Q: When comparing systems, I understand the concept of Expectancy, but I must have missed something related to selecting stock trading. It is this: the ratio of 1R to the price of the stock has to have a big impact on the profit of a trade. Let me explain.

Take two positions - traded by the same system/process.

1) Stock 1

Current Price $10. 1R = $1 with a system expectancy of 1.25R.
Using a position sizing model of 0.5% of asset base, let's say that was $5,000.
That means my risk is $5,000 - and if 1R = $1 I can buy 5,000 shares @ $10 each = $50,000 allocated in this position.
Now let us say that this particular trade resulted in a 2R gain (with a long term expectancy of 1.25R).
That is we sold the stock for $12 give us a gain of $2 x 5,000 = $10,000. We has allocated $50,000 on this position so our profit was 10,000/50,000 = 20%.

2) Stock 2

Current Price $4. 1R = $1 with a system expectancy of 1.25R.
Using a position sizing model of 0.5% of asset base, let's say that was $5,000.
That means my risk is $5,000 - and if 1R = $1 I can buy 5,000 shares @ $4 each = $20,000 allocated in this position.
Now let us say that this particular trade resulted in a 2R gain (with a long term expectancy of 1.25R).
That is we sold the stock for $6 give us a gain of $2 x 5,000 = $10,000. We has allocated $20,000 on this position so our profit was 10,000/40,000 = 50%.
Clearly 50% return is better than 20% return. Yet both have the same expectancy, the same R multiple distribution. But clearly the price of the stock related to the size of 1R is important.

I am missing something basic. What have I missed in your teachings? (Probably heaps because I am just a beginner!)

A: My account has $500,000 in it and I want to risk 1% or $5000.
In the first scenario with the $10 stock, you are up 2R or $10,000. 2R is a 2% gain.
In the second scenario with the $4 stock, you are up 2 R or $10,000. 2R is a 2% gain.
You were looking at the amount invested rather than the risk or the size of your portfolio. The amount invested has nothing do to with anything except to determine your worst case loss.