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, e p , 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 x th percentile can be calculated from a simple equation: P = e p (2−lg x ) . By taking the Leiden Ranking PP top 10% /100 as an approximation of the e p constant, our results demonstrate that other PP top x % indicators can be calculated applying this equation. Consequently, given a PP top x % indicator, all the others are redundant. Even accepting that the total number of papers and a single PP top 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 P top x % and PP top x % indicators are the most convenient for these comparisons to obtain reliable information that can be used in research policy.

Numerous EU documents praise the excellence of EU research without empirical evidence and in contradiction of academic studies. We investigated research performance in two fields of high socioeconomic importance, advanced technology and basic medical research, in two sets of European countries, Germany, France, Italy, and Spain (GFIS), and the UK, The Netherlands, and Switzerland (UKNCH). Despite their historical and geographical proximity, research performance in GFIS is much lower than in UKNCH, and well below the world average. Funding from the European Research Council (ERC) greatly improves performance in both GFIS and UKNCH, but ERC-GFIS publications are less cited than ERC-UKNCH publications. We conclude that research performance in GFIS and in other EU countries is intrinsically low, even in highly selected and generously funded projects. The technological and economic future of the EU depends on improving research, which requires structural changes in research policy within the EU, and in most EU countries.