A concise theoretical technique is presented for estimating the minimum miss distance capability of command guided missile systems using synthetic proportional navigation. The effect of the parameter values on the system capability is shown to be a function of range-to-intercept; the technique enables the system designer and analyst to quantify system performance and to develop a systematic understanding of the performance limitations of command guidance systems at each intercept range. New analytical equations based upon adjoint theory are developed for statistical miss distance caused by target maneuver, range-dependent, servo, glint and atmosphere noises for command guided systems. An optimal total system time constant is derived which yields the minimum statistical miss distance. Realistic constraints on the minimum achievable system time constant are considered. The equations derived for the optimal total system time constant are valuable to the system designer for minimizing miss distance over the ranges of system parameters and limitations, and intercept conditions.