Polarization effects of channels such as turbulent free space and optical fibers can deteriorate the quality of polarization-sensitive communication schemes, for example, quantum key distribution. The exact nature of the channel is problematic to determine, and most theoretical results are based on approximations. We introduce a general model with probabilistic polarization angle rotation and analyze the average error it causes in terms of the moments of the probability distribution. For a small rotation angle variance, an inequality between distributions’ errors is considered based on their kurtosis values and potentially higher-order central moments. An upper bound is determined for the error probability, holding for all practically interesting scenarios.