Analytical models to evaluate and predict "precision" performance of indoor positioning systems based on location fingerprinting are lacking. Such models can be used to improve the design of positioning systems, for example by eliminating some fingerprints and reducing the size of the location fingerprint database. In this paper, we develop a new analytical model that employs proximity graphs for predicting performance of indoor positioning systems based on location fingerprinting. The model allows computation of an approximate probability distribution of error distance given a location fingerprint database based on received signal strength and its associated statistics. The performance results from the simulation and the analytical model are found to be congruent. This model also allows us to perform analysis of the internal structure of location fingerprints. We employ the analysis of the internal structure to identify and eliminate unnecessary location fingerprints stored in the database, thereby saving on computation while performing location estimation.