Quantitative Risk Management & Expectancy Guide
Judging a trading setup by win rate alone is misleading. A strategy that wins 70% of the time can lose money, and one that wins 35% of the time can be very profitable. What matters is how win rate, reward size and risk size combine. That combination is called mathematical expectancy.
How expectancy is calculated
Measured in units of risk (R), expectancy per trade is: E = (Win Rate × Reward) − (Loss Rate × 1). For example, a setup that wins 40% of the time with a 1:3 risk-to-reward ratio has E = (0.40 × 3) − (0.60 × 1) = +0.60R. Over many trades, each trade is worth 0.6 times the amount you risk, on average. With 1% risk per trade, that is about 0.6% of the account per trade before costs.
The break-even win rate for any risk-to-reward ratio is 1 ÷ (1 + R). At 1:1 you need to win more than 50%. At 1:2 you need more than 33.3%. At 1:3 you need more than 25%. If your real win rate is above that line, the setup has a positive edge; if it is below, the edge is negative no matter how good individual trades feel.
Why the binomial distribution matters
Expectancy describes the average, but you only ever live through one sequence of trades. If each trade is independent with the same win probability, the number of wins in a fixed number of trades follows a binomial distribution. The table above shows the probability of every possible record, and the chance that a run of N trades ends in profit or in loss. Even with a positive edge, a short run can finish red. That is why 20 trades say very little about a strategy and 200 say much more.
Losing streaks and drawdown
The chance of losing N trades in a row is the loss rate raised to the power N. At a 50% loss rate, five straight losses happen about 3.1% of the time on any given sequence, but across 100 trades a streak of five or more is likely. With 1% risk, five losses cost roughly 4.9% of the account. With 5% risk the same streak costs about 22.6%. Position size, not the entry signal, is what decides whether a normal losing streak is survivable. The Monte Carlo tab runs 1,000 random sequences with your inputs so you can see realistic drawdowns and streak lengths instead of a single average.
Fixed risk versus compounding
Fixed risk risks the same dollar amount on every trade, so equity grows roughly in a straight line. Compounding risks a percentage of the current balance, so wins are larger when the account grows and losses are smaller when it shrinks. Compounding produces steeper growth when the edge is positive. Because losses are taken as percentages, it is also impossible to lose the whole account in a finite number of losing trades, but drawdowns can still be deep. Rules at prop firms are usually written as percentage loss limits, so the percentage model is often the closer match.
Limits of these models
The calculator assumes independent trades, a constant win rate, and a constant risk-to-reward ratio. Real trading has slippage, spreads, commissions, partial exits and changing market conditions, and your win rate is an estimate from past trades, not a fixed property of the strategy. Treat the outputs as a way to stress-test your assumptions, not as a forecast.
Frequently asked questions
What is a good expectancy?
Any value above zero is a positive edge before costs. Many traders look for at least +0.2R to +0.3R after spreads and commissions, because small edges are easy to erase with costs.
How many trades do I need before trusting my win rate?
There is no single number, but a sample of fewer than 100 trades has wide uncertainty. Use the number-of-trades slider to see how much the range of outcomes narrows as the sample grows.
Does a higher risk-to-reward ratio always mean better results?
No. A larger target usually lowers the win rate. Compare ratios by their expectancy, not by how big the target is.
ExpectancyLab is an educational calculator. It does not provide financial advice or trade signals, and trading involves a substantial risk of loss. See the Terms of Service.