Computing f-vectors of polytopes is in general hard, and only little is known about their shape. We initiate the study of properties of f-vector of matroid base polytopes, by focusing on the class of split matroids, i.e., matroid polytopes arising from compatible splits of a hypersimplex. Unlike valuative invariants, the f-vector behaves in a much more unpredictable way, and the modular pairs of cyclic flats play a role in the face enumeration. We give a concise description of how the computation can be achieved without performing any convex hull or face lattice computation. As applications, we deduce formulas for sparse paving matroids and rank 2 matroids. These are two families that appear in other contexts within combinatorics.