Degrees of the stretched Kostka quasi-polynomials

We provide a type-uniform formula for the degree of the stretched Kostka quasi-polynomial $K_{\lambda,\mu}(N)$ in all classical types, improving a previous result by McAllister in $\mathfrak{sl}_r(\mathbb{C})$. Our proof relies on a combinatorial model for the weight multiplicity by Berenstein and Zelevinsky.