High-energy x-ray diffraction coupled with atomic pair distribution analysis and large-scale computer simulations are used to study the relationship between the local structure and piezoelectric response of an exemplary ferroelectric from the BaTiO3 family where Ti is partially replaced by nonferroelectric Ce. Our results indicate that, likely, the increase in the piezoelectric response observed for Ce concentration <10% is due to an increased local rhombohedral distortion of the perovskite lattice. Despite a further increase in the distortion, the piezoelectric response for Ce concentration >10% decays quickly, likely because of rapidly increasing nonuniform strain fields due to the size mismatch between Ti- and Ce-centered octahedra and loss of electric dipoles due to the nonferroactivity of the latter. Thus, the transition between the observed two regimes of piezoelectric response does not appear to involve a crossing of a morphotropic phase boundary where the crystallographic symmetry changes abruptly but is likely to be percolative in nature. A similar behavior, referred to as tricritical phenomenon, is observed with other B-site substituted ferroelectrics from the BaTiO3 family, indicating the presence of a common structural origin. Our results highlight the importance of chemical substitution-driven rhombohedral distortions in achieving control over the piezoelectric response of perovskite ferroelectrics, thereby providing a different perspective on the ongoing effort to improve their performance in practical applications.