When using a MMP for a detection or identification task, a user considers certain elements of the Mueller matrix. The usual way of performing this task is to measure the full Mueller matrix and discard the unused elements. For polarimeter designs with speed, miniaturization, or other constraints it may be desirable to have a system with reduced dimensionality that measures only the important elements of the Mueller matrix as efficiently as possible. In this paper, we develop a framework that allows partial MMPs to be analyzed. Quantitative metrics are developed by considering geometrical relationships between the space spanned by a particular MMP and the space occupied by the scene components. The method is generalized to allow the effects of noise to come into the equation when noise performance is important as well.