  Given a fibration of simply connected CW complexes of finite type, we study
the evaluation subgroup of the fibre inclusion as an invariant of
fibre-homotopy type. For spherical fibrations, we show the evaluation subgroup
may be expressed as an extension of the Gottlieb group of the fibre sphere
provided the classifying map induces the trivial map on homotopy groups. We
extend this result after rationalization: We show that the rationalized
evaluation subgroup of the fibre inclusion decomposes as the direct sum of the
rationalized Gottlieb group of the fibre and the rationalized homotopy group of
the base if and only if the classifying map induces the trivial map on rational
homotopy groups.
