  Let $X$ be a spherical variety for a connected reductive group $G$. Work of
Gaitsgory-Nadler strongly suggests that the Langlands dual group $G^\vee$ of
$G$ has a subgroup whose Weyl group is the little Weyl group of $X$.
Sakellaridis-Venkatesh defined a refined dual group $G^\vee_X$ and verified in
many cases that there exists an isogeny $\phi$ from $G^\vee_X$ to $G^\vee$. In
this paper, we establish the existence of $\phi$ in full generality. Our
approach is purely combinatorial and works (despite the title) for arbitrary
$G$-varieties.
