The Expectancy Formula in Plain Text
Expectancy is one number that combines your win rate and your risk-reward ratio into a single answer: does your strategy make money over time, or not?
Where Loss Rate = 1 − Win Rate. Average Loss is entered as a positive number.
You can also express this in R-multiples (per dollar risked):
If your average winner is 2.5R and your win rate is 40%: (0.40 × 2.5) − (0.60 × 1) = 1.00 − 0.60 = +0.40R per trade
A positive number means the strategy makes money over enough trades. A negative number means it loses money — regardless of how individual trades feel. Zero means breakeven before fees (which makes it negative in practice).
Example 1: Positive Expectancy (Profitable Strategy)
A swing trader takes 200 trades over 6 months with these results:
Swing Trader — Trend Following
Step-by-step calculation:
- Win component: 0.41 × $480 = $196.80
- Loss component: 0.59 × $190 = $112.10
- Expectancy = $196.80 − $112.10 = +$84.70 per trade
Over 200 trades, this strategy produced approximately $16,940 in profit. The trader lost 59% of their trades but made money because every winner was 2.5× larger than every loser on average. This is why win rate without risk-reward context is meaningless.
This trader lost more trades than they won. In any given week, they probably felt like they were losing. But the math was on their side the entire time. Expectancy turns that emotional uncertainty into a concrete number you can trust.
Example 2: Negative Expectancy (Losing Strategy)
A day trader takes 300 trades over 3 months with these results:
Day Trader — Scalping Reversals
Step-by-step calculation:
- Win component: 0.62 × $75 = $46.50
- Loss component: 0.38 × $155 = $58.90
- Expectancy = $46.50 − $58.90 = −$12.40 per trade
Over 300 trades, this strategy lost approximately $3,720. The trader won 62% of the time — which felt great day-to-day — but gave back more on losing trades than they captured on winners. This is one of the most common failure patterns in trading and a core reason why traders lose money.
A 62% win rate feels good. You win most days. Your journal shows green more often than red. But the losses are twice the size of the wins, and the math is brutal. Without calculating expectancy, this trader would keep trading a losing strategy indefinitely — confident they have an edge because they "win more than they lose."
Example 3: Breakeven Expectancy (No Edge)
A forex trader takes 150 trades over 4 months:
Forex Trader — Range Trading
Step-by-step calculation:
- Win component: 0.50 × $210 = $105.00
- Loss component: 0.50 × $205 = $102.50
- Expectancy = $105.00 − $102.50 = +$2.50 per trade
Technically positive at +$2.50, but after spreads, commissions, and swap fees (~$3–8 per trade in forex), the real expectancy is negative. This is a breakeven strategy that becomes a slow bleeder once trading costs are included. Many traders operate here for months or years without realizing it — they are neither obviously losing nor making progress.
Why a 40% Win Rate Can Be Highly Profitable
Many traders believe you need to win at least half your trades to make money. That is mathematically false. Here is why:
At a 40% win rate with a 2.5:1 R:R ratio (risking $100 to make $250 on average):
- Win component: 0.40 × $250 = $100
- Loss component: 0.60 × $100 = $60
- Expectancy = $100 − $60 = +$40 per trade
That is +$40 profit expected per trade with a 40% win rate. Over 100 trades, you expect $4,000 in profit. The key is that winners are 2.5× larger than losers — big enough to more than compensate for the lower win frequency.
Compare that to a trader with 65% win rate and 0.8:1 R:R (risking $100 to make $80):
- Win component: 0.65 × $80 = $52
- Loss component: 0.35 × $100 = $35
- Expectancy = $52 − $35 = +$17 per trade
The 40% win rate strategy produces more than double the expectancy of the 65% win rate strategy. This is the mathematical argument for risk management and letting winners run: a higher R:R ratio is a more powerful lever than a higher win rate in most scenarios.
Expectancy Table: Win Rate × R:R Combinations
This table shows expectancy per $1 risked for different combinations of win rate and average risk-reward ratio. Use it to find where your strategy sits and how much a small improvement in either metric affects your bottom line.
| Win Rate | 0.5:1 R:R | 1:1 R:R | 1.5:1 R:R | 2:1 R:R | 2.5:1 R:R | 3:1 R:R |
|---|---|---|---|---|---|---|
| 30% | −$0.55 | −$0.40 | −$0.25 | −$0.10 | +$0.05 | +$0.20 |
| 35% | −$0.48 | −$0.30 | −$0.13 | +$0.05 | +$0.23 | +$0.40 |
| 40% | −$0.40 | −$0.20 | $0.00 | +$0.20 | +$0.40 | +$0.60 |
| 45% | −$0.33 | −$0.10 | +$0.13 | +$0.35 | +$0.58 | +$0.80 |
| 50% | −$0.25 | $0.00 | +$0.25 | +$0.50 | +$0.75 | +$1.00 |
| 55% | −$0.18 | +$0.10 | +$0.38 | +$0.65 | +$0.93 | +$1.20 |
| 60% | −$0.10 | +$0.20 | +$0.50 | +$0.80 | +$1.10 | +$1.40 |
| 65% | −$0.03 | +$0.30 | +$0.63 | +$0.95 | +$1.28 | +$1.60 |
| 70% | +$0.05 | +$0.40 | +$0.75 | +$1.10 | +$1.45 | +$1.80 |
Values are per $1 risked. Green = profitable. Red = losing. The breakeven diagonal runs roughly from 70%/0.5:1 to 25%/3:1.
Find your win rate on the left, then find your average R:R across the top. The intersection is your expected return per dollar risked. If you are at 45% win rate and 2:1 R:R, you expect +$0.35 for every dollar you risk. Multiply by your risk per trade to get dollar expectancy. At $200 risk per trade: $200 × $0.35 = $70 expected per trade.
How to Calculate Expectancy From Your Journal Data
Here is the exact process, step by step. You need a minimum of 30 closed trades, but 100+ is strongly recommended for a reliable number.
Export Your Closed Trades
Pull all closed trades from your journal for the period you want to analyze. Include: entry price, exit price, position size, and net P&L (after commissions). If you use Trader's Second Brain, filter by date range or setup tag and the expectancy is calculated automatically.
Separate Winners and Losers
Split your trades into two groups: winning trades (net P&L > $0) and losing trades (net P&L < $0). Breakeven trades (exactly $0 after fees) can be excluded or counted as losses — the impact is minimal with a decent sample size.
Calculate the Four Inputs
- Win Rate = Number of winners ÷ Total trades. Example: 47 wins out of 120 trades = 39.2%
- Loss Rate = 1 − Win Rate. Example: 1 − 0.392 = 60.8%
- Average Win = Sum of all winning P&L ÷ Number of winners. Example: $22,560 total wins ÷ 47 = $480
- Average Loss = Sum of all losing P&L (as positive) ÷ Number of losers. Example: $13,870 total losses ÷ 73 = $190
Plug Into the Formula
Expectancy = (0.392 × $480) − (0.608 × $190) = $188.16 − $115.52 = +$72.64 per trade
This trader expects to make $72.64 per trade on average. At 30 trades per month, that is $2,179/month in expected profit — a concrete, projectable number.
Validate With Sample Size
Ask yourself: does this number hold up if you remove the single largest winner? If removing one trade flips your expectancy from positive to negative, your sample is too small or your edge depends on rare outliers. Calculate expectancy again with your top 3 winners removed — the number should still be positive for a robust strategy.
For deeper analysis of what to look for in your journal beyond expectancy, see how to analyze trading performance and what to track in a trading journal.
How to Improve Negative Expectancy
If your expectancy is negative, the formula tells you exactly what to fix. There are only two levers: win rate and R:R ratio. Here is how to pull each one.
Lever 1: Increase Your Average R:R
This is the higher-impact lever for most traders because the common psychological pattern works against R:R: traders cut winners early (reducing average win) and hold losers too long (increasing average loss).
- Hold winners to target. Compare your planned exit vs. actual exit on winning trades. If you consistently exit at 60–70% of your target, that alone is destroying your R:R. Set price alerts at targets instead of watching positions tick-by-tick.
- Cut losers at planned stops. Review your losing trades — are you moving stops further away or adding to losers? Each time you widen a stop, you increase average loss and push expectancy further negative.
- Use a trailing stop on winners. If your strategy allows partial profit-taking, take 50% at 1R and trail the rest. This locks in some R while allowing the trade to reach 2–3R on the remaining position.
- Only take setups with 2:1 minimum R:R. Before entering any trade, calculate the distance to your stop and your target. If target ÷ stop < 2.0, skip the trade. This single filter can transform a negative-expectancy strategy into a positive one.
Lever 2: Increase Your Win Rate
Improving win rate usually means being more selective — taking fewer, higher-quality setups rather than trying to catch every move.
- Add confluence filters. If you trade breakouts, require volume confirmation + higher-timeframe trend alignment. Each filter reduces trade count but should increase the percentage that work.
- Eliminate your worst setup. Review your trades by setup type. Your lowest win-rate setup is dragging down the overall number. Stop taking it for 30 days and recalculate.
- Avoid trading during your worst sessions. Filter by time of day or day of week. Most traders have clearly unprofitable time windows where win rate drops significantly — often the first and last 30 minutes of the session.
- Wait for your A+ setups only. Your best setups (top 20% by hit rate) likely have dramatically higher expectancy than your average trade. If you traded only those setups, your win rate would increase and your expectancy with it.
Expectancy and the Kelly Criterion
Once you know your expectancy is positive, the next question is: how much should you risk per trade to maximize growth without blowing up?
The Kelly Criterion provides a mathematically optimal answer:
Or simplified: Kelly % = Expectancy ÷ Average Win
Using the positive expectancy example from above (41% win rate, $480 avg win, $190 avg loss):
- Kelly % = $84.70 ÷ $480 = 17.6%
Full Kelly says to risk 17.6% of your account per trade. In practice, this is dangerously aggressive — most professional traders use half-Kelly or quarter-Kelly (4.4%–8.8% in this case) because it dramatically reduces drawdown volatility while capturing 75–90% of the growth rate.
Use the Kelly Criterion Calculator to run your own numbers. Input your win rate and average win/loss, and it will show you the optimal risk percentage and the expected growth curve at full, half, and quarter Kelly.
Kelly Criterion assumes your edge is precisely estimated and constant. In real trading, your edge varies by market conditions, and your estimates contain error. This is why fractional Kelly (0.25× to 0.5×) is standard practice. Risking 1–2% per trade is a reasonable default for most retail traders — it keeps you in the game through inevitable estimation errors and drawdown periods.
Connecting Expectancy to Position Sizing
Expectancy tells you if your strategy makes money. Position sizing determines how much money it makes — and whether you survive the drawdowns along the way.
The formula for expected monthly income from your strategy:
At $70 expectancy and 25 trades/month: $70 × 25 = $1,750 expected monthly profit
But this only works if you are still trading after the inevitable drawdowns. A strategy with +$70 expectancy that risks 10% per trade will have massive equity swings. The same strategy risking 1% per trade will have a smooth equity curve but slower absolute growth.
Use the Position Size Calculator to convert your risk percentage into actual lot sizes or share quantities for each trade. The key principle: your position size should be derived from your risk tolerance and stop distance, not from a gut feeling about how much you "should" be making.
Common Mistakes When Calculating Expectancy
Using planned R:R instead of actual R:R. Your plan says 1:3. You actually exit winners at 1:1.5 on average because you fear giving back profits. Your real R:R is 1:1.5, and your real expectancy is likely half of what you think. Track both planned and actual exit prices in your journal.
Ignoring commissions and fees. An expectancy of +$8 per trade sounds positive until you realize you pay $5 in commissions and $4 in spread per trade. Net expectancy: −$1. Always calculate with after-fee P&L numbers.
Small sample size. Twenty trades is not enough. You need 100+ trades minimum, and 200+ for high confidence. A 60% win rate over 20 trades has a confidence interval so wide that the true win rate could easily be 40–80%. Your expectancy calculation is only as good as the data it sits on.
Mixing strategies. If you trade breakouts, pullbacks, and mean-reversion, calculate expectancy for each strategy separately. A blended number hides the fact that one strategy may have strong positive expectancy while another is deeply negative — and the negative one is dragging the overall number down.
Not recalculating regularly. Markets change. Your edge in trending markets may disappear in choppy markets. Recalculate expectancy every quarter (or every 50–100 trades) to catch degradation early. If expectancy drops below your cost per trade, stop trading that strategy until you understand why.
Manually calculating expectancy from spreadsheets is tedious and error-prone. A dedicated trading journal like Trader's Second Brain calculates expectancy automatically for any date range, setup type, or market — and updates in real time as you log trades. You see your expectancy degrade before it becomes a problem.
What Good Expectancy Looks Like by Trading Style
| Trading Style | Typical Win Rate | Typical R:R | Expected Expectancy | Trades/Month |
|---|---|---|---|---|
| Scalping | 55–70% | 0.5:1 – 1:1 | $0.05 – $0.20/R | 200–500 |
| Day Trading | 45–60% | 1:1 – 2:1 | $0.15 – $0.50/R | 40–100 |
| Swing Trading | 35–50% | 2:1 – 4:1 | $0.30 – $0.80/R | 10–30 |
| Position Trading | 30–45% | 3:1 – 6:1 | $0.40 – $1.20/R | 3–10 |
These are typical ranges for profitable traders. Scalping makes less per trade but compensates with volume. Swing and position trading make more per trade but need fewer, higher-quality setups. Total monthly return depends on expectancy × frequency × position size.
Notice the tradeoff: scalpers have the smallest expectancy per trade but the highest trade count, while position traders have the largest expectancy but the fewest trades. Monthly returns converge because frequency compensates for per-trade edge. The best style for you depends on your schedule, personality, and market access — not on which style has the highest per-trade expectancy.
