The law of averages is the commonly held belief that a particular outcome or event will, over certain periods of time, occur at a frequency that is similar to its probability.
As invoked in everyday life, the "law" usually reflects wishful thinking or a poor understanding of statistics rather than any mathematical principle.
While there is a real theorem that a random variable will reflect its underlying probability over a very large sample, the law of averages typically assumes that an unnatural short-term "balance" must occur.
[3] Typical applications also generally assume no bias in the underlying probability distribution, which is frequently at odds with the empirical evidence.
Another application of the law of averages is a belief that a sample's behaviour must line up with the expected value based on population statistics.
For example, a job seeker might argue, "If I send my résumé to enough places, the law of averages says that someone will eventually hire me."