Law of averages

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The law of averages is a lay term used to express a belief that outcomes of a random event shall "even out" within a small sample.

As invoked in everyday life, the "law" usually reflects bad statistics or wishful thinking 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 unnatural short-term "balance" must occur.

[edit] Examples

Belief that an event is "due" to happen: For example, "The roulette wheel has landed on red three consecutive times. The law of averages says it's due to land on black!" Of course, the wheel has no memory and its probabilities do not change according to past results. Similarly, there is no statistical basis for the belief that a losing sports team is due to win a game or that lottery numbers which haven't appeared recently are due to appear soon.

Belief that a sample's average must equal its expected value. For example, Daily Show host Jon Stewart joked that out of ten Republican candidates for president, "the law of averages says one of these guys is a little Barney in the Franks." Even if 10% of the population is homosexual, there is no guarantee that exactly one member in a group of ten must be homosexual. Similarly, if you flip a fair coin 100 times, there is only an 8% chance that there will be exactly 50 heads.

Belief that a rare occurrence will happen given enough time: For example, "If I send my résumé to enough places, the law of averages says that someone will eventually hire me." This may actually be true assuming nonzero probabilities and the law of averages is simply named in place of the Law of Large Numbers.