In this paper, we consider the academic department ranking system of Italy, which is based on a performance index named Indice Standardizzato di Performance Dipartimentale (ISPD). While critiques to the ISPD have been moved for its marked tendency to polarization, we here formalize a yet unexplored determinant of this phenomenon, that is, the presence of within-department homogeneity among the standardized scores used to build the index. We account for this intra-departmental correlation by modeling it as a function of departments' size. The proposed model, estimated via Maximum Likelihood, allows to build a fairer ranking procedure via the definition of a properly adjusted version of the ISPD. The estimation framework is also adapted to fit publicly available data, which are coarsened by rounding and/or left-truncated. To this end, a novel probability distribution termed Betoidal is introduced. Empirical evidence in favor of the proposed model is found in the 2017 and 2022 data. Moreover, a simulation study shows that the adjusted index significantly overcomes not only the original ISPD, but also other more data-demanding competing proposals.

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