We present the development of an analytical model that can be used for the rational design of a biosensor based on shifts in the local surface plasmon resonance (LSPR) of individual gold nanoparticles. The model relates the peak wavelength of light scattered by an individual plasmonic nanoparticle to the number of bound analyte molecules and provides an analytical formulation that predicts relevant figures-of-merit of the sensor such as the molecular detection limit (MDL) and dynamic range as a function of nanoparticle geometry and detection system parameters. The model calculates LSPR shifts for individual molecules bound by a nanorod, so that the MDL is defined as the smallest number of bound molecules that is measurable by the system, and the dynamic range is defined as the maximum number of molecules that can be detected by a single nanorod. This model is useful because it will allow a priori design of an LSPR sensor with figures-of-merit that can be optimized for the target analyte. This model was used to design an LSPR sensor based on biotin-functionalized gold nanorods that offers the lowest MDL for this class of sensors. The model predicts a MDL of 18 streptavidin molecules for this sensor, which is in good agreement with experiments and estimates. Further, we discuss how the model can be utilized to guide the development of future generations of LSPR biosensors.