The Trader's Math: Win Rate, Reward-to-Risk, and the Recovery Problem
Three tables decide whether a strategy makes money — and most traders have never seen them laid out. Here's the exact win rate you need at every reward-to-risk ratio, what your edge is worth per trade, and why a losing streak costs more to climb out of than it did to fall in.
Published 2026-07-24 · Free to cite with a link to this page.
The numbers worth memorizing
- At 2:1 reward-to-risk you only need to win 33.3% of the time to break even — reward-to-risk buys you a lower win rate.
- A 50% drawdown requires a 100% gain to recover. Losses are asymmetric, and it gets brutal fast: down 75% needs +300%.
- A 40% win rate is profitable at 2:1 (+0.20R per trade) but only breaks even at 1.5:1 and bleeds at 1:1.
- Below 1:1 reward-to-risk you must win the majority of trades just to tread water — the math is working against you.
1. The break-even win rate by reward-to-risk
The minimum win rate that keeps you at zero. Win more often than this and the strategy is profitable;
less often and it loses — before costs. Formula: break-even % = 1 ÷ (R + 1), where R is your
reward-to-risk ratio.
| Reward : risk | Break-even win rate | What it means |
|---|---|---|
| 0.5:1 | 66.7% | Must win the majority of trades |
| 1:1 | 50% | A coin flip breaks even |
| 1.5:1 | 40% | A minority of wins still profits |
| 2:1 | 33.3% | A minority of wins still profits |
| 2.5:1 | 28.6% | A minority of wins still profits |
| 3:1 | 25% | A minority of wins still profits |
| 4:1 | 20% | A minority of wins still profits |
| 5:1 | 16.7% | A minority of wins still profits |
2. Expectancy: what your edge is worth per trade
Expectancy is the average result of a trade, measured in units of risk (R). Green cells make money over
time; red cells lose. Formula: E[R] = (win% × R) − (loss% × 1). A 55% win rate at 2:1 nets
about +0.65R every trade you take.
| Win rate ↓ / R:R → | 1:1 | 1.5:1 | 2:1 | 3:1 |
|---|---|---|---|---|
| 30% | -0.40R | -0.25R | -0.10R | +0.20R |
| 40% | -0.20R | 0.00R | +0.20R | +0.60R |
| 50% | 0.00R | +0.25R | +0.50R | +1.00R |
| 60% | +0.20R | +0.50R | +0.80R | +1.40R |
| 70% | +0.40R | +0.75R | +1.10R | +1.80R |
Positive = profitable edge over many trades. Zero = break-even. Negative = a losing system, however good any single trade feels.
3. The recovery problem: gains needed after a loss
Drawdowns are asymmetric — the deeper the hole, the disproportionately larger the gain needed to climb out.
This is the single strongest argument for capping risk per trade. Formula:
gain to recover = loss ÷ (1 − loss).
| Account drawdown | Gain needed to recover | Recovery bar |
|---|---|---|
| −5% | +5.3% | |
| −10% | +11.1% | |
| −20% | +25% | |
| −25% | +33.3% | |
| −30% | +42.9% | |
| −40% | +66.7% | |
| −50% | +100% | |
| −60% | +150% | |
| −75% | +300% | |
| −90% | +900% |
Put the math to work
These tables are the theory. TradeCaliper's free calculators run them on your actual trades and account:
Methodology & formulas
Every figure here is exact arithmetic — no estimates, no historical data, no assumptions about any market. You can reproduce all three tables:
- Break-even win rate solves expectancy = 0 for the win probability:
p × R − (1 − p) = 0 → p = 1 / (R + 1). - Expectancy (in R) is
p × R − (1 − p) × 1, treating one unit of risk (1R) as the loss size and R as the win size. - Drawdown recovery is the gain that restores a balance reduced by loss fraction L:
1 / (1 − L) − 1 = L / (1 − L).
All figures are before commissions, slippage, and taxes, which shift the break-even lines modestly in the trader's disfavor. TradeCaliper is a planning and education tool, not financial advice.
Reuse: these tables are free to cite or republish with attribution and a link to this page (https://tradecaliper.com/trader-math/).