  The near-threshold clustering phenomenon is well understood by the low-energy
universality, for shallow bound states below the threshold. Nevertheless, the
characteristics of resonances slightly above the threshold still lack thorough
elucidation. We introduce a novel probabilistic interpretation scheme for
complex compositeness of resonances, in which resonances with unphysically
large decay widths are inherently excluded. Employing this scheme to analyze
resonances via the effective range expansion, we demonstrate that
near-threshold resonances have small composite fraction, in sharp contrast to
shallow bound states below the threshold.
