Since the introduction of model predictive control (MPC), control practitioners have been faced with the following question: for what class of processes MPC should be implemented? MPC provides a control sequence that is optimal in the presence or absence of constraints. However, it requires (i) numerically solving a constrained optimization problem repeatedly on-line and (ii) an adequately reliable model. Alternatively, one can implement analytical control, such as proportional-integral-derivative (PID) control and differential geometric control, which does not require the on-line optimization but generally cannot provide the optimal performance. This paper presents an answer to the following question: for what class of processes can analytical control provide control quality that is close to the optimal control quality that MPC can provide? Here, an analytical controller is defined as the one whose implementation does not require solving a constrained optimization problem numerically. A measure that quantifies the degradation in the closed-loop performance of a given process when the process is controlled using analytical control instead of MPC has been defined. The measure is used to characterize the class of input-constrained processes for which MPC provides significantly higher control quality; processes with directionality and active input constraints benefit more from MPC. It is shown that structural information on the characteristic (decoupling) matrix of a process is often adequate for the characterization. Four input-constrained process examples are considered. On the basis of structural information on the characteristic matrices of the four processes, the processes that can be controlled satisfactorily using analytical control are specified. Simulated closed-loop responses are then presented, to show the validity of the characterization.