Use of a nested bivariate binomial distribution in presence of covariates applied to a Brazilian soccer league data

This study introduces a nested bivariate binomial (BVB) regression model under a Bayesian logistic regression framework to evaluate offensive efficiency in football, with application to the 2023 Brazilian Série A league. The BVB model characterizes offensive performance as a two-stage process: (i) the number of shots on target given total shot attempts, and (ii) the number of goals scored given shots on target. Financial covariates—namely, club investment during the 2023 season and estimated market value—are incorporated at both stages to assess their association with team efficiency. The analysis is based on data from 20 teams across the first 12 rounds of the season, mitigating mid-season variability and transfer effects. Results indicate that higher market value is positively associated with scoring efficiency, whereas recent financial investment does not exhibit a significant effect. These findings constitute a primary investigation into the influence of financial variables on offensive performance in football. By introducing the BVB model within a sports analytics framework, the study provides preliminary evidence of the explanatory and predictive utility of financial indicators—particularly market value—in modeling sporting outcomes.