94% certain that the player's actual finishing ability lies between these two values. If the entire range is positive (above zero), we can be highly confident that their performance is due to genuine skill rather than luck.

How much impact does elite finishing skill actually have on goal scoring?

Elite finishing skill has significant real-world impact. For example, Lionel Messi's skill level (+0.292) increases a standard 10% chance shot to nearly 13% - a 30% relative increase in scoring probability. Over 100 such shots, an average player would score 10 goals while Messi would score 13, creating 3 extra goals from identical chances.

How can football clubs use this Bayesian finishing analysis?

Clubs can use Bayesian finishing analysis for several strategic purposes: 1) Recruitment - identify undervalued strikers who consistently outperform xG while avoiding players on unsustainable hot streaks, 2) Risk assessment - players with wide credible intervals are riskier investments than those with tight intervals, 3) Contract negotiations - provide objective evidence of true finishing ability separate from temporary form, 4) Squad planning - avoid building attacks around players whose apparent skill is actually statistical noise.

What data and methodology was used in this analysis?

The analysis used non-penalty shots from the Premier League, Ligue 1, Serie A, Bundesliga 1, and La Liga for seasons 2014/2015 to 2025/2026. Rankings were produced using a multilevel Bayesian logistic regression with crossed random effects for player and competition to isolate finishing skill from league differences. The model used weakly informative priors and NUTS MCMC sampling with multiple chains, with convergence confirmed by r_hat statistics below 1.01.

Why is Son Heung-Min ranked as the top finisher?

Son Heung-Min ranks as the top finisher because the Bayesian model identified him as having the highest mean finishing skill (0.354) with strong statistical confidence. The model is 100% certain he is an above-average finisher, and his credible interval (0.192 to 0.543) shows consistently elite performance. This aligns with his reputation for clinical finishing and consistent overperformance of expected goals throughout his career.

What are the advantages of using Bayesian methods in soccer analytics?

Bayesian methods offer several key advantages in soccer analytics: 1) Uncertainty quantification - they provide confidence intervals rather than false precision, 2) Small sample handling - they naturally account for limited data by shrinking estimates toward reasonable priors, 3) Hierarchical modeling - they can simultaneously analyze players, teams, and leagues while accounting for their relationships, 4) Prior knowledge incorporation - they can include domain expertise and historical data, 5) Probabilistic reasoning - they answer questions like 'how likely is this player to be above average?' rather than just providing point estimates.

Why don't more soccer analysts use Bayesian statistics?

Most soccer analysts don't use Bayesian statistics due to several barriers: 1) Technical complexity - Bayesian methods require more advanced statistical knowledge and computational skills than traditional approaches, 2) Computational requirements - they often need specialized software and longer processing times, 3) Education gap - most analysts are trained in frequentist statistics rather than Bayesian approaches, 4) Industry inertia - established metrics like Goals-xG are widely understood and accepted, 5) Communication challenges - probabilistic results can be harder to explain to non-technical stakeholders than simple point estimates.

How do Bayesian models handle small sample sizes in soccer data?

Bayesian models excel at handling small sample sizes through 'shrinkage' and 'borrowing strength.' When a player has limited data, the model pulls their estimate toward the population average rather than trusting noisy individual statistics. This prevents a player with 2 goals from 2 shots being labeled a perfect finisher. The model also 'borrows strength' from similar players and situations, using the collective data to inform individual estimates. The resulting uncertainty intervals clearly show when we have insufficient data to make confident claims.

What makes Bayesian player evaluation better than traditional soccer statistics?

Bayesian player evaluation surpasses traditional soccer statistics by addressing their core limitations: 1) It separates signal from noise by accounting for sample size and random variation, 2) It provides uncertainty measures showing how confident we should be in each assessment, 3) It naturally handles the hierarchical nature of soccer (players within teams within leagues), 4) It can incorporate multiple factors simultaneously while isolating individual skill, 5) It makes probabilistic statements that directly answer recruitment questions like 'what's the chance this player is actually elite?' Traditional statistics often mistake luck for skill or provide false precision.

Introduction

In football analytics, we often turn to a simple metric: Goals minus Expected Goals (G-xG) to assess a player's finishing ability. It’s a decent first look, often used to argue that a player is "running hot" or getting lucky.

However, it has a fundamental flaw: it struggles to separate temporary overperformance from genuine, repeatable ability.

Imagine two players:

Player A scores 4 goals from 2.0 xG. His G-xG is +2.0.
Player B scores 20 goals from 18.0 xG. His G-xG is also +2.0.

Are they equally good finishers?

Our intuition says no. Player A might just be on a lucky hot streak over a handful of shots, while Player B has a more proven track record. The core problem is that simple metrics, such as G-xG, can't distinguish between repeatable skill and random luck. To do that, we need a better approach.

The Trouble with a Single Number

The issue with a simple metric like Goals - xG is that it hides the two most important factors in any analysis: context and confidence.

It Ignores Sample Size: A player who scores one goal from a 0.1 xG chance (+0.9 G-xG) looks like a world-class finisher. But with only one shot, we have almost no information. Simple metrics treat this the same as a player who consistently overperforms over hundreds of shots.
It Gives a False Sense of Precision: By providing a single number, G-xG suggests a definitive value for a player's skill. But in reality, there's a range of plausible skill levels for every player. A striker's +5.0 G-xG might be a true reflection of their talent, or it might be the high end of a lucky season where their "true" skill is closer to +2.0. We have no way to know how certain we are.

To truly measure finishing, we need a model that can think more like a human scout: it should be skeptical of small samples and express its confidence in its own conclusions.

A Better Approach: Thinking in Probabilities

Instead of relying on simple subtraction, we can get a much truer picture of finishing skill using a Bayesian hierarchical model. While that sounds complex, the idea behind it is intuitive.

The model assumes that most players are average finishers and requires significant evidence to believe a player is truly exceptional. It achieves this in two ways:

"Borrowing Strength" and Shrinkage: The model analyzes all players simultaneously and learns the skill distribution of the entire league. For players with little data, their skill estimate is "shrunk" towards this league average. A player with 2 goals from 3 shots won't be crowned a superstar as the model remains skeptical and keeps their estimate stable. This prevents outliers from topping the leaderboards by luck alone.
Quantifying Uncertainty: This is the biggest advantage. Instead of a single number, the model produces a full range of plausible skill levels for each player, known as a credible interval. We can finally move from "Player X is a +2.0 finisher" to "We are 95% certain that Player X is between a +1.5 and +2.5 finisher." This allows us to see not just what the model thinks a player's skill is, but how confident it is in that assessment.

To achieve this, the model intelligently isolates a player's individual talent. For every shot, it accounts for three key factors: the quality of the chance (the xG), the baseline difficulty of the competition (it's harder to score in the Premier League than in some other leagues), and finally, the unique skill of the player taking the shot. This final value - the player's individual contribution after all other factors are considered - is what we define as true finishing skill. We'll call this metric Finishing Skill Above Average (FSAA).

The Results: Ranking Europe's Elite Finishers

After running the model on hundreds of thousands of non-penalty shots from Europe’s top leagues, we get a stable, uncertainty-aware ranking of finishing skill.

The table below shows the top 10, a list dominated by players renowned for their clinical ability in front of goal.

Player	FSAA	HDI 3%	HDI 97%	Prob > Average
Son Heung-Min	0.354	0.192	0.543	1.00000
Lionel Messi	0.292	0.151	0.425	1.00000
Antoine Griezmann	0.305	0.138	0.471	0.99950
James Rodríguez	0.324	0.108	0.555	0.99600
Harry Kane	0.247	0.101	0.381	0.99875
Kylian Mbappe-Lottin	0.246	0.097	0.392	0.99925
Kevin De Bruyne	0.256	0.076	0.456	0.99250
Iago Aspas	0.245	0.069	0.413	0.99725
Manolo Gabbiadini	0.266	0.061	0.476	0.98975
Dries Mertens	0.232	0.051	0.424	0.98800

Understanding the Rankings: What Do the Numbers Mean?

The table provides a rich picture of each player's finishing ability, far beyond a simple rank. Here’s a quick guide to interpreting the columns:

FSAA: This is the model's best estimate of a player's finishing skill. A positive number means they are an above-average finisher, while a negative number indicates a below-average one. The higher the value, the more goals a player adds compared to an average player taking the same shots.

HDI 3% / HDI 97%: This is our "confidence" range. We can be 94% certain that the player's true finishing skill lies between these two values. If the entire range is positive (above zero), as it is for all the players in the top 10, we can be highly confident that their performance is due to genuine skill, not just a lucky streak.

Prob > Average: This is the most direct measure of confidence. It tells us the probability that a player is a better-than-average finisher. For the truly elite, this number is very close to 100%. For example, the model is 100% certain that both Son Heung-Min and Lionel Messi are above-average finishers.

Sense Check: The Elite (Lionel Messi)

The model ranks Son Heung-Min and Lionel Messi as the top two finishers, a result that makes perfect sense. Both are famous for consistently outperforming their expected goals. For Messi, the model is 100% certain he is an above-average finisher, which I don't think many people would disagree with.

Sense Check: The Not-so Elite (Jesús Navas)

To show the model works at both ends of the spectrum, consider Jesús Navas. Famous for his hard work but not his finishing, the model ranks him in the bottom 10 of the 7,500+ players analysed by the model. It is 88% certain he is a below-average finisher, confirming that the model's rankings align with reality. Here's the rest of the bottom 10 finishers.

Player	FSAA	HDI 3%	HDI 97%	Prob > Average
Rodrigo Palacio	-0.178	-0.405	0.045	0.06750
Jesús Navas	-0.158	-0.406	0.105	0.12225
Dominic Calvert-Lewin	-0.199	-0.409	0.006	0.03575
Giampaolo Pazzini	-0.159	-0.412	0.101	0.12350
Florian Sotoca	-0.189	-0.413	0.046	0.06050
Keane Lewis-Potter	-0.138	-0.413	0.121	0.17050
Emmanuel Rivière	-0.152	-0.414	0.093	0.13200
Hans Hateboer	-0.160	-0.416	0.092	0.11475
Alexander Djiku	-0.152	-0.419	0.100	0.13075
Mijat Gacinovic	-0.167	-0.426	0.088	0.10725

Putting It Into Practice

So, what does a FSAA of +0.292 for Lionel Messi actually mean?

It's an estimate of Messi's finishing skill compared to an "average" finisher on a log-odds scale, but we can translate it into real-world impact. For a standard shot with a 10% chance of being a goal (0.10 xG), Messi's skill increases that probability to nearly 13%.

While an absolute increase of 3% may not sound like a lot, it's a nearly 30% relative increase in the likelihood of scoring from a given shot compared with an "average" player.

Over the course of 100 of these shots, an average player would score 10 goals. Messi would be expected to score 13. His elite finishing ability creates 3 extra goals from the exact same set of chances.

Practical Applications for Clubs

This finishing skill model offers several advantages for professional clubs over traditional metrics.

In recruitment, scouts can identify undervalued strikers who consistently outperform their Expected Goals but haven't yet caught the market's attention, while avoiding overpaying for players on unsustainable hot streaks.

The uncertainty intervals help clubs assess risk - a striker with a wide credible interval might represent a bigger gamble, while one with tighter intervals represents a safer investment.

The model also supports contract negotiations by providing objective evidence of a player's true finishing ability, separate from temporary form or lucky seasons.

Perhaps most valuably, the approach helps clubs avoid the costly mistake of building their attack around a player whose apparent finishing prowess is actually just statistical noise. Looking at you Dominic Calvert-Lewin.

Methodology Details

Data for the analyses were collected for non-penalty shots for the Premier League, Ligue 1, Serie A, Budesliga 1, La Liga for seasons 2014/2015 to 2025/2026.

The rankings were produced by a multilevel Bayesian logistic regression. The model included crossed random effects for player and competition to isolate finishing skill from league-wide differences. Priors were chosen to be weakly informative, and inference was performed using a NUTS MCMC sampler with multiple chains. Convergence was confirmed by ensuring the r_hat statistic for all parameters was below 1.01.

Conclusion

For years, Goals - xG has been the default metric for finishing skill, but it's a noisy measure that can be misleading.

As any clichéd football pundit will tell you, "form is temporary, class is permanent" - but most finishing metrics struggle to separate the two. By using Bayesian approaches, we can build models that properly account for sample size and quantify uncertainty, giving us a much truer and more stable picture of player ability.

This model provides more than just a ranking; it offers objective evidence of a player's true finishing ability backed by statistical confidence. We can now quantify exactly how much better one finisher is than another - Messi's +0.292 skill creates 3 extra goals per 100 shots compared to an average player, while Son's +0.354 creates nearly 4. The credible intervals tell us precisely how confident we should be in these assessments.

The results speak for themselves, identifying a list of world-class players whose elite finishing talent is not just a lucky streak but a genuine, repeatable skill. Bayesian methods offer a robust way to evaluate one of football's most crucial talents.