  We investigate theoretically and experimentally the statistical properties of
the inhomogeneous order-parameter distribution (OPD) at the verge of the
superconductor-insulator transition (SIT). We find within two prototype
fermionic and bosonic models for disordered superconductors that one can
identify a universal rescaling of the OPD. By performing scanning-tunneling
microscopy experiments in three samples of NbN with increasing disorder we show
that such a rescaling describes also with an excellent accuracy the
experimental data. These results can provide a breakthrough in our
understanding of the SIT.
