The radiation performance of circularly bound random arrays with uniform and Gaussian distributions is analyzed statistically to identify regions of deterministic, transitional, and random behavior. Isotropic radiators are preferred in this analysis as they provide relevant information on fundamental beamforming behavior. This can be applied to provide practical estimates and ideal limitations on the maximum peaking sidelobe located in the stochastically described 3dB region with non-deterministic behavior. The mathematical process required for this analysis includes a statistical formulation of the array factor, including the mean, or expected value, and the variance. Analysis from prior work on random arrays provides the framework for this work, but the intuitive and streamlined analytical approach developed here forms an accurate estimate for the maximum peaking sidelobe behavior in a volumetric scan region.