Risk-Reward Ratio Calculator: Trade Expectancy Formula
Calculate risk-reward ratios and trade expectancy to evaluate trading strategy viability. Understand win rate vs risk-reward trade-offs and optimal R:R ratios.
Risk-Reward Ratio Calculator: Trade Expectancy Formula
My neighbor Tom called himself a "trader" for about six months. He'd pick stocks based on gut feeling, never once calculated a risk-reward ratio, and blew through $3,000 before he realized he'd been gambling, not trading. When I finally showed him the expectancy formula, he went quiet. Turns out his strategy had negative expectancy from day one.
The risk-reward ratio is the backbone of rational trading. Combine it with win rate analysis through the expectancy formula, and you've got a powerful framework for figuring out whether your strategy actually makes money—or just feels like it does.
Photo by Maxim Hopman on Unsplash
The Expectancy Formula
Expectancy tells you your average profit (or loss) per trade, factoring in both wins and losses:
Expectancy = (Win% × Average Win) − (Loss% × Average Loss)
Or as a risk-reward multiple:
Expectancy = (Win% × R) − (1 − Win%)
Where R is your risk-reward ratio. Positive expectancy? Your strategy prints money over time. Negative? You're bleeding slowly.
Risk-Reward Ratio Calculation
The ratio compares potential profit to potential loss:
R:R = Potential Reward / Potential Risk
Example:
Entry at $100, stop loss at $95 (risk: $5), take profit at $115 (reward: $15).
R:R = $15 / $5 = 3:1. For every dollar risked, you stand to make three.
The Win Rate vs R:R Trade-Off
Here's the beauty of the math: there's a clear trade-off between how often you need to win and how much you make per win.
Break-Even Win Rate = 1 / (1 + R)
- R:R = 1:1 → You need to win 50% to break even
- R:R = 2:1 → Just 33%
- R:R = 3:1 → Only 25%
- R:R = 0.5:1 → You'd better win 67%+ of the time
A 2:1 strategy only needs to win a third of the time to break even. Every percentage point above that is pure profit.
Optimal R:R Ratio Analysis
There's no universal "best" R:R—it depends on your edge and trading style.
High R:R (3:1 or higher):
You win less often but each win is chunky. Trend-following strategies often land here. Brace yourself for losing streaks.
Moderate R:R (1.5:1 to 2:1):
The sweet spot for many systematic traders. Balanced win rate requirement, plenty of flexibility in trade management.
Low R:R (1:1 or lower):
High win rate required. Common in scalping and high-frequency strategies, where transaction costs eat into thin margins.
Expectancy Calculation Example
Let's crunch the numbers:
- Win rate: 45%
- Average win: $300
- Average loss: $150
- R:R: 2:1
Expectancy = (0.45 × 2) − 0.55 = 0.35R per trade
That means each trade earns 0.35× your risk amount on average. Over 1,000 trades at $100 risk each, that's roughly $35,000 in expected profit.
Position Sizing Implications
Expectancy directly feeds into how much you should risk per trade.
Kelly Criterion:
Kelly % = W − [(1−W)/R]
For the example above: Kelly % = 0.45 − (0.55/2) = 17.5%
Sounds great—risk 17.5% per trade for maximum growth! But most practitioners use fractional Kelly (1/4 to 1/2) to dial down the volatility. Full Kelly is a rollercoaster nobody needs.
Realistic Expectancy Calculations
Raw expectancy is the fantasy. Net expectancy is reality.
Net Expectancy = Gross Expectancy − Transaction Costs
Example:
Gross expectancy: 0.35R
Commission: 0.05R
Slippage: 0.02R
Net expectancy: 0.28R
Transaction costs are brutal for high-frequency, low R:R strategies—watch them closely.
Common Mistakes in R:R Analysis
Ignoring Win Rate: Setting arbitrary R:R targets without knowing your actual performance.
Curve Fitting: Optimizing on historical data that won't repeat.
Emotional Adjustments: Abandoning a winning R:R after a few losses.
Ignoring Sample Size: Drawing big conclusions from a handful of trades. Stats need volume.
Risk-Reward in Different Markets
Forex: 1:1 to 2:1 for intraday, higher for swing trades.
Stocks: 2:1 to 3:1 for swing trades, higher for position trades.
Options: All over the map depending on strategy.
Futures: Often 1:1 to 2:1 for day trading.
Strategy Evaluation Framework
When vetting any strategy:
Conclusion
The expectancy formula and risk-reward ratio give you the math behind profitable trading. Nail the relationship between win rates and R:R, and you can build strategies with genuine long-term edge—not just stories you tell yourself after a winning streak.