Probing absolute values of spin polarization at the nanoscale offers insight into the fundamental mechanisms of spin-dependent transport. Employing the Zeeman splitting in superconducting tips (Meservey-Tedrow-Fulde effect), we introduce a novel spin-polarized scanning tunneling microscopy that combines the probing capability of the absolute values of spin polarization with precise control at the atomic scale. We utilize our novel approach to measure the locally resolved spin polarization of magnetic Co nanoislands on Cu(111). We find that the spin polarization is enhanced by 65% when increasing the width of the tunnel barrier by only 2.3 angstrom due to the different decay of the electron orbitals into vacuum.