The expectancy formula
Expectancy = win rate × average win − (1 − win rate) × |average loss|
If you keep losses as negative numbers, as a trade log does, the same formula is written with a plus: =B22*B23+(1-B22)*B24, where B24 is −100. In the example: 0.40 × 250 + 0.60 × (−100) = 100 − 60 = $40.00.
The loss rate is 1 − win rate only if every trade is either a win or a loss. If your journal has break-even trades, count them separately or treat them as small losses after costs.
Worked example: expectancy from a 20-trade journal
Rows 2 to 21 are the net P&L of 20 closed trades, losses negative. Rows 22 to 32 calculate the statistics. The trades are synthetic.
| A | B | Formula in B | |
|---|---|---|---|
| 1 | Trade | P&L ($) | |
| 2 | Trade 1 | 310 | |
| 3 | Trade 2 | -100 | |
| 4 | Trade 3 | -95 | |
| 5 | Trade 4 | 180 | |
| 6 | Trade 5 | -110 | |
| 7 | Trade 6 | -80 | |
| 8 | Trade 7 | 265 | |
| 9 | Trade 8 | -120 | |
| 10 | Trade 9 | -100 | |
| 11 | Trade 10 | 420 | |
| 12 | Trade 11 | -105 | |
| 13 | Trade 12 | -90 | |
| 14 | Trade 13 | 150 | |
| 15 | Trade 14 | -100 | |
| 16 | Trade 15 | 230 | |
| 17 | Trade 16 | -115 | |
| 18 | Trade 17 | -85 | |
| 19 | Trade 18 | 205 | |
| 20 | Trade 19 | -100 | |
| 21 | Trade 20 | 240 | |
| 22 | Win rate | 40.0% | =COUNTIF(B2:B21,">0")/COUNT(B2:B21) |
| 23 | Average win ($) | 250.00 | =AVERAGEIF(B2:B21,">0") |
| 24 | Average loss ($) | -100.00 | =AVERAGEIF(B2:B21,"<0") |
| 25 | Payoff ratio (avg win ÷ |avg loss|) | 2.50x | =B23/-B24 |
| 26 | Expectancy per trade ($) | 40.00 | =B22*B23+(1-B22)*B24 |
| 27 | Check: average of all P&Ls ($) | 40.00 | =AVERAGE(B2:B21) |
| 28 | Risk per trade, 1R ($) | 100 | |
| 29 | Expectancy in R | 0.40 | =B26/B28 |
| 30 | Break-even win rate | 28.6% | =-B24/(B23-B24) |
| 31 | Edge (win rate − break-even) | 11.4% | =B22-B30 |
| 32 | Profit factor | 1.67 | =SUMIF(B2:B21,">0")/-SUMIF(B2:B21,"<0") |
Educational only, not investment or trading advice. A sample of 20 trades is far too small to prove an edge.
The cross-check: it is just the average trade
Expectancy is nothing more than the mean P&L per trade, so =AVERAGE(B2:B21) must give the same $40.00. If the two disagree, the win rate or one of the averages is wrong, typically because a zero trade was counted in one formula but not in the other. The value of splitting the average into win rate and payoff is that it shows why a strategy makes money, and which part to work on.
Expectancy in R-multiples
Dollar expectancy depends on position size. Dividing by the amount risked per trade, 1R, makes strategies and periods comparable: $40.00 ÷ $100 = 0.40R. For every dollar risked, the trader made 40 cents on average. That is attractive only if it holds over many more trades: 20 trades are far too few to separate skill from luck.
Break-even win rate and edge
For a given payoff ratio (average win ÷ |average loss|, here 2.5x), the win rate at which expectancy is exactly zero is
break-even win rate = |average loss| ÷ (average win + |average loss|) = 1 ÷ (1 + payoff)
Here 100 ÷ 350 = 28.6%. The actual 40.0% is 11.4 percentage points above it, and that gap is the edge. A trend-following strategy can be profitable with 35% winners if the wins are large, and a strategy with 80% winners can lose money if the few losses are big. Win rate alone tells you very little.
Profit factor and payoff ratio
The profit factor is gross profit ÷ gross loss, 1.67 in the example. Above 1 means the strategy made money. Expectancy, profit factor and payoff all come from the same journal but answer different questions: expectancy how much per trade, profit factor how much per dollar lost, payoff how big the wins are relative to the losses. For the risk-adjusted performance of a whole account, see the Sharpe ratio in Excel.
Expectancy after costs, and what it does not promise
Use net P&L after commissions, spreads, fees and slippage. A thin edge disappears quickly when costs rise: if costs took another $15 from every trade in the example, wins would shrink, losses would grow and the expectancy would fall from $40.00 to $25.00. Expectancy also describes the past sample only. Markets change, and a strategy with a positive expectancy can still have long losing streaks and deep drawdowns, so size positions for the bad runs, not for the average.
Common mistakes
- Looking at the win rate alone. 40% winners can be very profitable and 80% winners can lose money. Win rate and payoff only mean something together.
- Mixing signs. If losses are negative in the log, add the loss term. If you use |average loss|, subtract it. Doing both counts the loss twice.
- Ignoring costs. Commissions, spreads and slippage come off every trade. Use net results.
- Counting break-even trades inconsistently. Then win rate plus loss rate is not 100%, and the formula no longer matches the average trade.
- Trusting a small sample. 20 trades say very little. Wait for a large number of trades in similar market conditions before relying on the number.
- Comparing dollar expectancy across position sizes. Convert it to R-multiples first.
Frequently asked questions
What is a good expectancy in trading?
There is no universal benchmark. Any positive expectancy after costs means the strategy has made money on average, but it only counts if it holds over a large sample of trades and survives realistic costs.
How do you calculate expectancy in Excel?
Calculate the win rate with COUNTIF, the average win and loss with AVERAGEIF, then =win_rate*avg_win+(1-win_rate)*avg_loss with the average loss as a negative number. =AVERAGE of all P&Ls is a quick cross-check.
What is the break-even win rate?
The win rate at which expectancy is zero for your payoff: |average loss| / (average win + |average loss|), or 1 / (1 + payoff ratio). With wins 2.5 times the size of losses, you need 28.6% winners to break even.
Is expectancy the same as profit factor?
No. Expectancy is the average result per trade, in dollars or in R. Profit factor is gross profit divided by gross loss. A profitable strategy has a positive expectancy and a profit factor above 1, but the two measure different things.