  We prove the elementary but surprising fact that the Hofer distance between
two closed subsets of a symplectic manifold can be expressed in terms of the
restrictions of Hamiltonians to one of the subsets; this helps explain certain
energy-capacity inequalities that appeared recently in work of Borman-McLean
and Humiliere-Leclercq-Seyfaddini. We also build on arXiv:1201.2926 to obtain
new vanishing results for the Hofer distance between subsets, applicable for
instance to singular analytic subvarieties of Kahler manifolds.
