Trading Expectancy: Your Mathematical Edge

Expectancy is the mathematical formula that determines whether your trading system makes or loses money over time. Understanding it is essential for systematic traders. [DEFINITION] Trading Expectancy: The average amount you can expect to win or lose per trade over time, calculated from your win rate, average win size, and average loss size. Positive expectancy = profitable system. ### The Expectancy Formula [FORMULA] Expectancy = (Win Rate × Average Win) - (Loss Rate × Average Loss) Where: - Win Rate = Percentage of winning trades - Loss Rate = 1 - Win Rate - Average Win = Average profit on winning trades - Average Loss = Average loss on losing trades ### Calculating Your Expectancy [EXAMPLE] Your trading results: - 100 trades - 45 winners (45% win rate) - Average win: $500 - Average loss: $300 Expectancy = (0.45 × $500) - (0.55 × $300) Expectancy = $225 - $165 = $60 per trade This system makes $60 on average per trade—positive expectancy. [KEY] A positive expectancy system makes money over time, regardless of individual trade outcomes. It's the mathematical foundation of profitable trading. ### Why Expectancy Matters **Removes emotion:** Individual trades don't matter; the aggregate does. **Allows losing:** You can lose 55% of trades and still profit (as in the example above). **Focuses on process:** Right process → right results over time. ### Breaking Down the Components **Win rate alone doesn't determine profitability:** - 80% win rate with small wins and big losses = negative expectancy - 30% win rate with big wins and small losses = positive expectancy **Risk-reward ratio matters:** - Even low win rates profit if wins are much larger than losses - High win rates can lose money if losses are larger than wins ### Improving Expectancy **Increase win rate:** - Better entry signals - Improved analysis - Market selection **Increase average win:** - Let winners run - Trail stops effectively - Add to winning positions **Decrease average loss:** - Cut losses quickly - Tighter stop-losses - Better position sizing [TIP] Most traders focus on win rate, but risk-reward (average win vs average loss) often has more impact on expectancy. ### Expectancy in Practice [EXERCISE] System A: 60% win rate, $200 average win, $300 average loss. System B: 35% win rate, $600 average win, $150 average loss. Which has better expectancy? |ANSWER| System A: (0.60 × $200) - (0.40 × $300) = $120 - $120 = $0 (break-even). System B: (0.35 × $600) - (0.65 × $150) = $210 - $97.50 = $112.50 per trade. System B is more profitable despite losing 65% of trades because winners are much larger than losers. ### The Expectancy Mindset **Individual trade thinking:** "I need this trade to work!" → Emotional, attached to outcomes **Expectancy thinking:** "I need to follow my system over many trades." → Process-focused, detached from individual outcomes ### Tracking Your Expectancy Record for every trade: 1. Entry price and date 2. Exit price and date 3. Profit or loss (in $ and %) 4. Position size 5. Notes on setup quality Calculate monthly: - Win rate - Average win - Average loss - Expectancy [WARNING] Expectancy requires sufficient trades to be meaningful. 10 trades isn't enough. Calculate over at least 50-100 trades for statistical significance. ### When Expectancy Turns Negative If your expectancy is negative: 1. Stop trading real money 2. Analyze what's not working 3. Paper trade refinements 4. Return to real money when positive [SCENARIO] Your system has 50% win rate, $400 average win, $500 average loss. Expectancy = (0.50 × $400) - (0.50 × $500) = $200 - $250 = -$50 per trade. How should you address this? You're losing $50 per trade on average. Options: 1) Reduce average loss (tighter stops, maybe accepting lower win rate). 2) Increase average win (trail stops, let winners run longer). 3) Improve win rate (better entry criteria). 4) Combination approach. You need to turn that -$50 positive. A 10% improvement in any component could flip expectancy positive.