The concept of vectorial spin analysis in spin and angle-resolved photoemission is illustrated in this paper. Two prototypical systems, Bi/Ag(111)(sqrt(3)×sqrt(3))R30° and Pb/Ag(111)(sqrt(3)×sqrt(3))R30°, which show a large Rashba-type spin-orbit splitting, were investigated by means of spin and angle-resolved photoemission. The spin polarization vectors of individual bands were determined by a two-step fitting routine. First, the measured intensities are fitted with an appropriate number of suitable peaks to quantify the contributions of the individual bands; then, the measured spin polarization curves are fitted by varying the polarization direction and its magnitude for each band. We confirm that the surface states experience a large spin splitting. Moreover, we find that all surface state bands are 100% spin polarized, and that for some states, spin polarization vectors rotate out of the surface plane.