  This paper shows that the multiplicity of the base points locus of a
projective rational surface parametrization can be expressed as the degree of
the content of a univariate resultant. As a consequence, we get a new proof of
the degree formula relating the degree of the surface, the degree of the
parametrization, the base points multiplicity, and the degree of the rational
map induced by the parametrization. In addition, we extend both formulas to the
case of dominant rational maps of the projective plane and describe how the
base point loci of a parametrization and its reparametrizations are related. As
an application of these results, we explore how the degree of a surface
reparametrization is affected by the presence of base points.
