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Leicester's Tale: Another Perspective on the EPL 2015/16 Through Expected Goals (xG) Modelling

This study employs an expected goals (xG) probabilistic framework to analyze the 2015/16 English Premier League season, demonstrating that while Leicester City's title win was a statistical anomaly with low predicted probability, their underlying performance metrics justified a small but non-negligible chance of success, positioning xG models as effective tools for early diagnostics and performance baselines rather than definitive predictors of rare outcomes.

Original authors: Sheikh Badar Ud Din Tahir, Leonardo Egidi, Nicola Torelli

Published 2026-02-18

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Sheikh Badar Ud Din Tahir, Leonardo Egidi, Nicola Torelli

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are watching a football season unfold like a long, dramatic movie. Usually, we judge the movie by its ending: who won the trophy, who got relegated, and who finished in the middle. But what if we wanted to know if the ending was "fair" based on how the actors performed throughout the film?

This paper is about Leicester City's miraculous 2015/16 season, where a small, underdog team won the English Premier League against all odds (bookmakers gave them 5,000-to-1 odds). The authors ask a simple but deep question: Was this win a complete fluke, or was there a hidden signal in the data that hinted at their greatness all along?

To answer this, they used a tool called Expected Goals (xG). Here is how the paper works, explained with simple analogies:

1. The Core Concept: "Quality of Chances" vs. "The Scoreboard"

Think of football like a casino.

Goals are the money you win.
Shots are the bets you place.

Sometimes, you can place a terrible bet (a shot from 40 yards out) and get lucky, winning the jackpot. Other times, you can place a perfect bet (a shot right in front of the goal) and lose because the dice just didn't roll your way.

Traditional league tables only look at the money won (goals scored). This paper argues that's misleading. Instead, they built a model to measure the quality of the bets (Expected Goals or xG).

If a team takes 10 shots that are all "jackpot bets," their xG is high, even if they only score 1 goal.
If a team takes 10 shots that are "losing bets" but scores 3 goals by luck, their xG is low.

2. The Experiment: The Crystal Ball Test

The researchers built a simulation engine (a digital time machine). They fed this engine data from the first half of the 2015/16 season.

The Setup:

They didn't look at the final league table.
They only looked at the "quality of chances" (xG) created by each team in the first 19 games.
They asked the computer: "Based on how good these teams' shots were in the first half, what should the rest of the season look like?"

They ran the season 1,000 times on the computer to see what usually happens.

3. The Big Surprise: Leicester City

Here is where the story gets interesting.

The "Real" Leicester: In reality, Leicester was leading the league by the halfway point.
The "xG" Leicester: In the computer simulations, Leicester was not the favorite. The model predicted that Arsenal and Manchester City (the big spending teams) were much more likely to win.

However, the model did not say Leicester had zero chance.

The model gave Leicester a 16.7% chance of winning the title.
In the world of statistics, 16% is like rolling a 1 on a six-sided die. It's unlikely, but it happens.
The model also predicted Leicester would finish in the Top 4 (Champions League spots) very often.

The Takeaway: Leicester's win was a "rare event" (like winning the lottery), but it wasn't a "miracle" that defied physics. Their underlying performance (the quality of their shots) was actually strong enough to make them a contender. They just got incredibly lucky with the "dice rolls" (finishing) and the other teams got unlucky.

4. The "Early Warning System"

The paper argues that xG is best used as an early warning system, not a crystal ball that predicts the exact future.

The Mid-Season Check: If you look at the league table at Christmas, you might think a team is doing great because they have 40 points. But if their xG is low, the model warns you: "Hey, they are getting lucky. They might crash later."
The Reverse: If a team has low points but high xG, the model says: "They are playing well but getting unlucky. They are likely to improve soon."

In Leicester's case, the mid-season xG data correctly identified them as a "Top 4" team. The fact that they went on to win the whole league was just them riding a wave of extreme luck on top of that solid foundation.

5. The Limitations: Why the Model Can't Predict Everything

The authors admit their model isn't perfect. It's like a weather forecast that predicts rain but can't tell you if you'll get wet because you forgot your umbrella.

The Model sees the shots: It knows a shot was taken from a good spot.
The Model misses the magic: It doesn't know if a goalkeeper had a "bad day," if a player was injured, or if a team had a sudden burst of tactical genius.
The "Long Shot" Problem: Because football is random, the model sometimes underestimates the underdogs. It thinks Leicester has a 16% chance, but in reality, they won. The model says, "This is rare," but it doesn't say, "This is impossible."

Summary: What Does This Mean for Us?

This paper tells us that Leicester's 2016 title wasn't just a fairy tale.

Luck plays a huge role: You can have the best team in the world and still lose if the "dice" don't roll your way.
xG is a better truth-teller than the scoreboard: It reveals who is actually playing well, regardless of whether they are winning or losing at that moment.
Rare things happen: Even with a perfect model, the "long shot" (Leicester winning) can still happen. The model's job isn't to say "No, that won't happen," but rather to say, "That is very unlikely, but if it does happen, it's because the team was actually better than the scoreboard showed."

In short, the paper uses math to show that while Leicester City won the lottery, they were actually holding a very good ticket all along.

1. Problem Statement

The paper addresses a critical gap in sports analytics: the disconnect between cumulative Expected Goals (xG) and actual league standings. While xG is widely used to evaluate shot quality, its ability to serve as a reliable probabilistic baseline for predicting rare, season-long outcomes (such as an underdog winning a title) remains under-explored.

The authors specifically investigate ranking uncertainty: the phenomenon where a team's final position in the league table deviates significantly from their underlying performance metrics. Using the 2015/16 English Premier League (EPL) season—where Leicester City won the title against 5000-1 odds—as a case study, the study asks:

Can xG-based models simulate full-season league standings and quantify the probability of such rare events?
Does xG provide meaningful ex ante (pre-season/mid-season) diagnostic signals, or is it only useful for ex post (retrospective) analysis?
Is Leicester's success a statistical anomaly completely detached from performance, or was it a low-probability but feasible outcome given their underlying metrics?

2. Methodology

The authors developed a transparent, three-stage statistical framework combining logistic regression for shot-level modeling and Poisson processes for season-level simulation.

A. Data Source

Dataset: EPL 2015/16 season (380 matches, 20 teams).
Granularity: Shot-level event data (975 goals, 760 team-level observations) linked to match-level data.
Variables: Shot location, placement, body part, match situation (open play, set piece), assist method, and counter-attack status.

B. Feature Engineering & xG Estimation

The core of the model is a Logistic Regression classifier to estimate the probability ( $p$ ) that a specific shot results in a goal.

Predictors: Categorical variables including distance zones (close, medium, outside box, long range), shot placement, body part, situation, assist method, and fast break status.
Model Selection: Three specifications were compared:
1. Base Model: Distance zones + standard features.
2. Interaction Model: Added interaction terms between distance zone and body part (e.g., headers are more effective at close range).
3. Granular Spatial Model: Replaced broad distance zones with finer pitch location categories.
Selection Criteria: The Granular Spatial Model was selected as optimal based on the lowest Akaike Information Criterion (AIC = 5261.82) and residual deviance.
Output: The model outputs $\hat{p}_i$ (xG) for every shot $i$ , calculated via the inverse logit function.

C. Season-Level Simulation Framework

To move from shot-level probabilities to season outcomes, the authors employed a Poisson-based simulation:

Temporal Split: Data was split into the first half (19 matches) and second half (19 matches).
Strength Estimation: First-half xG data was aggregated to calculate team-specific attacking ( $\lambda_{for}$ ) and defensive ( $\lambda_{against}$ ) intensities.
Simulation: The remainder of the season was simulated 1,000 times. For each simulated match, goals were drawn from Poisson distributions:
- $G_{home} \sim \text{Poisson}(\lambda_{home})$
- $G_{away} \sim \text{Poisson}(\lambda_{away})$
Inference: The simulations generated distributions for final points, rankings, and outcome probabilities (Title, Top-4, Relegation).

3. Key Contributions

Quantification of Ranking Uncertainty: The study formalizes the concept of "ranking uncertainty," demonstrating that league tables often mask underlying performance consistency. It provides a probabilistic distribution of possible league tables rather than a single point forecast.
Ex Ante Diagnostic Value: The paper proves that mid-season xG profiles are strong predictors of second-half performance trends, even when controlling for current league position.
Rare Event Analysis: It offers a rigorous statistical explanation for Leicester City's title win, framing it not as a "miracle" disconnected from data, but as a low-probability realization within the upper tail of a feasible distribution.
Methodological Pipeline: The authors provide a reproducible pipeline using hand-crafted, domain-informed features (spatial zones, body parts) to enhance model interpretability over "black box" machine learning approaches.

4. Key Results

A. Mid-Season Diagnostic Performance

Correlation: There is a monotonic relationship between first-half xG quartiles and second-half point accumulation.
Leicester City's Profile: At mid-season, Leicester was 2nd in points but 4th in xG. Despite this, their underlying xG profile was strong enough to place them in the top tier of contenders.
Predictive Accuracy: The model correctly identified the top-four contenders (Arsenal, Man City, Tottenham, Leicester) and relegation candidates (Aston Villa, Sunderland, Newcastle) based solely on first-half data.

B. Outcome Probabilities (Mid-Season Ex Ante)

Using only first-half data to simulate the second half:

Leicester City: Assigned a 16.7% probability of winning the title and an >80% probability of finishing in the Top 4. Their average simulated rank was 3.12.
Favorites: Arsenal (49.0% title probability) and Manchester City (26.6%) were correctly identified as the primary favorites.
Relegation: Aston Villa had a >90% relegation probability, aligning with reality.
Variance: The model showed that while Leicester's title win was in the "extreme tail" of the distribution, it was not impossible. Their actual second-half points fell within the upper tail of the simulated distribution, not outside it.

C. Full-Season (Ex Post) Benchmark

When the model was run with full-season xG data (retrospectively):

It achieved a Spearman rank correlation of 0.837 and explained 75.8% of the variance in final points.
However, even with full information, the model struggled to predict the exact extreme outcome of Leicester winning, reinforcing that xG is a baseline for plausibility, not a deterministic predictor of specific rare events.

5. Significance and Conclusion

The paper concludes that Expected Goals models are best utilized as probabilistic baselines and early-warning diagnostics rather than deterministic predictors of specific season outcomes.

For Analysts: xG helps distinguish between "good luck" (overperforming xG) and "bad luck" (underperforming xG), providing a more stable metric for team quality than points alone.
For Rare Events: The Leicester City case study demonstrates that historic upsets are often the result of a combination of strong underlying performance (high xG) and favorable variance (finishing efficiency). The model successfully captured the potential for such an outcome, even if it assigned it a low probability.
Limitations & Future Work: The authors acknowledge that the current model treats shots as independent events (ignoring momentum) and lacks defensive pressure/goalkeeper positioning data. Future work should incorporate player-specific finishing abilities and sequence-aware models (e.g., RNNs) to better capture tactical dynamics.

In summary, the study validates that while the 2015/16 Leicester title was a statistical anomaly, it was statistically grounded in their mid-season performance, and probabilistic modeling is the correct tool to quantify the likelihood of such "black swan" events in sports.