law of averages

from The American Heritage® Dictionary of the English Language, 5th Edition.

• noun The principle holding that the relative frequency with which an event occurs in repeated trials will converge to a stable value over time as the number of samples increases.

from Wiktionary, Creative Commons Attribution/Share-Alike License.

• noun statistics 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.
• noun informal An imaginary or perceived "law" of probabilities which is wrongly used to predict results in the short-term.

from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.

• noun a law affirming that in the long run probabilities will determine performance