Ready to go further
Next: convert expectancy into a target
The risk to reward calculator shows how large winners must be, compared with losers, for a given win rate to break even.
What is included
- What it is, in plain words
- The formula or mechanism, with exact arithmetic
- How it hits grid, martingale and DCA bots
- A check you can run before you switch a bot on
Who it is for
- People who run or plan to run a trading bot
- Anyone reading a backtest or a bot sales page
- Readers who want the numbers, not the pitch
- Not advice, and not a signal service
Key facts
- Expectancy is the average result per trade, measured in R. One R is the amount you risk on a trade, so a trade that reaches its stop loses 1R.
- Expectancy = win rate x average win in R - loss rate x average loss in R. If stops hold, the average loss is 1R by definition.
- Three made-up strategies below have win rates of 80%, 40% and 30%. The first two have the same expectancy (+0.20R), the third is much lower (+0.05R).
- It is the same idea as expected value, written in R instead of dollars, which makes strategies of different size comparable.
- It needs many trades to estimate, and it only means something after spread, commission and slippage.
What expectancy is
Every strategy has an average result per trade. In dollars it is called expected value (see the expected value calculator). In R multiples it is called expectancy, and it is the same quantity measured in a different unit.
R is the amount you risk on one trade. If you risk $50, then R is $50. A trade that makes $100 is +2R. A trade that is stopped out for $50 is -1R. Measuring in R removes the size of the account. A $500 account and a $50,000 account with the same rules have the same expectancy.
If stops hold, average loss = 1R, so Expectancy = (win rate x average win in R) - loss rate
A positive expectancy means that, over many trades, the average trade adds to the account. A negative one means it takes away. Zero means the strategy only moves with luck and pays costs on the way.
A worked example: three strategies
These three are made-up. In all of them, the average loss is 1R. Only the win rate and the size of the average win differ.
| Strategy | Win rate | Average win | Loss rate | Expectancy before costs |
|---|---|---|---|---|
| A: high win rate | 80% | 0.50R | 20% | +0.20R |
| B: low win rate | 40% | 2.00R | 60% | +0.20R |
| C: trend following | 30% | 2.50R | 70% | +0.05R |
The working for each, which you can check by hand:
- A: 0.80 x 0.5 - 0.20 x 1 = 0.40 - 0.20 = +0.20R. It wins four times in five and each win is small.
- B: 0.40 x 2.0 - 0.60 x 1 = 0.80 - 0.60 = +0.20R. It loses more often than it wins, with wins twice the size of losses.
- C: 0.30 x 2.5 - 0.70 x 1 = 0.75 - 0.70 = +0.05R. Trend following often looks like this: a low win rate, big winners, long periods of small losses.
A and B have completely different feels. One wins 80 percent of the time and the other loses 60 percent of the time. Their expectancy is the same. Win rate alone told you nothing about which is better, which is why a bot advertised by its win rate has not been described yet. C looks reasonable at 30 percent wins and 2.5R winners, and it is worth only +0.05R per trade, a quarter of A or B.
Why it must be net of costs
The numbers above ignore costs. A real trade pays spread, commission and slippage, each of which is a loss on every trade whatever happens. Convert them to R by dividing by the dollars at risk. Suppose all three strategies pay 0.05R per trade:
| Strategy | Before costs | Cost per trade | After costs | Per 100 trades |
|---|---|---|---|---|
| A: high win rate | +0.20R | -0.05R | +0.15R | +15R |
| B: low win rate | +0.20R | -0.05R | +0.15R | +15R |
| C: trend following | +0.05R | -0.05R | 0.00R | +0R |
A and B keep +0.15R each. C drops from +0.05R to 0.00R, which is zero. The same cost that took a quarter of A's edge took all of C's. Costs matter most when expectancy is small, which is exactly when bots advertise a high trade count.
Why it needs enough trades
Expectancy is an average of random results. With few trades, the average wanders. The spread of single trades is the standard deviation, and the uncertainty in the average is about that standard deviation divided by the square root of the number of trades. For the three strategies above, calculated by us on 27 Oct 2026, exact:
| Strategy | Standard deviation of one trade | Uncertainty after 100 trades | Uncertainty after 400 trades | True expectancy |
|---|---|---|---|---|
| A: high win rate | 0.60R | +/- 0.06R | +/- 0.03R | +0.20R |
| B: low win rate | 1.47R | +/- 0.15R | +/- 0.07R | +0.20R |
| C: trend following | 1.60R | +/- 0.16R | +/- 0.08R | +0.05R |
Strategy C has a true expectancy of +0.05R, but after 100 trades the measured average could easily be -0.27R or +0.37R (roughly two standard errors either side). A hundred trades cannot tell C from zero. Even after 400 trades the range is -0.11R to +0.21R. Small edges need very many trades. See the win rate calculator for the same idea applied to win rate.
Also, the average loss is only 1R if stops hold. A stop that slips, a gap, or a bot with no stop breaks the assumption. The average loss of a martingale or grid bot is often much larger than 1R once its worst case is counted, which is why its expectancy cannot be read from the win rate.
How it hits bots
- Grid and martingale bots look like strategy A taken to the extreme: a win rate of 90 percent or more, with a very small average win. The average loss is not 1R. When it comes, it is a stack of positions closed together, and it can be dozens of times the average win. Include it in the average and the expectancy can be negative while the win rate looks excellent.
- DCA bots have no fixed R, because there is no stop. Define the amount at risk as the capital committed, or the loss you decided to accept, and compute from that.
- EAs are often reported with profit factor and win rate. Ask for average win and average loss, and compute expectancy yourself.
How to check it before running a bot
- Get the trade list, not the summary. Compute win rate, average win and average loss, in R if possible.
- Use the largest losses honestly. If the worst loss is 12R, it belongs in the average loss.
- Subtract realistic costs per trade in R.
- Count the trades. Fewer than a few hundred means a wide uncertainty.
- Compare backtest and forward-test expectancy.
What it does not tell you
Expectancy is an average. It says nothing about the order of results, the longest losing run, or the worst drawdown. Two strategies with the same expectancy can have very different runs of losses. It also assumes the future looks like the sample. Use it to say whether a strategy has an edge on paper, then look at drawdown and margin to say whether you can survive running it.
Keep Going
Related Tools and Guides
Keep exploring
FAQ
Frequently Asked Questions
What is the difference between expectancy and expected value?
They are the same idea. Expected value is usually in money per trade, and expectancy is in R, a multiple of the amount risked. R lets you compare strategies and account sizes on one scale.
What is a good expectancy?
Anything above zero after costs is positive, but how much is useful depends on costs, trade count and drawdown. A tiny positive number is easily erased by a wider spread. Check how it holds when costs are doubled.
Can a strategy with a low win rate have a good expectancy?
Yes. If winners are large compared with losers, a win rate under 50 percent can still average positive, as strategy B shows. Trend following often works this way.
Why is my expectancy different from my backtest report?
The report may be before costs, may use a flat spread, or may show profit factor instead of average R. Recompute from the trade list with realistic costs.
Does 1R mean the same on every trade?
Only if you risk a consistent amount per trade. If size varies, R varies, and you should record R per trade using the amount actually at risk on each one.
Are the numbers on this page real?
Example numbers are made up to show how the maths works, and the page says so. A figure only counts as exact when the page says it was calculated on a stated date. Nothing you enter in a calculator leaves your browser.
Can I use this to decide whether to run a bot?
It can show whether a bot's numbers hold together and how much an account can lose. It cannot say what the market will do, and it is not advice. Use it to ask better questions, then read the terms of your own broker or exchange.
Is this financial advice?
No. It explains a measurement in general terms. The three strategies are made up, and the uncertainty figures are exact arithmetic on them.
Know the Risk Before You Run It
Free calculators and guides, added every week. Leave your details and we will email you when new ones go up.
Trading carries a risk of loss