  We establish an equality between two multiplicities: one in the restriction
of tempered representations of a $p$-adic group to its closed subgroup with the
same derived group; and one occurring in their corresponding component groups
in Langlands dual sides, so-called $\mathcal{S}$-groups, under working
hypotheses about the tempered local Langlands conjecture and the internal
structure of tempered $L$-packets. This provides a formula of the multiplicity
for $p$-adic groups by means of dimensions of irreducible representations of
their $\mathcal{S}$-groups.
