  For any non-trivial convex and bounded subset $C$ of a Banach space, we show
that outside of a $\sigma$-porous subset of the space of non-expansive mappings
$C\to C$, all mappings have the maximal Lipschitz constant one witnessed
locally at typical points of $C$. This extends a result of Bargetz and the
author from separable Banach spaces to all Banach spaces and the proof given is
completely independent. We further establish a fine relationship between the
classes of exceptional sets involved in this statement, captured by the
hierarchy of notions of $\phi$-porosity.
