From Wikipedia, the free encyclopedia.
The law of averages is a common statistal fallacy. It results from an intuitive misunderstanding of the law of large numbers.
The law of large numbers states that a large sample of a particular probabilistic event will tend to reflect the underlying probabilities. For example, after tossing a "fair coin" 1000 times, we would expect the result to be approximately 500 heads results, because this would reflect the underlying .5 chance of a heads result for any given flip.
However, it is important that while the average will move closer to the underlying probability, in absolute terms deviation from the expected value will increase. For example, after 1000 coin flips, we might see 520 heads. After 10,000 flips, we might then see 5096 heads. The average has now moved closer to the underlying .5, from .52 to .5096. However, the absolute deviation from the expected number of heads has gone up from 20 to 96.
There are two common ways to misunderstand and misapply the law of large numbers:
- "If I flip this coin 1000 times, I will get 500 heads results." False. While we expect approximately 500 heads, it is not the case that we will always get exactly 500 heads results. Similarly, getting 520 heads results is not conclusive proof that the coin's true probability of getting heads on a single flip is .52
- "I just got 5 tails in a row. My chances of getting heads must be very good now." False. Many probabilistic events are independent of one another, which means the result of one event does not in any way influence the outcome of another. Coin flips are independent events. The coin does not "remember" what it has flipped previously and self-adjust to get an overall average result. The coin is not "due" for a heads. The probability remains .5 for each individual flip. A belief in this fallacy can be devastating for amateur gamblers. The thought that "I have to win soon now, because I've been losing and it has to even out" can encourage a gambler to continue to bet more than they can afford.
