In the present study, we investigate patterns in the postural sway that characterize the static balance in human beings. To measure the postural sway, sixteen healthy young subjects performed quiet stance tasks providing the center-of-pressure (COP) trajectories. From these trajectories, we obtained the COP velocities. We verified that the velocity distributions exhibit non-normal behavior and can be approximated by generalized Gaussians with fat tails. We also discuss possible implications of modeling COP velocity by using generalized Fokker-Planck equations related to Tsallis statistics and Richardson anomalous diffusion