R-multiple and expectancy, explained

What is an R-multiple?

An R-multiple expresses a trade's result in units of the risk you took on that trade. 1R is the distance from your entry to your stop loss, in dollars. Risk $250 and make $500, and the trade is +2R. Get stopped out, and it is −1R.

The point of R is comparability. A $180 gain in a small account and an $1,800 gain in a large one are the same trade if both were +2R. Once every result is in R, you can average them, rank setups against each other, and spot the one that quietly bleeds the account.

How do you calculate position size?

position size = (account size × risk %) ÷ (entry price − stop price)

On a $25,000 account risking 1%, you are allowed to lose $250. Buy at $50 with a stop at $47.50 and each share carries $2.50 of risk, so the position is 100 shares. Notice what decides the size: the stop does. A wider stop means a smaller position, not a bigger loss.

This is the single mechanical habit that separates traders who survive from traders who do not. It also means "I bought 100 shares because that felt right" is not a sizing method.

Run it in the free position sizer →

How do you calculate expectancy?

expectancy (R) = (win rate × avg win in R) − (loss rate × avg loss in R)

Take a system that wins 40% of the time for +2R and loses 60% of the time for −1R:

(0.40 × 2) − (0.60 × 1) = 0.80 − 0.60 = +0.20R per trade

Over 100 trades risking 1% of a $25,000 account, +0.20R per trade is roughly $500 of expected profit before costs. That is what a real edge looks like: small, boring, and only visible across a large sample.

What win rate do I need to break even?

break-even win rate = 1 ÷ (1 + reward-to-risk)

Reward : risk	Break-even win rate	What that means
0.5R	66.7%	You must be right two times out of three just to tread water
1R	50.0%	A coin flip with no edge left over
2R	33.3%	Wrong two times out of three and still profitable
3R	25.0%	Wrong three times out of four and still profitable

Can a 70% win rate lose money?

Easily. Win 70% of trades at +0.3R and lose 30% at −1R:

(0.70 × 0.3) − (0.30 × 1) = 0.21 − 0.30 = −0.09R per trade

That is a losing system with a win rate most traders would brag about. The mirror image is also true — a 35% win rate at +3R is strongly profitable and feels awful to trade. Win rate is a feeling; expectancy is the result.

What is risk of ruin?

Risk of ruin is the probability that an ordinary losing streak takes the account somewhere it cannot come back from. It depends on win rate and reward-to-risk, but it is dominated by risk per trade. The same edge risking 3% instead of 1% per trade converts a survivable drawdown into a terminal one, because the recovery math is brutal: a 50% drawdown needs a 100% gain to get back to flat.

Because streaks are random, the honest way to estimate this is a Monte Carlo simulation over thousands of shuffled sequences rather than a formula applied to your last twenty trades. The free risk-of-ruin simulator does that in the browser →

How many trades before the number means anything?

At least 30 for a rough read, and 100 or more before you trust it. Expectancy measured over ten trades is noise wearing a decimal point.

This matters more than it sounds. When I ran my own swing setups through a no-lookahead walk-forward test, most of them died: only the anchored-VWAP reclaim survived — and even that shrank to +0.117R over 4,933 trades (95% CI +0.057 to +0.174) once I re-tested it on a 129-symbol, 10-year universe. The +0.23R over 101 trades I first reported did not survive that re-test. A VCP variant came out breakeven, and a gap and opening-range-breakout proxy came out at −0.28R and was dropped entirely. Nothing about that was visible in a small recent sample — which is exactly the point. The full write-up is here →

Putting it together

• Set the stop first, then let it determine position size.
• Record every outcome in R, not dollars.
• Compute expectancy per setup, not just for the account — one bad setup can eat the profits of three good ones.
• Check your reward-to-risk against the break-even table before blaming your entries.
• Keep risk per trade small enough that a ten-loss streak is an inconvenience, not an ending.

Educational content, not financial advice. No live profit-and-loss figures are claimed anywhere on this site; backtest and walk-forward results are always labelled as such. Full terms: /terms.html

Tools referenced in this guide

• Trader's risk toolkit — position sizer, R-multiple, expectancy, risk of ruin, Kelly, break-even win rate. Free, no signup.
• TradeLog — an R-multiple trading journal that computes expectancy per setup. Installs offline, stores data on your device.
• Swing Screener — the screener and no-lookahead backtest engine behind the walk-forward results above.