The maths of an edge
One of the most liberating realisations in trading is that you do not need to be right most of the time to make money. Profitability is the product of two numbers: how often you win (your win rate) and how much you win versus lose when you do (your risk-to-reward ratio). Get the second number working for you, and you can lose the majority of your trades and still come out ahead.
The risk-to-reward ratio compares the money you stand to lose if your stop is hit against the money you stand to gain if your target is reached. Risking 30 pips to make 60 is a 1:2 ratio; risking 30 to make 90 is 1:3. A favourable ratio means each winner more than pays for several losers.
Break-even win rates
Every risk-to-reward ratio has a break-even win rate — the percentage of trades you must win just to avoid losing money over time. The relationship is simple: break-even win rate = 1 ÷ (1 + reward/risk). At 1:1 you need to win 50% of the time. At 1:2 the figure drops to about 33%. At 1:3 it falls to just 25%. The better your ratio, the more losing trades your strategy can absorb and still be profitable.
This is exactly why disciplined traders hunt for high-quality setups with good ratios rather than chasing a high win rate. A strategy that wins 40% of the time at 1:2 is comfortably profitable; a strategy that wins 70% of the time at 1:0.5 (risking more than it makes) can quietly bleed an account dry.
Key points
- 1:1 ratio → break even by winning ~50% of trades.
- 1:2 ratio → break even by winning ~33% of trades.
- 1:3 ratio → break even by winning ~25% of trades.
- A high win rate with a poor ratio can still lose money.
Putting expectancy to work
The number that ties it all together is expectancy — the average profit or loss you can expect per trade. Expectancy = (win rate × average win) − (loss rate × average loss). Suppose you win 40% of trades, your average winner is $200 and your average loser is $100. Expectancy is (0.40 × $200) − (0.60 × $100) = $80 − $60 = $20 per trade. Over 100 trades that is roughly $2,000 of edge, even though you lost 60 of them.
Positive expectancy is the entire game. It also explains why a single trade's outcome tells you almost nothing — a good trade can lose and a bad trade can win. What matters is whether your process carries positive expectancy across a large sample, which is why traders judge themselves over dozens of trades, not one.
Key takeaways
Profitability comes from the combination of win rate and risk-to-reward, not from being right all the time. A strong ratio lowers the win rate you need to break even, so prioritise quality setups where the potential reward clearly outweighs the risk. Think in terms of expectancy across many trades, accept that any single result is largely noise, and let a positive edge compound over a large sample.
Knowledge check
Test what you've learned
1.Approximately what win rate is needed to break even with a 1:3 risk-to-reward ratio?
2.If you win 40% of trades, the average win is $200 and the average loss is $100, what is the expectancy per trade?