Graph of the number of counterparts to ICRF2 sources found in SDSS DR9 as a function of the search radius. The continuous curve represents the total number of hits (N), whereas the dot-dashed curve shows the results corrected with the false match ratio derived from Monte Carlo simulation (N − p_fN) detailed in Sect. 2.3. The growing deviation of the two curves is caused by the increase of false identifications at larger search radii. The curves nearly coincide up to 500 mas search radius, the value used in this case study, therefore the number of false optical-radio identifications is negligible.