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Although not explicitly declared, most research rankings of countries andinstitutions are supposed to reveal their contribution to the advancement ofknowledge. However, such advances are based on very highly cited publicationswith very low frequency, which can only very exceptionally be counted withstatistical reliability. Percentile indicators enable calculations of theprobability or frequency of such rare publications using counts of much morefrequent publications; the general rule is that rankings based on the number oftop 10% or 1% cited publications (Ptop 10%, Ptop 1%) will also be valid for therare publications that push the boundaries of knowledge. Japan and itsuniversities are exceptions, as their frequent Nobel Prizes contradicts theirlow Ptop 10% and Ptop 1%. We explain that this occurs because, in singleresearch fields, the singularity of percentile indicators holds only forresearch groups that are homogeneous in their aims and efficiency. Correctcalculations for ranking countries and institutions should add the results oftheir homogeneous groups, instead of considering all publications as a singleset. Although based on Japan, our findings have a general character. Commonpredictions of scientific advances based on Ptop 10% might be severalfold lowerthan correct calculations.

Common bibliometric approaches fail to assess correctly the number of important scientific advances for most countries and institutions