  Our main result is a generalization, to all affine Weyl groups, of P.
Johnson's proof of D. Armstrong's conjecture for the expected number of boxes
in a simultaneous core. This extends earlier results by the second and third
authors in simply-laced type. We do this by modifying and refining the
appropriate notion of the "size" of a simultaneous core. In addition, we
provide combinatorial core-like models for the coroot lattices in classical
type and type $G_2$.
