Trading expectancy formula, with a worked example

What is the expectancy formula?

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

Win rate is winning trades divided by all trades. Loss rate is 1 − win rate (count break-even trades separately or as zero). Average win and average loss are both written as positive amounts. The result is in the same unit you used: dollars per trade, or R per trade if you measure results in R-multiples.

The same number can be computed directly: Expectancy = total net P&L / number of trades. Both versions agree when they use the same trades.

Worked example

You took 40 trades: 18 winners averaging $320 and 22 losers averaging $180.

• Win rate = 18 / 40 = 45%; loss rate = 55%
• Expectancy = (0.45 × $320) − (0.55 × $180) = $144 − $99 = +$45 per trade
• Check: total P&L = 18 × $320 − 22 × $180 = $5,760 − $3,960 = $1,800; $1,800 / 40 = $45

A strategy can win less than half the time and still have positive expectancy, because the average win is larger than the average loss.

Expectancy in R (risk units)

Dollar expectancy changes when position size changes. Dividing each result by the amount risked gives R-multiples, and the same formula then gives expectancy in R: E(R) = (Win rate × Avg win in R) − (Loss rate × Avg loss in R). With a 45% win rate, +2R average win and −1R average loss: 0.45 × 2 − 0.55 × 1 = +0.35R per trade. Multiply by your risk per trade to get dollars.

Expectancy ratio and profit factor

Some traders divide expectancy by the average loss to compare systems (“expectancy ratio”): in the example, $45 / $180 = 0.25. Profit factor is gross profit divided by gross loss ($5,760 / $3,960 = 1.45). Both are positive-edge signs only when computed on enough trades with commissions and slippage included.

Does positive expectancy predict profit?

No. It describes a past sample. A few outliers, a short history, missing trades, changing market regimes, fees and slippage can all change the number. Treat 30 trades as a rough sketch and 100+ as a more useful sample. It is not a forecast, trading signal, or financial advice.

How FillScope calculates it

FillScope computes expectancy as the average FIFO realized P&L per imported Interactive Brokers trade row for the active filters (date, symbol, asset class, side): Σ FIFO realized P&L / trade-row count. Win rate, average win, average loss and profit factor are reported as separate metrics, so you can see which part of the formula moved.

Frequently asked questions

What is a good expectancy in trading?

Any expectancy above zero after commissions and slippage means the sample made money on average. In R terms, +0.1R to +0.5R per trade over 100 or more trades is a realistic range for many discretionary traders; higher values on small samples are usually noise.

Can expectancy be positive with a win rate under 50%?

Yes. If the average win is larger than the average loss, expectancy can be positive even with a 30-45% win rate. Example: 40% wins at +2.5R and 60% losses at -1R gives +0.4R per trade.

How many trades do I need to trust expectancy?

There is no fixed number, but under 30 trades the average is dominated by one or two outliers. 100 or more trades from the same setup and market conditions give a far more stable estimate.

What is the difference between expectancy and win rate?

Win rate only counts how often you win. Expectancy combines how often you win with how much you win and lose, so it tells you the average result per trade.