  We derive a formula expressing the joint distribution of the cyclic valley
number and excedance number statistics over a fixed conjugacy class of the
symmetric group in terms of Eulerian polynomials. Our proof uses a slight
extension of Sun and Wang's cyclic valley-hopping action as well as a formula
of Brenti. Along the way, we give a new proof for the $\gamma$-positivity of
the excedance number distribution over any fixed conjugacy class along with a
combinatorial interpretation of the $\gamma$-coefficients.
