Related Experiment Video
Updated: May 28, 2026
05:37
An R-Based Landscape Validation of a Competing Risk Model
Published on: September 16, 2022
From Expected Goals to Scoring at Least Once: An Event-Specific Summary of Aggregated Bernoulli Risk
1Faculty of Mathematics and Computer Science, Adam Mickiewicz University, 61-614 Poznań, Poland.
Entropy (Basel, Switzerland)
|May 26, 2026
Summary
A new metric, xG+, refines football analytics by measuring the probability of scoring at least one goal, unlike traditional expected goals (xG) which only summarizes scoring volume. This offers a more nuanced view of offensive performance.
Area of Science:
- Sports Analytics
- Probability Theory
- Football Statistics
Background:
- Expected goals (xG) quantifies offensive performance using shot probabilities but ignores scoring distribution.
- Identical xG values can mask different probabilities of scoring at least one goal.
Purpose of the Study:
- Introduce and analyze xG+ (-logP(G=0)) as a novel metric for football analytics.
- xG+ provides a complementary measure to xG, focusing on the probability of scoring at least once.
Main Methods:
- Interpreted xG+ as an additive summary of aggregated Bernoulli risk.
- Analyzed structural properties of xG+ and derived a second-order approximation.
- Empirically illustrated xG+ using football data.
Main Results:
- Demonstrated that xG+ is always greater than or equal to xG (xG+ ≥ xG).
- Showed how concentrated shot profiles enhance scoring certainty compared to total xG.
- Highlighted discrepancies between exact Bernoulli aggregation and Poisson approximations.
Conclusions:
- xG+ offers a valuable complement to xG for assessing football offensive performance.
- The study provides a deeper understanding of scoring probability aggregation beyond simple expected values.
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