Nonrandom distributions of ages of mass extinctions, magnetic reversals, and other geologic phenomena have been used to support the hypothesis that catastrophic events driven by the periodic motions of planets, stars, or our galaxy play a major role in the history of Earth and its life. Such conclusions have been based on statistical comparison of observed ages to a single reference model, the Poisson distribution. However, probability grids based on multiple reference models show that a wide range of distributions, including some that are periodic and some that are intrinsically random (episodic), can fit the observations. Viable models include some with a fairly large variability in age interval (∼30%). There is no statistical motivation for favoring periodic motions of extraterrestrial objects over the organized, dissipative processes that operate on Earth as an explanation for mass extinctions.