Cosmic acceleration may be due to modifications of cosmic gravity and to test this we need robust connections between theory and observations. However, in a model independent approach like effective field theory or a broad class like Horndeski gravity, several free functions of time enter the theory. We show that simple parametrizations of these functions are unlikely to be successful; in particular the approximation $α_i(t)\proptoΩ_{\rm de}(t)$ drastically misestimates the observables. This holds even in simple modified gravity theories like $f(R)$. Indeed, oversimplified approximations to the property functions $α_i(t)$ can even miss the signature of modified gravity. We also consider the question of consistency relations and the role of tensor (gravitational wave) perturbations.

10 pages, 5 figures; v2 new Appendix on f(R) with new figure; v3 accepted to PRD, new figure, reordering and clarification, conclusions unchanged