Expectancy: The Number That Decides Everything
Expectancy combines win rate and reward-to-risk into the average amount you make per trade. It is the metric that predicts survival.
Win rate is the number traders brag about and the number that matters least. Expectancy combines win rate, average win, and average loss into a single figure: what you make on average per trade.
It is the closest thing trading has to a bottom line. If expectancy is positive and you survive long enough to place enough trades, you make money. If it is negative, no amount of discipline saves you.
The formula
Expectancy equals the average win multiplied by the win rate, minus the average loss multiplied by the loss rate. All figures should be net of costs, because costs are real and they are paid regardless of outcome.
If your average win is $300 with a 40% win rate, and your average loss is $150 with a 60% loss rate, expectancy is (0.4 × 300) − (0.6 × 150) = 120 − 90 = $30 per trade. Positive, and modest.
Monte Carlo Simulation
Simulation Parameters
Method: one synthetic list of 100 trades (40 wins, 60 losses) is reshuffled 1000 times. Every path holds the same trades — only the order changes. Stats use all 1000 shuffles; the chart draws 20. The trade list is synthetic and the two inputs above may be illustrative, so treat every number here as a worked example, not a forecast.
Projected Outcomes
Why a low win rate can be excellent
A trend-following strategy may win only 35% of the time and still be highly profitable, because the winners run for multiples of the risk taken. The maths works because the average win is large relative to the average loss.
This is the part that is psychologically hardest. Most people cannot tolerate losing two out of three trades, so they interfere — cutting winners early to book a win. That single intervention destroys the expectancy that made the method work.
Why a high win rate can be terrible
The mirror image is more dangerous because it feels good. A strategy that wins 90% of the time by taking tiny profits and refusing to accept losses will produce a beautiful equity curve right up until one large loss erases months of gains.
This is the structural flaw in many grid and martingale approaches. The win rate is genuinely high. The expectancy, once the distribution of losses is accounted for, is negative.
Expectancy is not destiny
A positive expectancy needs enough trades to express itself. Twenty trades is not a sample; two hundred is a start. Until you have that many, your realised result is dominated by variance, and you cannot distinguish a good method from a lucky run.
This is why the practical advice is to keep size small while you gather a statistically meaningful sample. You are buying information, not returns, and you want to still be trading when the information arrives.
Three strategies with identical trade counts and very different shapes
| High win rate | Balanced | Trend follower | |
|---|---|---|---|
| Win rate | 85% | 55% | 35% |
| Average win | $80 | $220 | $700 |
| Average loss | $400 | $180 | $150 |
| Expectancy per trade | −$4 | +$40 | +$200 |
Key takeaways
- Expectancy is average win times win rate, minus average loss times loss rate
- A 35% win rate is fine if the average win is large enough
- A 90% win rate is dangerous if the average loss is larger still
- Positive expectancy needs hundreds of trades to show up above variance
- Expectancy equals average win times win rate, minus average loss times loss rate
- A 40% win rate can be highly profitable with a large enough average win
- A 90% win rate can be catastrophic with a large enough average loss
- Costs must be subtracted before expectancy means anything
Chasing a higher win rate by cutting winners short, which lowers expectancy.
Reading is not verification
Take the concept you just read and turn it into explicit rules, then test it. That is the only way to know whether it actually works.
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