Risk-reward ratio, expectancy and risk of ruin: the maths every mentor should teach
By Karel Moreau, editor of tradingmentorreviews ·
Your risk-reward ratio decides the win rate you need; your expectancy decides whether you make money; your position size decides whether you survive long enough to find out. At 1:2 risk-reward you break even winning 33.3% of trades. A trader winning 45% at 1:1.5 has a positive expectancy of +0.125R per trade — and still, risking 5% per trade, hits a 50% drawdown in 48% of simulated 200-trade runs. Every number here is computed, not quoted.
Risk-reward ratio and break-even win rate
If you risk 1 unit (1R) to make R units, you break even when your win rate equals 1 ÷ (1 + R).
| Risk : reward | Break-even win rate |
|---|---|
| 1 : 0.5 | 66.7% |
| 1 : 1 | 50.0% |
| 1 : 1.5 | 40.0% |
| 1 : 2 | 33.3% |
| 1 : 3 | 25.0% |
Expectancy: the number that actually matters
Expectancy = (win rate × average win) − (loss rate × average loss), measured in R. It is what a setup earns per trade on average.
| Win rate | Risk : reward | Expectancy per trade | Per 100 trades |
|---|---|---|---|
| 60% | 1 : 0.5 | -0.10R | -10R |
| 50% | 1 : 1 | 0.00R | 0R |
| 45% | 1 : 1.5 | +0.125R | +12.5R |
| 40% | 1 : 2 | +0.20R | +20R |
| 30% | 1 : 3 | +0.20R | +20R |
| 55% | 1 : 1 | +0.10R | +10R |
Notice the first row: a 60% win rate at 1:0.5 loses money. A high win rate is the most-advertised and least-meaningful number in trading marketing. Ask any mentor for win rate and average win and loss in R.
Losing streaks are normal
A trader who wins 45% of the time should expect a longest losing streak of about 8 trades in a typical 200-trade stretch, and 11 or more in one stretch out of ten (simulation, 20,000 runs). If a streak like that would break your account or your nerve, your size is too big.
Position sizing and risk of ruin
Same trader — 45% win rate at 1:1.5, a genuinely positive edge — risking a fixed percentage of the account per trade over 200 trades:
| Risk per trade | Chance of a 20% drawdown | Chance of a 50% drawdown |
|---|---|---|
| 0.5% | 0% | 0.0% |
| 1% | 7% | 0.0% |
| 2% | 64% | 0.5% |
| 5% | 100% | 47.8% |
The edge is identical in every row. Only the size changes, and it changes everything. This is why nearly every professional risk framework caps risk per trade at around 1–2%.
Position size formula
Position size = (account × risk %) ÷ (distance from entry to stop). On a $10,000 account risking 1% with a stop $0.50 away, that is $100 ÷ $0.50 = 200 shares. For futures, divide by the dollar value of the stop distance per contract.
What to ask a mentor
Only 6 of the 49 mentorships we track mention risk management, position sizing or risk-reward explicitly in their listing (BH Insights, 444 Capital Club, Cerulean Mind Academy, Botos Trading Academy, LionFX Academy, Trading Options Academy TOA). Ask every mentor: what is the average R won and lost, what is the risk per trade, and what was the worst drawdown? A mentor who cannot answer in those terms is not measuring what matters. Track your own numbers in a trading journal.
Frequently asked questions
What is a good risk-reward ratio?
There is no universal one; it depends on win rate. At 1:2 you break even at 33.3% wins, at 1:1 at 50%. Expectancy, not the ratio, tells you if a setup works.
How do you calculate expectancy in trading?
Win rate × average win − loss rate × average loss, in R. 45% wins at 1.5R: 0.45 × 1.5 − 0.55 × 1 = +0.125R per trade.
What is risk of ruin?
The probability that a sequence of losses takes your account below a level you cannot recover from. It rises sharply with position size even when the edge is positive.
How much should I risk per trade?
Most risk frameworks cap it around 1–2% of the account. In our simulation a positive-edge trader risking 5% hit a 50% drawdown far more often than one risking 1%.
Is a high win rate good?
Not on its own. A 60% win rate at 1:0.5 risk-reward loses money.
