Risk to Reward Ratio, Win Rate and Expectancy: The Math Every Trader Needs
Risk to reward and win rate only matter together. Learn the expectancy formula, break even win rates, and what a daily loss limit does to them.
Risk to reward ratio compares what a trade can make with what it can lose, and win rate is how often you win. Neither tells you anything alone. Expectancy combines them into the average result per trade, which decides whether a method makes or loses money over time. Below are the formulas, worked examples, a break even table, and what a prop firm daily loss limit does to the picture.
Key takeaways
- Expectancy is the win rate times the average win, less the loss rate times the average loss.
- The break even win rate for a reward of R times your risk is 1 ÷ (1 + R), before costs.
- Costs raise your break even win rate, most of all with tight stops and frequent trades.
- A daily loss limit leaves each trade’s expectancy alone, but caps how many trades you get and how bad a day can be.
What is risk to reward ratio?
Risk is the distance from entry to stop, in money. Reward is the distance from entry to target. A trade risking $100 to make $200 has a reward to risk of 2, often written 1:2 or 2R.
Using R as a unit lets you compare trades of different sizes. A $250 win on $125 of risk is a 2R win, the same as a $500 win on $250 of risk. It also makes your journal honest about size changes.
Planned and actual are different. If you move targets, exit early or get slippage, your real average win and loss will differ from the plan. Always calculate from your journal, not your intentions. Our guide to journaling trades shows how to log R on every trade.
Win rate and expectancy: the formula
Expectancy per trade = (win rate × average win) − (loss rate × average loss)
The loss rate is one minus the win rate. Treat scratch trades consistently: either count them as small wins and losses, or leave them out of both.
Worked example: three traders
Example figures:
| Trader | Win rate | Average win | Average loss | Expectancy per trade |
|---|---|---|---|---|
| A | 40% | $300 | $150 | $30 |
| B | 60% | $100 | $150 | $0 |
| C | 70% | $80 | $200 | A $4 loss |
Trader A: 0.40 × $300 = $120, and 0.60 × $150 = $90. Then $120 minus $90 gives $30 per trade. In R, that is 0.4 × 2R minus 0.6 × 1R, or 0.2R per trade.
Trader B wins 60% of the time and makes nothing on average: 0.60 × $100 = $60, and 0.40 × $150 = $60. Trader C wins 70% of the time and still loses $4 per trade. Here 0.70 × $80 = $56, but 0.30 × $200 = $60. The average loss is two and a half times the average win. A high win rate feels good. Expectancy does not care how it feels.
Break even win rates by reward to risk
Break even win rate = 1 ÷ (1 + R)
| Reward to risk (R) | Break even win rate, before costs |
|---|---|
| 0.5 | 66.7% |
| 1 | 50.0% |
| 1.5 | 40.0% |
| 2 | 33.3% |
| 3 | 25.0% |
| 4 | 20.0% |
Bigger targets lower the bar, but they are hit less often. Moving a target from 1R to 3R does not keep your win rate the same. The only way to know the real trade off for your setup is to test both versions.
Costs move the break even point
Break even win rate with costs = average loss ÷ (average win + average loss)
Example figures: $100 of risk, a 2R target, and $10 of round trip costs for commission and typical slippage. A win nets $200 minus $10, or $190. A loss costs $100 plus $10, or $110. The break even win rate is $110 ÷ ($190 + $110) = $110 ÷ $300 = 36.7%, up from 33.3% before costs.
Now tighten the stop and trade more contracts for the same $100 of risk. Commission is charged per contract, so say costs rise to $25. A win nets $175, a loss costs $125, and the break even rises to $125 ÷ $300 = 41.7%.
How a daily loss limit changes the math
Expectancy is a long run average. A prop challenge is a short run with hard limits, and those limits care about streaks.
If trades are independent, the chance that a given run of trades are all losers is the loss rate multiplied by itself. Example figures with a 40% win rate, so a 60% loss rate:
| Trades in the run | Chance all of them lose |
|---|---|
| 2 | 36.0% |
| 4 | 13.0% |
| 6 | 4.7% |
| 8 | 1.7% |
Over a long challenge you take many such runs, so a streak of four losses is very likely at some point. Now apply a $1,000 daily loss limit. At $250 per trade, four losses end the day. At $125 per trade it takes eight losses to reach the limit, and a personal daily stop would end the day well before that.
Stopping for the day does not change the expectancy of each trade, if your trades are independent. It changes how many trades you take and how big your worst day can get. That is the deal a prop trader makes: fewer trades, but the account survives.
From expectancy to days to target
Example figures: an expectancy of $30 per trade and three trades a day averages $90 a day. A $3,000 profit target then takes about 33 trading days on average, before the normal swings in real results. If that is longer than the time allowed, or you would need triple the size to fit, the account does not suit the method.
How this fits prop firm rules
- Daily loss limit: sets how many losses in a row you can take in one day. See daily loss limits explained.
- Maximum drawdown: sets how many losses in a row you can take overall. Divide it by your risk per trade.
- Consistency rules: a low win rate with large winners can produce one dominant day, which some consistency rules penalize. See the consistency rule guide.
- Minimum days and time limits: expectancy per day tells you whether the target is reachable in the time allowed.
Rules vary by firm; check each firm’s page in the prop firm directory, or filter accounts by rules and budget with find an account.
Questions traders ask
What is a good risk to reward ratio?
There is no single good ratio. A 1:1 ratio needs a win rate above 50% after costs, while a 1:3 ratio needs one above 25%. What matters is positive expectancy after costs.
Can a 30% win rate be profitable?
Yes, if the average win is big enough. With 3R winners and 1R losers, a 30% win rate gives 0.3 × 3 minus 0.7 × 1, or 0.2R per trade before costs.
Should I calculate expectancy in dollars or in R?
Use R to compare setups and dollars to plan against prop firm limits. R hides changes in size, so convert back to dollars before you check a daily loss limit.
Trading carries a high risk of loss, and a positive expectancy in a test does not guarantee future results. Most prop firm accounts are simulated. All figures here are examples, and nothing here is financial advice.