Expected Value (EV) is the long-run average outcome of a repeated process. In trading, EV per trade is the probability-weighted average profit or loss across all possible trade outcomes. A positive EV strategy will, over a sufficiently large number of trades, produce a positive total return. A negative EV strategy will, over the same number of trades, produce a loss — regardless of short-term luck or favorable market conditions. EV is the foundational concept underlying all professional trading: no systematic edge without positive EV, and a consistent positive EV strategy that is mechanically executed will produce profits in the long run even through periods of individual trade losses. For automated bot traders, EV provides the mathematical framework for evaluating any strategy before deployment and for understanding why certain strategies are profitable while others are not.
Related guides: Profit Factor, Win Rate vs Profit Factor, Position Sizing, Backtesting.
Expected Value Formula for Trading
EV per trade = (Win Rate × Average Win) - (Loss Rate × Average Loss) Where: Win Rate = fraction of trades that win (e.g., 0.55 = 55%) Loss Rate = 1 - Win Rate (e.g., 0.45 = 45%) Average Win = average profit per winning trade Average Loss = average loss per losing trade (positive number) Example: Win Rate = 55%, Average Win = $200, Average Loss = $120 EV = (0.55 × $200) - (0.45 × $120) EV = $110 - $54 = +$56 per trade This strategy earns an average of $56 per trade over the long run. Zero EV: Win Rate = 55%, Average Win = $109, Average Loss = $133 EV = (0.55 × $109) - (0.45 × $133) = $59.95 - $59.85 ≈ $0 (before fees)
EV and the Reward-to-Risk Ratio
Reward-to-Risk Ratio (RRR) = Average Win / Average Loss EV is positive when: Win Rate × RRR > Loss Rate Or equivalently: Win Rate > 1 / (1 + RRR) Breakeven win rates by RRR: RRR 1:1 (equal wins and losses): Need win rate > 50% RRR 1.5:1: Need win rate > 40% RRR 2:1: Need win rate > 33.3% RRR 3:1: Need win rate > 25% Key insight: A strategy with 35% win rate and 2:1 RRR has POSITIVE EV. A strategy with 65% win rate and 1:3 RRR has NEGATIVE EV.
Connecting EV to Profit Factor
Profit Factor = (Win Rate × Average Win) / (Loss Rate × Average Loss) If EV is positive → Profit Factor > 1.0 If EV is zero → Profit Factor = 1.0 If EV is negative → Profit Factor < 1.0 EV per dollar risked = (Win Rate × RRR) - Loss Rate Example: 55% win rate, 1.5 RRR: EV per dollar risked = (0.55 × 1.5) - 0.45 = 0.825 - 0.45 = +$0.375
See our Profit Factor guide for the relationship to backtest metrics.
Fee Impact on EV
Fees reduce EV per trade. The adjusted EV including round-trip fees:
Net EV = Gross EV - Round-trip fee cost Example: Gross EV = +$56, position size = $1,000, round-trip fee = 0.20% Fee cost = $1,000 × 0.20% = $2 Net EV = $56 - $2 = $54 (3.6% fee impact) For tight-spread strategies (grid trading): Gross EV per level = $5 (0.5% on $1,000 position) Round-trip fee = $2 Net EV = $3 (40% fee impact — very sensitive to fees) This is why fee minimization matters most for high-frequency, low-profit-per-trade strategies.
See our fees guide for fee optimization strategies.
EV in Multi-Trade Sequences: The Law of Large Numbers
EV only converges to the expected value over many trades — not in a few. With 10 trades, a +$56 EV strategy could easily produce a net loss of $200 or a net gain of $500 due to variance. With 100 trades, the actual result is likely within ±$150 of the expected $5,600 cumulative return. With 1,000 trades, the variance as a percentage of total expected return shrinks dramatically. This means: a positive EV strategy that is abandoned after 20 losing trades (before the law of large numbers can operate) will never deliver its positive EV. Consistent execution over sufficient trade count is required. See our journal guide for tracking.
Using EV to Compare Strategies in DennTech
- Run backtests on two candidate strategies with the same capital and risk settings
- Record win rate, average win, and average loss from each backtest report
- Calculate gross EV per trade for each: (Win Rate × Avg Win) - (Loss Rate × Avg Loss)
- Subtract round-trip fees from each to get net EV per trade
- Compare net EV per trade — the higher net EV strategy produces more profit per trade, all else equal
- Also compare trade frequency: EV per trade × trades per month = monthly EV (capital efficiency)
Full documentation at DennTech docs. All strategies at strategies page. Start at pricing page.
Frequently Asked Questions
- Can a high win rate strategy have negative EV?
- Yes — and this is one of the most important counterintuitive insights in trading. A strategy with 80% win rate but average wins of $50 and average losses of $300 has: EV = (0.80 × $50) - (0.20 × $300) = $40 - $60 = -$20 per trade. The strategy loses money on average despite winning 80% of the time because the losses are 6× larger than the wins. This negative EV strategy is the classic "pick up nickels in front of a steamroller" pattern — many small wins followed by occasional catastrophic losses. Always calculate EV from both win rate AND average win/loss, never from win rate alone. See our Win Rate vs Profit Factor guide.
- How does Kelly Criterion relate to Expected Value?
- Kelly Criterion uses EV components to calculate the optimal position size fraction that maximizes long-run geometric growth. Kelly % = (Win Rate × RRR - Loss Rate) / RRR. A higher EV strategy produces a higher Kelly fraction — the math recommends allocating more capital to higher-EV opportunities. In practice, full Kelly is too aggressive (produces excessive variance); most professional traders use 0.25–0.50× Kelly. The relationship is important because it shows position sizing and EV are mathematically linked — maximizing long-run growth requires combining a positive EV strategy with appropriately sized positions. See our position sizing guide. Start at the pricing page.
- Is Expected Value the most important metric for evaluating a DennTech strategy?
- EV is the foundational metric that must be positive for any strategy to be worth running — it is the first filter. But it is not sufficient alone: a strategy with high EV per trade but only 5 trades per year has low capital efficiency; a strategy with positive EV but massive variance (huge individual wins and losses) may be psychologically unmanageable; a strategy with positive gross EV but negative net EV after fees and slippage is not deployable. The complete evaluation framework uses EV as the foundation, then applies Profit Factor (confirms EV sign), Maximum Drawdown (confirms risk tolerance), Calmar Ratio (confirms capital efficiency of risk), and trade frequency (confirms capital deployment rate). All these metrics are available in DennTech's backtest report. Compare editions at the pricing page. Explore the live demo.
Performance math: EV (this guide), Profit Factor, Win Rate vs PF. All strategies at the strategies page.