# Mathematics of trading & Expectancy Curve

The issue we have is that our society naturally rewards those who do well. High School students with the best marks become eligible for the better university degrees. A better university degree enables better job prospects and potentially a higher income in the workforce and therefore potential for a higher standard of living. Unfortunately when it comes to the markets the same is not always true. In fact pursuing that same logic in the market can cause severe frustration and disappointment. A trader / investor who makes ten trades and gets eight correct can mathematically still lose.

An edge is the outcome, the mathematical outcome, of the buying and selling process. All successful traders / investors create a positive edge.

There are three factors to consider when determining if your edge will be a success:

1. How much you win when you win
2. How much you lose when you lose
3. How often you win

We can combine 1 and 2 and call the resultant number the win/loss ratio.

The larger that win/loss ratio grows, the higher your profitability will be and the less important the win rate becomes. Unfortunately the win rate is where most novices, and indeed many experienced market professionals, come unstuck. It is human nature to think that a high winning percentage of transactions equates to higher profits.

The Expectancy Curve shows an important yet consistent relationship between the winning percentage and the win/loss ratio; moreover it shows the point at which a strategy will move from a losing proposition to a profitable proposition. It must be understood that these two statistics move in a converse manner: when one moves higher, the other moves lower. A trader wanting a higher percentage win rate will forego a high win/loss ratio.

Successful trading &  investing comes down to how much you win when you win and how much you lose when you lose.