Risk-Reward and Win Rate: The Maths of Expectancy

Ask most new traders what makes a good strategy and they will say a high win rate. It feels intuitive: win more often than you lose and you make money. It is also wrong. A strategy that wins 80% of the time can lose money, and a strategy that wins 35% of the time can be solidly profitable. The difference is reward-to-risk, and the tool that ties them together is called expectancy.

Thinking in R

The cleanest way to measure trades is in units of risk, called R. One R is the amount you lose if your stop is hit. If you risk $50 on a trade, then 1R = $50. A trade that makes $100 is +2R; one that stops out is −1R.

Measuring in R removes account size and position size from the comparison. A +2R trade is equally good on a $500 account and a $50,000 account.

The expectancy formula

Expectancy = (Win rate × Average win) − (Loss rate × Average loss)

Expressed in R, with the average loss equal to 1R:

• Strategy A: wins 70% of the time at +0.5R, loses 30% at −1R. Expectancy = 0.7 × 0.5 − 0.3 × 1 = 0.35 − 0.30 = +0.05R per trade.
• Strategy B: wins 40% of the time at +2R, loses 60% at −1R. Expectancy = 0.4 × 2 − 0.6 × 1 = 0.80 − 0.60 = +0.20R per trade.

Strategy B wins far less often but has four times the edge. Over 100 trades risking $50 each, A makes around $250 before costs, and B around $1,000. Fees and slippage also hurt A much more, because they take a bigger share of its small winners.

Breakeven win rates

For any reward-to-risk ratio, there is a win rate at which you exactly break even (before costs). The formula is 1 ÷ (1 + R), where R is the reward per unit of risk:

• 1:0.5 — breakeven win rate 66.7%
• 1:1 — breakeven win rate 50.0%
• 1:1.5 — breakeven win rate 40.0%
• 1:2 — breakeven win rate 33.3%
• 1:3 — breakeven win rate 25.0%
• 1:4 — breakeven win rate 20.0%
• 1:5 — breakeven win rate 16.7%

Read that list the other way round and it tells you how much room for error each ratio gives you. At 1:1, you need to be right more than half the time just to stand still. At 1:2, you can be wrong on two out of every three trades and still not lose money.

Why 1:2 matters

A minimum of 1:2 is a common rule for good reasons:

1. It survives realistic win rates. Well-filtered discretionary and systematic strategies often land somewhere around 35–55%. At 1:2, that range is comfortably above the 33% breakeven.
2. It absorbs costs. Fees, funding and slippage effectively shave a little off every win and add a little to every loss. With small targets, they can eat most of the edge.
3. It survives losing streaks. Even at a 50% win rate, runs of five or six losses in a row happen regularly over a few hundred trades. With 1:2, a couple of wins recover a bad streak.
4. It forces better entries. You can only get 1:2 with a sensible target if the stop is tight and logical. The rule filters out trades entered in the middle of nowhere.

The catch: the ratio has to be real

Setting a target at 3R does not make a trade 1:3. The target must be somewhere price can plausibly reach — the next structural high, a liquidity pool, an unfilled imbalance. Stretching targets to hit a ratio just lowers the win rate and pushes you back toward breakeven.

Similarly, moving your stop further away once in the trade quietly turns a 1:2 trade into 1:1 or worse. Your actual average win and average loss, measured over many trades, are the only numbers that count.

Putting it to work

• Log every trade in R: planned risk, result, and whether the stop or target was hit.
• After 30–50 trades, calculate your real win rate and average R per win.
• Compare your win rate with the breakeven rate for your actual average ratio. The gap between them is your edge.
• Skip trades where the nearest logical target is less than 2R from entry.

No ratio guarantees profit. It only gives an edge room to show up over a large number of trades, if the edge is real.

Leveraged trading carries a high risk of loss. This article is educational and is not financial advice.