Ultrasensitive detectors based on localized surface plasmon resonance refractive index sensing are capable of detecting very low numbers of molecules for biochemical analysis. It is well known that the sensitivity of such sensors crucially depends on the spatial distribution of the electromagnetic field around the metal surface. However, the precise connection between local field enhancement and resonance shift is seldom discussed. Using a quasistatic approximation, we developed a model that relates the sensitivity of a nanoplasmonic resonator to the local field in which the analyte is placed. The model, corroborated by finite-difference time-domain simulations, may be used to estimate the magnitude of the shift as a function of the properties of the sensed object - permittivity and volume - and its location on the surface of the resonator. It requires only a computation of the resonant field induced by the metal structure and is therefore suitable for numerical optimization of nanoplasmonic sensors.