Expectancy
Also called: expectancy, expected value per trade, average trade, edge per trade.
Formula
Expectancy = (Hit rate x Average win) - ((1 - Hit rate) x Average loss) - Cost per round trip.
How it is read
Expectancy is the one number that combines everything else on this subject. It is where three things meet: the hit rate, the size of a win against the size of a loss, and the charge stack. Reading it is mostly about the sign. A sequence with a negative expectancy does not become positive through more activity. It does not become positive through better discipline about entries either. A larger position does not do it either. All of those multiply the same average. So the whole question is establishing the sign, with enough observations to know it.
What it does not tell you
Expectancy is an average. It therefore says nothing about the order outcomes arrive in. A positive one can still produce a long losing run. That run can end an account before the average asserts itself. It is also only as good as the inputs. Take a hit rate from a small sample. Or take an average win measured on marks rather than on prices actually filled. Either one produces an expectancy that is precise and wrong. It is computed on the past, which does not commit the future to anything.
Related concepts
Break-Even Hit Rate: How Often You Have to Be Right to Stand Still
If wins and losses are the same size, and every trade costs the same to place, the fraction that must be right just to stand still is fixed by arithmetic. With no costs at all it is 50%. Every rupee of cost pushes it above 50%. The smaller the bracket, the harder it pushes. A cost equal to a fifth of the bracket needs 60%, a huge difference in how good a decision process has to be.
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