This paper presents a new analysis tool for predicting the closed-loop performance of a robust constrained model predictive control (MPC) scheme. Currently, performance is typically evaluated by numerical simulation, leading to an extensive computation when investigating the effect of controller parameters, such as the horizon length, the cost weightings and the constraint settings. The analytic method, in this paper, avoids this computational burden, thus enabling a rapid study of the trades between the design parameters and the performance. Previous work developed an MPC formulation employing constraint tightening to achieve robust feasibility and constraint satisfaction despite the action of an unknown but bounded disturbance. This paper shows that the expected performance of that controller can be predicted using a combination of the gains of two linear systems, the optimal control for the unconstrained system, and a candidate policy used in performing the constraint tightening. The method also accounts for the possible mismatch between the predicted level of disturbance and the actual level encountered. The analytic results are compared with simulation results for several examples and are shown to provide accurate predictions of performance and its variation with the system parameters.