ArticleEntropy (Basel, Switzerland)2026
From Expected Goals to Scoring at Least Once: An Event-Specific Summary of Aggregated Bernoulli Risk.
Article in Entropy (Basel, Switzerland), 2026. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Not yet cited in PubMed.
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Abstract
Expected goals (xG) is widely used to quantify offensive performance in football by summarizing the expected number of goals from shot-level scoring probabilities. However, xG reflects only the first moment of the underlying Bernoulli system and does not capture how scoring probability is distributed across shots. As a result, teams with identical total xG may nevertheless have different probabilities of scoring at least once. In this paper, we study the quantity xG+=-logP(G=0), which is a monotone transform of the exact no-goal probability and, equivalently, of the probability of scoring at least once. We interpret xG+ as an additive, event-specific summary of aggregated Bernoulli risk and analyze its main structural properties. In particular, we show that xG+≥xG, with equality only in the degenerate case pi=0 for all
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