Key takeaways
- Win rate and reward-to-risk only make sense together; expectancy combines them.
- Measure results in R so trades of different size and market can be compared.
- The break-even win rate is 1 ÷ (1 + ratio): 50% at 1:1 and about 33% at 2:1, before costs.
- Costs raise the break-even rate, most of all for tight stops.
- Small samples are noisy; 30 trades rarely prove or disprove a method.
A strategy that wins six trades in ten sounds impressive, and one that wins three in ten sounds hopeless. Neither description says whether money is made or lost. That depends on how much you gain on winners, how much you lose on losers and how often each happens. Expectancy is the single number that combines all three.
Thinking in R instead of money
Start by defining 1R as the amount you lose if a trade hits its stop. If you risk 50 on a trade and it stops out, that is -1R. If it closes with a profit of 100, that is +2R. Measuring in R strips away account size, lot size and currency, so a trade on a currency pair and a trade on a share can sit in the same list and be compared fairly.
The reward-to-risk ratio (often written 1:2 or 2R) is simply the planned profit divided by the planned loss. It is a plan on paper. The realised average win and average loss, taken from many trades, are what actually count.
The expectancy formula
Expectancy is the average result per trade, in R. Multiply the win rate by the average win, multiply the loss rate by the average loss, and subtract the second from the first. In symbols: expectancy = (win rate × average win) − (loss rate × average loss). A positive number means the method made money on average over the sample you measured. A negative one means it lost.
The table below compares three imaginary methods. All figures are illustrative and not drawn from any real strategy.
| Method | Win rate | Average win | Average loss | Expectancy per trade |
|---|---|---|---|---|
| A: frequent small wins | 60% | 0.5R | 1R | -0.10R |
| B: rare large wins | 35% | 3R | 1R | +0.40R |
| C: balanced | 45% | 1.5R | 1R | +0.125R |
Method A wins most of the time and still loses: 0.6 × 0.5 = 0.30, but 0.4 × 1 = 0.40, so it gives back 0.10R each trade. Method B loses nearly two trades in three and still earns: 0.35 × 3 = 1.05 against 0.65 lost. If you risked 1% of the account per trade, 100 trades of A would be expected to cost about 10% before compounding effects, and 100 trades of B would be expected to add about 40%. Real results scatter widely around those averages, so treat them as long-run tendencies and never as forecasts.
The break-even win rate for any ratio
You can turn the formula around and ask how often you must win to merely break even. The answer is 1 ÷ (1 + reward-to-risk), ignoring costs. At 1:1 you need to win half the time. At 2:1 you need to win one trade in three. The bars below show the pattern.
Calculated from 1 ÷ (1 + ratio), ignoring costs. Illustrative of the arithmetic, not a target.
Notice the catch. A wider target is not free: the further away it is, the less often price reaches it. Ratio and win rate are linked, which is why quoting either one alone says little. Stretching a 2R target to 4R lowers the break-even rate to 20%, but if the hit rate drops from 40% to 15% in the process, expectancy goes from +0.2R to -0.25R.
Costs shift both sides of the ratio
Spreads, commissions and slippage reduce every win and enlarge every loss. Suppose your stop is 20 pips away and your target is 40 pips, a planned 2:1. If the round-trip cost is 2 pips, a winner nets 38 pips and a loser costs 22 pips. The real ratio is 38 ÷ 22 = about 1.73, and the break-even win rate rises from 33.3% to 22 ÷ (38 + 22) = about 36.7%.
How many trades before the number means anything?
Expectancy measured on 20 or 30 trades is mostly noise. Take Method B: each trade is either +3R (35% of the time) or -1R (65%). The true average is +0.40R, but the standard deviation of a single outcome is about 1.9R. Over 30 trades the typical error in the measured average is roughly 1.9 ÷ √30 = 0.35R, almost as large as the edge itself. Over 100 trades it shrinks to about 0.19R.
In plain terms, a run of 30 trades can show a positive result for a method with no edge, or a negative one for a method that has one. This is why traders lean on larger samples, on out-of-sample tests, and on the logic behind a method, not on a short hot streak.
A quick expectancy audit of your own trades
- Record every trade in R. Use the planned stop to define 1R, then log each result as a multiple of it. Include partial exits and the cost of each trade.Tip: Skipping the awkward trades makes every number that follows look better than it was.
- Compute the three inputs. Count wins and losses to get the win rate, then average the winners and the losers separately.
- Apply the formula. Multiply, subtract, and look at the sign and size of the result. Compare it with the typical error for your sample size.
- Split by setup or market. If one setup carries all the profit and another all the losses, the blended figure hides it. Only split when each group still has a meaningful number of trades.
- Review the stop and target. Check whether the average loss is close to 1R. If losses regularly exceed 1R through slippage or moved stops, your real ratio is worse than the plan.
Frequently asked questions
Is a higher reward-to-risk ratio always better?
No. A wider target is reached less often, so the win rate usually falls as the ratio rises. What matters is the product of the two after costs, measured over enough trades.
What is a good expectancy number?
There is no universal threshold. Anything above zero after realistic costs is positive, but small values are fragile because estimation error and cost changes can erase them. Treat the figure as a diagnostic, not a goal.
Can I use expectancy for investing in shares or ETFs?
The arithmetic is the same, but long-term investors rarely use fixed stops, so R is harder to define. Many measure outcomes per holding or per rebalancing period instead.
Should I move my stop to protect profits and improve the ratio?
Moving stops changes the distribution of outcomes: it cuts some losses but also ends winning trades early. Test the effect on your own record in R before assuming it helps.