We estimate the excess chemical potential Δμ and excess entropy per particle Δs of computer-generated, monodisperse and polydisperse, frictionless hard-sphere fluids. For this purpose, we utilize the Widom particle insertion method, which for hard-sphere systems relates Δμ to the probability to successfully (without intersections) insert a particle into a system. This insertion probability is evaluated directly for each configuration of hard spheres by extrapolating to infinity the pore radii (nearest-surface) distribution and integrating its tail. The estimates of Δμ and Δs are compared to (and comply well with) predictions from the Boublík-Mansoori-Carnahan-Starling-Leland equation of state. For polydisperse spheres, we employ log-normal particle radii distributions with polydispersities δ = 0.1, 0.2, and 0.3.