We introduce expected information gain to quantify measurements and apply it to compare visual acuity (VA) and contrast sensitivity (CS) tests. We simulated observers with parameters covered by the visual acuity and contrast sensitivity tests and observers based on distributions of normal observers tested in three luminance and four Bangerter foil conditions. We first generated the probability distributions of test scores for each individual in each population in the Snellen, ETDRS and qVA visual acuity tests and the Pelli-Robson, CSV-1000 and qCSF contrast sensitivity tests and constructed the probability distributions of all possible test scores of the entire population. We then computed expected information gain by subtracting expected residual entropy from the total entropy of the population. For acuity tests, ETDRS generated more expected information gain than Snellen; scored with VA threshold only or with both VA threshold and VA range, qVA with 15 rows (or 45 optotypes) generated more expected information gain than ETDRS. For contrast sensitivity tests, CSV-1000 generated more expected information gain than Pelli-Robson; scored with AULCSF or with CS at six spatial frequencies, qCSF with 25 trials generated more expected information gain than CSV-1000. The active learning based qVA and qCSF tests can generate more expected information than the traditional paper chart tests. Although we only applied it to compare visual acuity and contrast sensitivity tests, information gain is a general concept that can be used to compare measurements and data analytics in any domain.