Expectancy
Expectancy is the average profit or loss a trading strategy produces per trade, combining how often its trades are profitable with the size of its average profit and its average loss.
The formula is expectancy = (win rate × average profit) − (loss rate × average loss), with the average loss counted as a positive amount. A positive figure means the strategy gains on average over many trades, and a negative one means it gives money back on average. Worked out from price distances, the figure reflects real results only once the costs of every trade are deducted: the spread and any commission, plus swap and slippage, which can add to the result as well as subtract from it.
This page covers the mechanic; it is not trading advice.
What expectancy measures, and what costs do to it
Expectancy is an average across many trades, not a forecast: the next trade still closes in profit, at a loss or at exactly zero. Its inputs are the Win rate, the share of closed trades that end in profit, and the loss rate, the share that end at a loss. The loss rate equals 1 minus the win rate only when no trade closes at exactly zero.
In multiples of the amount risked (R), the formula shortens to win rate × reward multiple − loss rate. At a 40% win rate and a 1:2.5 Risk-reward ratio, expectancy is 0.40 × 2.5 − 0.60 = +0.40R. That form assumes every loss-making trade gives up exactly 1R and every profitable trade gains exactly 2.5R, the model the Prop Challenge Calculator uses.
Win rate and ratio are commonly read as the whole answer, with costs a small fixed deduction. The R formula encourages that reading, as it contains neither costs nor the stop distance. Every trade pays the Spread and any commission, and both are charged per lot traded (the spread in pips, commission in cash) rather than per unit of R. A tight stop therefore pays more cost per unit of risk than a wide one, so identical win rates and ratios can carry different expectancy once costs are counted.
Expectancy before and after costs on EUR/USD
Take a long EUR/USD position at an illustrative 1.1253, with a Stop-loss 20 pips below at 1.1233 and a target 50 pips above at 1.1303. On 1 standard lot each Pip is worth $10, so 1R is $200 and a profitable trade gains $500 before costs.
Both costs are assumptions set by the broker, and both vary with account type, the spread with market conditions as well: a 0.6-pip Spread, paid once per round trip, and commission of $3.50 per side per standard lot, $7.00 per round turn. Cost per trade is 0.6 × $10 + $7.00 = $13.00. Swap and Slippage are excluded, with the position assumed closed before the broker's daily rollover.
Expectancy after costs
Expectancy = (win rate × average profit) − (loss rate × average loss)- Win rate
- 40%
- Average profit ($500 − $13.00 cost)
- $487.00
- Loss rate
- 60%
- Average loss ($200 + $13.00 cost)
- $213.00
Expectancy per trade, after costs
+$67.00
Before costs the strategy shows 0.40 × $500 − 0.60 × $200 = +$80.00 a trade, or +0.40R. After costs it is 0.40 × $487 − 0.60 × $213 = $194.80 − $127.80 = +$67.00, or +0.335R: exactly $13.00 less, because every trade pays the cost. Break-even win rate, the average loss divided by the sum of average profit and average loss, rises from 200 ÷ 700 = 28.57% to 213 ÷ 700 = 30.43%.
Why the stop distance changes net expectancy
At a fixed $200 risk, a tighter stop needs a larger Position size, and cost grows with the lots.
The 1.3 pips of cost per lot is 0.13R on a 10-pip stop but 0.0325R on a 40-pip stop, so the +0.40R strategy keeps about two thirds of its edge on the tightest stop, over nine tenths on the widest.
Planned expectancy versus measured expectancy
On a trade history, expectancy is net profit divided by the number of closed trades, the figure MetaTrader 5's strategy tester reports as Expected Payoff. It uses what each trade actually returned rather than exact 1R and target exits. The spread is already inside results from live fills, which are at the bid or the ask, while a backtest that fills at a single chart price leaves it out unless it is modelled; commission and swap are included only when the profit figures are net of them. How far the account falls along the way is a separate question, covered by Drawdown and Risk of ruin.
Related terms
Related articles
Common questions
Can a strategy with a 40% win rate have positive expectancy?
Yes. On 1 standard lot of EUR/USD at an illustrative 1.1253, a 20-pip stop and a 50-pip target (1:2.5) give +$80.00 a trade before costs at a 40% win rate, with break-even at 28.57%. After an assumed 0.6-pip spread and $7.00 round-turn commission, expectancy is +$67.00 and break-even 30.43%.
How do spread and commission change expectancy?
They cut it by one round-trip cost, paid on every trade. On 1 standard lot of EUR/USD at an illustrative 1.1253, an assumed 0.6-pip spread, paid once per round trip, costs $6.00 and an assumed $3.50-per-side commission costs $7.00, so +$80.00 of expectancy before costs becomes +$67.00 after them.
Does positive expectancy mean every run of trades ends in profit?
No. Take 1 standard lot of EUR/USD at an illustrative 1.1253, a 40% win rate, a 20-pip stop and a 50-pip target, worth +$67.00 a trade after assumed costs. With independent trades closing at +$487 or −$213, 25.00% of 20-trade runs still end below zero, and so do 2.48% of 100-trade runs.