This study uses the data provided by the Leiden Ranking 2020 to support the claim that percentile-based indicators are linked by a power law function. A constant calculated from this function, ep, and the total number of papers fully characterize the percentile distribution of publications. According to this distribution, the probability that a publication from a country or institution is in the global xth percentile can be calculated from a simple equation: P = ep(2−lgx). By taking the Leiden Ranking PPtop 10%/100 as an approximation of the ep constant, our results demonstrate that other PPtop x% indicators can be calculated applying this equation. Consequently, given a PPtop x% indicator, all the others are redundant. Even accepting that the total number of papers and a single PPtop x% indicator are sufficient to fully characterize the percentile distribution of papers, the results of comparisons between universities and research institutions differ depending on the percentile selected for the comparison. We discuss which Ptop x% and PPtop x% indicators are the most convenient for these comparisons to obtain reliable information that can be used in research policy.
Peer Review: https://publons.com/publon/10.1162/qss_a_00130