Although not explicitly declared, most research rankings of countries and
institutions are supposed to reveal their contribution to the advancement of
knowledge. However, such advances are based on very highly cited publications
with very low frequency, which can only very exceptionally be counted with
statistical reliability. Percentile indicators enable calculations of the
probability or frequency of such rare publications using counts of much more
frequent publications; the general rule is that rankings based on the number of
top 10% or 1% cited publications (Ptop 10%, Ptop 1%) will also be valid for the
rare publications that push the boundaries of knowledge. Japan and its
universities are exceptions, as their frequent Nobel Prizes contradicts their
low Ptop 10% and Ptop 1%. We explain that this occurs because, in single
research fields, the singularity of percentile indicators holds only for
research groups that are homogeneous in their aims and efficiency. Correct
calculations for ranking countries and institutions should add the results of
their homogeneous groups, instead of considering all publications as a single
set. Although based on Japan, our findings have a general character. Common
predictions of scientific advances based on Ptop 10% might be severalfold lower
than correct calculations.Comment: 30 pages, tables and figures embedded in a single pdf fil