We present a first approach to systematic characterization and interpretation of observed asymmetries of Stokes profiles as a function of spatial position within sunspots. Spatial maps of the full Stokes profiles of Fe I 6302.5 A gathered in large sunspots using the HAO Stokes II instrument reveal asymmetries that vary systematically across large sunspots observed during 1980. We use the inversion technique by Landolfi to extract the velocity gradients along the line of sight (LOS) which give rise to these asymmetries. The gradients derived from full Stokes profiles are in agreement with previous characterizations of the Evershed flow derived from Stokes I profiles alone (i.e., a flow increasing with depth in the atmosphere). By coupling this semiempirical gradient of velocity with a magnetic field inclination varying along the LOS, the synthesized profiles are able to mimic basic observed features of the broad-band circular polarization present in our data and observed previously by others. This characterization has magnetic field lines which become progressively more horizontal with depth in the penumbra.