Distances to spaces of affine Baire-one functions

Let E be a Banach space and let B(1) (B(E*)) and u(1) (B(E*)) denote the space of all Baire-one and affine Baire-one functions on the dual unit ball B(E*), respectively. We show that there exists a separable L(1)-predual E such that there is no quantitative relation between dist(f, B(1)(B(E)*)) and dist(f, u(1)(B(E*))), where f is an affine function on B(E*). If the Banach space E satisfies some additional assumption, we prove the existence of some such dependence.