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Wiktionary
law of averages

n. 1 (context statistics English) The statistical tendency toward a fixed proportion in the results when an experiment is repeated a large number of times; the law of large numbers. 2 (context informal English) An imaginary or perceived "law" of probabilities which is wrongly used to predict results in the short-term.

WordNet
law of averages

n. a law affirming that in the long run probabilities will determine performance

Wikipedia
Law of averages

The law of averages is a layman's term for a belief that the statistical distribution of outcomes among members of a small sample must reflect the distribution of outcomes across the population as a whole.

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 unnatural short-term "balance" must occur. Typical applications of the law also generally assume no bias in the underlying probability distribution, which is frequently at odds with the empirical evidence.

Usage examples of "law of averages".

Weve been lucky, but the law of averages eventually has to turn against us.

In the nature of things a good many somebodies are always in hospital, and the law of averages had picked on me to be one of them a week or so before.

If he keeps playing long enough, the law of averages catches up with him.

Any reasonable man who had survived fourteen bank robberies without being caught would have to wonder if he had pushed the law of averages too far.

But percentages are so unfairlike the law of averages, which does not prevent a coin from turning up heads nine times in a row.

Bearing in mind the millions of Scandinavians, Germans, French, and British who pour into Spain each spring and summer, and since the law of averages must provide that a certain percentage of them are up to no good, the authorities have quite a lot to put up with.

The law of averages dictates that Wraxilan should have been killed a hundred times over back in Megalithica.

The average human activity in Africa was dying, or so I perceived it then, and to be spared in this situation abrogated at least the law of averages, if not other, more consequential laws.

By the law of averages it simply is not possible in any sizeable group of women taken at random, for more than twenty-five per cent of them to be in the same stage of pregnancy at the same time.

We played piquet day after day in Malta, and throughout the whole period the law of averages was suspended in my favour.