How to use the trading expectancy calculator
The calculator has two tools for the two situations traders are usually in.
From win rate & averages is for when you already have summary statistics, from a backtest report or a journal:
- Enter the win rate: winning trades as a percentage of all trades.
- Enter the average winning trade and the average losing trade in dollars, the loss as a positive number.
- Optionally enter your risk per trade (1R), the amount you lose when the stop is hit. If you leave it empty, the average loss is used as 1R.
From a list of trades does the counting for you. Paste the result of each closed trade, one per line or separated by commas, with a minus sign on losses. Dollars, points, pips or R-multiples all work, as long as every trade uses the same unit. The example holds 40 trades of a fictional swing-trading system.
The formulas
Expectancy E = W × AvgWin − (1 − W) × AvgLoss
Expectancy in R = E ÷ RAvgWin and AvgLoss are the average winning and losing trades, both as positive numbers. R is the risk per trade; by default the average loss.
Payoff ratio = AvgWin ÷ AvgLoss
Break-even win rate = AvgLoss ÷ (AvgWin + AvgLoss) = 1 ÷ (1 + Payoff ratio)Gross profit is the sum of all winning trades and gross loss the sum of all losing trades as a positive number. A profit factor above 1 and a positive expectancy always go together.
A worked example
From averages. A system wins 40% of its trades. The average winner makes $300 and the average loser costs $150. Each trade is expected to make $30.00, or 0.20R: the winners are rarer, but each one is twice the size of a loser. The profit factor is 1.33, and the break-even win rate is 33.3%: the system can afford to win a third of the time and still not lose money.
From a list. The 40 example trades, in dollars, won 40.0% of the time. Winners averaged 293.38 and losers -135.17. The expectancy is 36.25 dollars per trade and the profit factor 1.45.
Win rate means nothing without the payoff ratio
The win rate a system needs depends entirely on how big its winners are compared with its losers. Holding the average loss at $100:
| Payoff ratio | Average win | Break-even win rate |
|---|---|---|
| 0.5 : 1 | $50 | 66.7% |
| 1 : 1 | $100 | 50.0% |
| 1.5 : 1 | $150 | 40.0% |
| 2 : 1 | $200 | 33.3% |
| 3 : 1 | $300 | 25.0% |
With the example averages, a 30% win rate gives an expectancy of -$15.00 a trade, and a 50% win rate $75.00. A system that wins 60% of the time but makes $100 per winner and loses $120 per loser still earns only $12.00 a trade, because it needs 54.5% just to break even.
Traders often push one side of this trade-off without noticing the other. Taking profits early raises the win rate and lowers the payoff ratio; wider targets do the opposite. The chart under the first tool shows how fast expectancy changes as the win rate moves, with your break-even point marked.
Expectancy, profit factor and SQN: what each tells you
- Expectancy is the money a trade makes on average. Multiply it by the number of trades you take and you have the expected result before costs. It is the number to compare with your trading costs per trade.
- Profit factor shows how many dollars of gains come in for each dollar of losses. It ignores how many trades it took, so a profit factor of 2 from five trades means far less than the same figure from five hundred.
- SQN brings variability in. A system with a modest expectancy but very consistent trades scores better than one with the same expectancy from a few huge winners. Tharp’s rough scale calls 1.6 to 2 tradable but below average, 2 to 2.5 average, 2.5 to 3 good and 3 to 5 excellent; the bands differ a little between his editions.
How many trades are enough?
Trade results are noisy, and short records mislead. A rough measure of the noise is the standard error of the expectancy, the standard deviation divided by the square root of the number of trades.
For the 40 example trades, the standard deviation is 231.55 and the standard error 36.61, almost exactly the size of the 36.25 expectancy. The average trade is only 0.99 standard errors above zero, which is also why the SQN is a low 0.99 despite a profit factor of 1.45. A record like this is consistent with a real edge, but also with luck. Quadrupling the number of trades halves the standard error.
What this calculator does not include
- Costs, unless your trade results already include them. Subtract commissions and slippage per trade, or use the trading cost calculator.
- Position sizing. Expectancy per trade assumes each trade is comparable. If you changed size over time, R-multiples give a fairer picture than dollars.
- Order and dependence. The statistics treat trades as independent. Drawdowns and losing streaks depend on the order of trades; the trading journal statistics calculator measures those, and the risk of ruin calculator shows the streaks to expect.
- The future. A backtest or past record estimates expectancy; markets change, and live results usually trail backtests.