How the Law of Large Numbers Can Help Your Trading

If you are struggling to become a profitable trader, it will probably help you in your quest if you understand the law of large numbers and try to make it work in your favor.

The law of large numbers says that if the probability of something happening is X%, the result will approach closer and closer to that probability the more attempts are made.

This is best illustrated by the example of a coin flip, which has a 50% chance of landing on heads. If you flip the coin twice, you have almost exactly equal chances of any scenario happening: heads twice, tails twice, or evenly split. If you flip the coin ten thousand times and record your results, you will find that the result is very, very close to 50/50. If you keep a running score as you flip the coin more and more, you will see that the variance of the tally reduces the longer you go on. The “magic number” is close to five hundred, so if you have a profitable trading strategy, you should expect results to vary from your expectations until count about five hundred trades. If the result is relatively poor after five hundred trades, you need to question the strategy.

This is the reason why:

  1. A strategy that has a positive expectancy of 20% per trade, and generates 500 trades per month, is far better than a strategy with the same expectancy which generates only 5 trades per month, even if your position sizing is reduced proportionately.
  2. Back testing needs to be conducted with as large a sample as possible, to give realistic results.
  3. It is important to continue to trade through losing streaks if you have faith in your strategy.
  4. Your best chance of coming out ahead at the end of the month is to have taken as many good trades as possible.

Watch out for a common mistake, though – don’t try to force yourself into trades! If you can’t identify a trade set-up that you have a good reason to think has an edge, don’t start taking more trades on flimsy pretexts and assume this will give you the beneficial effects of the law of large numbers. Stick to a good trading plan with firm discipline instead and trade small.

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