Expected value (EV) is the single most important concept in trading mathematics. It tells you how much you can expect to make or lose on average per trade. Professional traders evaluate every opportunity through the lens of expected value, ensuring they only take trades where the math is in their favor.
What is Expected Value?
Expected value is the average outcome of an action if you repeated it many times. In trading, it represents the average profit or loss per trade over the long run.
The EV Formula: EV = (Probability of Win x Average Win) - (Probability of Loss x Average Loss)
If EV is positive, you have a profitable trading system. If negative, you will lose money over time regardless of short-term wins.
Basic EV Calculation Example
Let us calculate expected value for a straightforward trading setup:
Trade Setup:
- Win rate: 40%
- Average winning trade: $500
- Loss rate: 60%
- Average losing trade: $200
EV Calculation:
- EV = (0.40 x $500) - (0.60 x $200)
- EV = $200 - $120
- EV = +$80 per trade
Despite losing 60% of the time, this strategy has positive expected value of $80 per trade. Over 100 trades, you would expect to profit $8,000.
Why Win Rate Alone is Misleading
Many traders focus on win rate, but this misses half the picture. Consider these two strategies:
Strategy A: High Win Rate
Win rate: 80%
Average win: $100
Average loss: $500
EV = (0.80 x $100) - (0.20 x $500) = $80 - $100 = -$20
Despite winning 80% of the time, this strategy loses money!
Strategy B: Low Win Rate
Win rate: 30%
Average win: $600
Average loss: $150
EV = (0.30 x $600) - (0.70 x $150) = $180 - $105 = +$75
Despite winning only 30% of the time, this strategy is profitable!
This is why you must consider both win rate AND win/loss ratio together.
The Risk-Reward Ratio Connection
Risk-reward ratio is directly connected to expected value. Here is how to calculate the minimum win rate needed for profitability at various risk-reward ratios:
Break-even Win Rate Formula: Win Rate = 1 / (1 + Reward/Risk)
| Risk:Reward | Break-even Win Rate | For Profit, Need |
|---|---|---|
| 1:1 | 50% | > 50% |
| 1:2 | 33% | > 33% |
| 1:3 | 25% | > 25% |
| 2:1 | 67% | > 67% |
EV for Options Trading
Options trading offers unique EV considerations. Let us analyze a credit spread:
Bull Put Spread Example:
- Credit received: $1.50 ($150 per contract)
- Maximum loss: $3.50 ($350 per contract)
- Probability of profit (from delta): 68%
EV Calculation:
- EV = (0.68 x $150) - (0.32 x $350)
- EV = $102 - $112
- EV = -$10 per contract
This trade has negative expected value at these prices. You would need either higher credit, lower max loss, or higher probability to make it worthwhile.
Adjusting for Transaction Costs
Real-world EV must account for commissions, fees, and slippage:
Adjusted EV = Raw EV - Transaction Costs
Example:
- Raw EV: +$25 per trade
- Commission: $1.30 round trip
- Estimated slippage: $5 per trade
- Adjusted EV: $25 - $1.30 - $5 = +$18.70
Transaction costs matter most for high-frequency strategies with small edges.
Multi-Outcome EV Calculations
Some trades have more than two outcomes. Here is how to calculate EV with multiple scenarios:
Iron Condor Example (4 Outcomes):
- Full profit (price stays in range): 45% chance, +$200
- Partial profit (minor breach): 25% chance, +$50
- Small loss (moderate breach): 20% chance, -$100
- Max loss (large move): 10% chance, -$400
EV Calculation:
- EV = (0.45 x $200) + (0.25 x $50) + (0.20 x -$100) + (0.10 x -$400)
- EV = $90 + $12.50 - $20 - $40
- EV = +$42.50 per trade
Edge and Expected Value
Your "edge" is simply your positive expected value expressed as a percentage of risk:
Edge Calculation: Edge % = EV / Average Risk x 100
Example:
- EV per trade: +$50
- Average risk per trade: $500
- Edge: $50 / $500 x 100 = 10%
A 10% edge means you expect to make 10% of your risk on average per trade.
Sample Size and Confidence
Expected value requires sufficient trades to manifest. With small sample sizes, variance dominates:
- 10 trades: Actual results can vary wildly from EV
- 50 trades: Results start converging toward EV
- 200+ trades: Results should closely match expected value
This is why traders say "trust the process" - with positive EV, results will come if you trade enough.
Evaluating New Strategies
Before trading a new strategy, calculate its expected value:
- Backtest or paper trade: Gather at least 50 sample trades
- Calculate statistics: Win rate, average win, average loss
- Compute EV: Use the formula to determine expected value
- Subtract costs: Account for real-world transaction costs
- Assess edge: Is the edge large enough to survive variance?
Calculate Your Edge Automatically
Pro Trader Dashboard tracks your win rate, average wins and losses, and calculates your expected value automatically from your trading history.
Common EV Mistakes
- Ignoring losing trades: Only counting winners skews calculations
- Using hypothetical numbers: Use actual trading data, not wishful thinking
- Forgetting costs: Transaction costs can erase small edges
- Changing strategies mid-stream: Consistent execution is needed for EV to work
- Small sample size: Drawing conclusions from too few trades
Summary
Expected value is the mathematical foundation of profitable trading. It combines win rate and risk-reward ratio into a single number that tells you whether a strategy will make money over time. Focus on taking trades with positive expected value, account for transaction costs, and trust that results will converge to expectation over many trades. Understanding and applying EV separates professional traders from gamblers.
Learn more about the Kelly Criterion for position sizing or probability of profit.