Before we talk about lowering the waves and moving forward…
Let's take a short detour and talk about the Law of Large Numbers. We've already brought up "large numbers" twice in the discussion of probabilistic thinking, so we can't really move on without addressing it.
The Law of Large Numbers is simple:
If you repeat the same random event, independently, its average outcome gets closer to the expected value of that random event.
Let's take an example.
Suppose you have a trading strategy with an expected return of +0.2R per trade. After ten trades, the actual average could be -0.5R. But after a thousand trades, the probability that the average will be close to +0.2R becomes very high.
There is an important point here.
The average you get after a thousand or even ten thousand trades is itself a random event.
It does not become exactly 0.2R. It is a random outcome that becomes increasingly likely to be close to 0.2R.
That raises an interesting question.
A single trade is a random event, and the average outcome of many trades is also a random event. So what has actually changed?
The expected value is the same: +0.2R. What has changed is the variance.
How far the outcome can deviate from the average has changed.
The outcome of a single trade has high variance, so there is a lot of room for luck. But as we average over more and more trades, the variance of that average decreases, leaving less and less room for luck to dominate.
There is one more point worth remembering. From the outcome of a single trade, you can learn almost nothing about the expected value of the strategy. But as you repeat the trade many times, the expected value begins to reveal itself.
Now it should be clear to anyone paying attention why the Law of Large Numbers had to be mentioned before we talk about lowering the waves. And, from the perspective of building a trading strategy, why the Law of Large Numbers is so important.
— To be continued —
This is educational writing about trading. It is not investment advice or a recommendation to make any particular trade.