Tools
How to Size a Position on Gold: 5 Steps With Real Numbers
How to size a position on gold to the risk you can afford: a five-step routine, worked numbers on a $2,400 account and the traps that turn 1% into 10%.
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Read more →Lesson 04 of 8 · Risk and Money Management
Expectancy: What Your Edge Is Worth
20 min4 topics
Topic 1 of 4
By the end of this lesson
- Calculate expectancy from win rate and average win and loss
- Convert expectancy per trade into expectancy per month
- Say why a positive expectancy can still ruin an account
Before this lesson
Expectancy is the average result of one trade, repeated. It is the number that decides whether a strategy makes money, and it is unimpressed by how any individual trade felt. It is also routinely trusted far too early, on far too few trades — which is the second half of this lesson.
The formula
Two equivalent versions. Use the first if you keep results in money, the second if you keep them in R — and after the previous lesson, you keep them in R.
Expectancy = (win rate x average win) - (loss rate x average loss)
What each variable means:
- win rate — Winning trades divided by all trades, as a decimal
- average win — Mean profit on winners, after costs
- average loss — Mean loss on losers, after costs, as a positive number
Expectancy in R = (win rate x average win in R) - loss rate
What each variable means:
- loss rate — Losers cost 1R each by construction, so the term is just the loss rate
A worked example
Sixty trades: 24 winners averaging +$180, 36 losers averaging −$100.
| Win rate | 24 / 60 = 40% |
| Average win | $180 |
| Average loss | $100 |
| Expectancy | (0.40 x $180) − (0.60 x $100) = $72 − $60 = +$12 |
| Same thing in R | (0.40 x 1.8R) − 0.60 = +0.12R |
Twelve dollars a trade, from a method that loses three times out of five. That is what a real edge usually looks like: small, positive, and unrecognisable from inside any individual week.
Note
Costs must already be inside the averages. Spread, commission and swap come out of every trade, and an expectancy computed on gross results is the most common way a losing system passes this test.
Per trade and per month
Per-trade expectancy says nothing about how fast the account grows. For that you need the second number: how many trades you actually take.
Expected return per month = expectancy in R x risk per trade x trades per month
What each variable means:
- expectancy in R — From your own results, after costs
- risk per trade — As a percentage of balance — 1% in these examples
- trades per month — Counted, not hoped for
| Expectancy | Trades per month | At 1% risk | Over a year, compounded |
|---|---|---|---|
| +0.20R | 20 | +4.0% per month | About +60% |
| +0.20R | 40 | +8.0% per month | About +152% |
| +0.05R | 40 | +2.0% per month | About +27% |
Two things follow. Frequency is a lever as real as edge — the same +0.20R doubles its monthly return when the trade count doubles. And a small edge traded often beats a large edge traded rarely, which is why the discipline of taking every valid setup matters more than it feels like it should.
Caution
The lever runs both ways. Trading more often than your method produces valid setups does not raise the trade count at the same expectancy — it lowers the expectancy, usually below zero. Frequency only helps when the extra trades are the same trades.
Sample size before you trust it
Expectancy computed from twenty trades is close to meaningless. The reason is that the number is dominated by the tails, and twenty trades is not enough for the tails to show up in their true proportion.
- Under 30 trades: noise. A single large winner can turn a losing system positive.
- 30 to 100 trades: a hint. Worth looking at; not worth sizing up on.
- 100 to 300 trades: meaningful, for a system with a win rate near 50%.
- Low win rate systems need more. A 25% win-rate method needs several hundred trades before the winners have arrived in anything like their long-run frequency.
There is a simple sanity check that costs nothing: remove your single best trade and recompute. If the expectancy goes negative, you do not have an edge — you have one lucky trade and a sample too small to hide it.
Good to know
Conditions matter as much as count. A hundred trades taken in one trending quarter measures the quarter, not the method. Expectancy becomes trustworthy when the sample spans conditions the strategy will meet again.
Why positive expectancy is not enough
Expectancy describes the long run. Accounts live in the short run, and the short run can end them before the long run arrives.
- It is an average and says nothing about the path. A +0.20R system will still produce eight-loss streaks. It does not tell you when.
- It ignores position size. The same expectancy at 1% per trade compounds steadily; at 10% per trade it has a real chance of ruin first. The next two lessons are entirely about this gap.
- It assumes the edge persists. Expectancy is measured backwards. Markets change, spreads change, and the regime a method was fitted to ends.
- It assumes you keep executing. An expectancy you abandon after four losses is not your expectancy; the results of the trades you actually took are.
What to do with the number
Treat expectancy as a screening tool, not a promise. It answers one question cleanly — is this worth trading at all? — and hands everything else to sizing.
A positive expectancy is the ticket to the next two lessons. Drawdown decides how much of the ride you have to sit through, and risk of ruin decides whether you are still in the seat when the average arrives.
Key takeaways
- Expectancy = (win rate x average win) − (loss rate x average loss), with all costs already inside the averages.
- Multiply by risk per trade and trades per month to get expected growth — frequency is as real a lever as edge.
- Under 100 trades the number is mostly noise; remove your best trade and recompute as a sanity check.
- Positive expectancy says a method is worth trading. It says nothing about surviving the path, which is what sizing is for.