Ellipsometry involves the solution of complicated mathematical relations between the measured data and the desired physical parameters. Dealing with these equations remains a central issue in the method, especially in light of the increased measurement speed and data set size. Here the sensitivity of ellipsometry measurements to parameters of interest for isotropic thin films is investigated as a first step to developing an ellipsometry expert system. A general approach to selecting incidence angles and light wavelengths is demonstrated for the particular case of ZrO2 films sputter deposited onto fused silica substrates. At first the measurements must be sensitive to changes in the parameter of interest and, beyond that, the system of equations must be sufficiently well posed considering measurement error and computer truncation and roundoff. Simulations of the ZrO2 film show that the incidence angles for best sensitivity do not correspond to those for the best equation conditions. This method can be applied to any reflecting surface to assist in the selection of angles and wavelengths. It is planned that a very large number of such simulations covering an increasing number of reflecting surface materials and configurations will be performed and stored in a high performance database for easy access. Such progress in the development of expert systems to make the equations work in the background for all but the most inquisitive ellipsometrist is described.