Here's an article by Chris Perruna on position sizing and expectation

How do we Calculate Position Size?

We can determine how much to place on each trade by assuming a $100,000 account with 1% risk on each position. Using a basic trading approach, I will place my stops approximately 8% below the ideal entry area or pivot point.

Please use more advanced methods for locating the ideal stop rather than a general 8% (I am doing this for example purposes only). Look for the ideal risk-to-reward setup based on recent support and resistance levels and set your stop and potential target accordingly.

$100,000 Account
1% Risk = $1,000
8% Stop Loss
Position Size will be $12,500

We calculate the position size by dividing the 1% risk by the 8% stop loss or $1000 / 8% = $12,500.

If the stock we are watching has an ideal entry of $50, we now know that we can buy 250 shares or $12,500 worth of stock. Our stop loss is $46 or 8% of $50 and our maximum loss is $1,000 of the original $100,000 portfolio.

What exactly is expectancy?

Expectancy tells you what you can expect to make (win or lose) for every dollar risked. Casinos make money because the expectancy of every one of their games is in their favor. Play long enough and you are expected to lose and they are expected to win because the “odds” are in their favor. Most games at a casino are completed in a short period of time so they can increase their odds of winning.

The same holds true for trading. If your expectancy is positive; you can make money with a certain number of trades within specified periods of time.

Expectancy is your profit percentage per win multiplied by your win rate minus your loss percentage per loss multiplied by your loss rate. I will use an example of Expectancy from Dr. Van K. Tharp’s Book: Trade your way to Financial Freedom:

Expectancy = (Probability of Win * Average Win) - (Probability of Loss * Average Loss) Expectancy = (PW*AW) less (PL*AL)

PW is the probability of winning and PL is the probability of losing.

AW is the average gain (win) and AL is the average loss

So let’s do an example using another basic approach (assume $12,500 per position, a $100,000 portfolio using 1% equity risk):
If my trades are successful 40% of the time and I realize an average profit of 20% but I lose an average of 5%, my expectancy is $625 per trade.

(0.4 * $2,500) - (0.6 * $625) = $1,000-$375 = $625

I lose 60% of the time yet I show a profit of $625 per trade. If I have a system that produces 65 trades per year, I would realize an annual gain of $40,625 (hypothetical scenario). A 40% gain on the original $100,000 (minus all commissions, fees, taxes and compounding).

Let’s look at the calculation one more time using only percentages:
PW: 40%
AW: 20%
PL: 60%
AL: 5%
(40% * 20%) - (60% * 5%) = 5.00%

What this tells me is that I have a positive expectancy of 5% or $625 per trade from the original $12,500. It doesn’t mean that I will make $625 on every single trade but my system will average a profit of $625 per trade over the course of a year with a combination of winners and losers. I can always make more trades or fewer trades in a year so my total profit will be adjusted accordingly.