# Law of Small Numbers

The law of small numbers is a fallacy that leads people to believe that a small sample size of data will be enough to resemble the normal data of the whole and determine the probabilities of future sample sizes.

In trading this error would lead someone to backtest one year’s worth of price action signals and believe that a system is valid if it is profitable. In reality, the law of large numbers more closely represents data and backtests must be done on a decade or more of price action to see how a system performed during all market environments like uptrends, downtrends, going sideways, and volatile. A small number of samples can reflect a specific time period and not show the larger picture over multiple types of time frames.

If a coin is flipped ten times it is possible for it to land on heads all ten times. However, the more times it is flipped the more the results will tend to be closer to 50% heads and 50% tails with larger numbers of flips showing the true probabilities more accurately. Smaller sample sizes tend to be more random and larger sample sizes begin to show the real probabilities and patterns.

The larger the sample size of a backtest the greater the odds of its validity. The smaller the size of data the more the chance that it is just a small snap shot and not the full picture of how a strategy will play out over time.

The law of small numbers is a fallacy that fools people with randomness and luck. The law of large numbers is the theorem that explains results approaching their average probabilities as it increases in sample size.

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