Through a direct statistical approach, analytic expressions are derived for the second moment, the variance ratio, and benefit functions of a model for n-surface geometric splitting. The model is general in that it can be applied to many geometric and material conditions, energy dependence, and biasing methods besides splitting. The model applies to any detector, provided that the detector region is separated from the source region. The model has the following limitations: (a) every source particle reaching the detector must cross all splitting surfaces, (b) particles are allowed to split only once on each surface, (c) weight-dependent biasing schemes are not included, and (d) reactions that bifurcate the particle are excluded. The derived expressions depend linearly on n unknown constants that are bulk properties of the medium in a given problem. These constants may be estimated approximately from one small sample run invoking the point-surface approximation or from (n + 1) consecutive small sample runs. Numerical examples are given in verification of the theory, and the possibility of using the expressions in an in-code optimization or self-optimizing code is discussed.