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High Quality Content by WIKIPEDIA articles! Statistical regularity is a notion in statistics and probability theory that random events exhibit regularity when repeated enough times or that enough sufficiently similar random events exhibit regularity. It is an umbrella term that covers the law of large numbers, all central limit theorems and ergodic theorems. If one throws a die once, it is difficult to predict the outcome, but if we repeat this experiment many times, we will see that the number of times each result occurs divided by the number of throws will eventually stabilize towards a specific value. Repeating a series of trials will produce similar, but not identical, results for each series: the average, the standard deviation and other distributional characteristics will be around the same for each series of trials.