  We describe an approach, via Malle's permutation $\Psi$ on the set of
irreducible characters $\text{Irr}(W)$, that gives a uniform derivation of the
Chapuy-Stump formula for the enumeration of reflection factorizations of the
Coxeter element. It also recovers its weighted generalization by delMas,
Reiner, and Hameister, and further produces structural results for
factorization formulas of arbitrary regular elements.
