We present a statistical study of the largest bibliographic compilation of stellar and orbital parameters of W UMa stars derived by light-curve synthesis with Roche models. The compilation includes nearly 700 individually investigated objects from over 450 distinct publications. Almost 70% of this sample is comprised of stars observed in the past decade that have not been considered in previous statistical studies. We estimate the ages of the cataloged stars, model the distributions of their periods, mass ratios, temperatures, and other quantities, and compare them with the data from the Catalina Real-Time Transient Survey, LAMOST, and Gaia archives. As only a small fraction of the sample has radial-velocity curves, we examine the reliability of the photometric mass ratios in totally and partially eclipsing systems and find that totally eclipsing W UMa stars with photometric mass ratios have the same parameter distributions as those with spectroscopic mass ratios. Most of the stars with reliable parameters have mass ratios below 0.5 and orbital periods shorter than 0.5 days. Stars with longer periods and temperatures above 7000K stand out as outliers and should not be labeled W UMa binaries.