  A normal variety $X$ is called $H$-spherical for the action of the complex
reductive group $H$ if it contains a dense orbit of some Borel subgroup of $H$.
We resolve a conjecture of Hodges--Yong by showing that their spherical
permutations are characterized by permutation pattern avoidance. Together with
results of Gao--Hodges--Yong this implies that the sphericality of a Schubert
variety $X_w$ with respect to the largest possible Levi subgroup is
characterized by this same pattern avoidance condition.
