Risk/reward and expectancy: the maths that tells you whether a system works

I'll tell you something that surprises almost everyone: you can be wrong more often than right and still make money. And you can be right 70% of the time and lose money. What makes the difference is a single thing: the maths of the relationship between what you make when you win and what you lose when you're wrong. Understanding it frees you from the obsession with "getting everything right" and gives you an objective way to judge any strategy.

The risk/reward ratio (R:R)

Risk/reward compares how much you can lose with how much you can win on a trade. It's measured as the ratio between the distance to the target and the distance to the stop.

• Stop 30 pips, target 60 pips → R:R = 1:2 (risk 1 to make 2).
• Stop 20 pips, target 20 pips → 1:1.
• Stop 30 pips, target 90 pips → 1:3.

For convenience we use the letter R as the unit of risk: a stopped trade = −1R. A target at 2 times the stop = +2R. With this unit you can compare trades of different sizes and currencies.

The breakeven point: how much must you win?

The minimum percentage of winning trades not to lose is:

Breakeven win rate = 1 ÷ (1 + R:R)

With an R:R of 1:2 you only need to win one trade in three to break even (before costs). This changes everything: if you have a system aiming for 2R, you can afford to be wrong 60% of the time and stay positive.

You can try the numbers with the risk/reward calculator.

Expectancy

The ratio alone isn't enough: you have to combine it with the real win rate. Expectancy is the average gain per trade, in R:

Expectancy = (win % × average win in R) − (loss % × average loss in R)

A system is interesting if it has positive expectancy over a large sample and with costs included. Careful: that "+0.40R" is an average; in the short run you can have long losing streaks even with an excellent system.

Consecutive losses: how many to expect

Even a valid system has losing streaks. The probability of n losses in a row with a loss rate p is approximately pⁿ. With 60% losing trades (a 40% win-rate system):

Over hundreds of trades, a streak of 8-10 losses is far from rare. That's why risk per trade must be small: at 1% per trade, 10 losses in a row cost about 10% of the account, which is bearable. At 5% it isn't.

Other useful measures

• Profit factor: sum of gains ÷ sum of losses (in absolute value). Above 1 the system makes money; values between 1.3 and 2 are considered good. Very high values on little data are suspicious.
• Maximum drawdown: the maximum loss from the capital peak. It tells you whether you could endure that system.
• Average R per trade: the expectancy. It's the most important figure.

Sample uncertainty

If you've made 20 trades and won 12 (60%), you don't know what your system is truly worth: with little data the statistical error is huge. With 100 trades and 50% observed wins, the "true" rate could comfortably be between 40% and 60%. Rule of thumb: don't draw conclusions before at least 50-100 trades recorded with fixed rules.

Why you don't need to be right often

Many beginners chase a high win rate because "feeling right" is pleasant. But closing gains quickly and letting losses run (so as not to be "wrong") is the way to build a system with an unfavourable R:R. A good system accepts being wrong often but limits losses and lets profits run.

In short

• R:R compares risk and potential gain; measure everything in R (−1R the stop, +2R a double target).
• Breakeven win rate = 1 ÷ (1 + R:R): with R:R 1:2, 33% is enough.
• Expectancy = win% × win R − loss% × loss R: if positive, the system earns on average.
• Even a good system has losing streaks: size the risk accordingly.
• You need at least 50-100 trades to judge, costs included.

Practical exercise

1. Take your last 30 trades (even demo) and note each result in R.
2. Calculate win rate, average R of wins, average R of losses and expectancy.
3. With the risk/reward calculator check which win rate you need to break even with your typical R:R.