Level 6 · Lesson 10
Expectancy
& Edge
The only number that determines whether you make money or lose it. Everything else is noise.
First — Why This Matters
🔍 The Casino's Secret
A casino does not know if the next hand will win or lose. It does not care. It knows that across thousands of hands, the house edge of 1-5% guarantees profit. The casino does not gamble — it operates a mathematical system. Expected Value is positive, volume is high, and time does the rest.
Your trading strategy works identically. You do not need to know if the NEXT trade will win. You need to know that across 100+ trades, your Expected Value is positive. If it is, you are the casino. If it is not, you are the gambler. This lesson teaches you how to calculate, measure, and protect your edge.
🔎 REAL SCENARIO
A trader was losing money with a 58% win rate. His wins averaged £75, his losses averaged £130. EV = (0.58 × £75) − (0.42 × £130) = £43.50 − £54.60 = −£11.10 per trade. He was winning MORE often but losing MORE per loss. The fix: tighter stops (smaller losses) + wider targets (bigger wins). New stats: 49% WR, £160 avg win, £100 avg loss. EV = +£27.40/trade. Lower win rate, higher profit.
01 — The EV Balance
Wins vs Losses on the Scale
Watch the scale tip. When wins outweigh losses (positive EV), you are the casino. When losses outweigh wins, you are the gambler.
02 — Edge Erosion
What Eats Your Profit
Your gross edge gets taxed at every step. See how a £50 edge becomes £22 after real-world costs.
03 — The 4 Components
What Makes an Edge
04 — Breakeven Win Rates
How R:R Changes the Game
| R:R | Breakeven WR | Verdict |
|---|---|---|
| 1:0.5 | 67% | Very hard — need to win 2 of every 3 trades |
| 1:1 | 50% | Coin flip territory — commissions push you negative |
| 1:1.5 | 40% | Achievable — this is the minimum viable R:R |
| 1:2 | 33% | Comfortable — miss 2 of 3 and still break even |
| 1:3 | 25% | Strong edge territory — 1 in 4 wins covers everything |
| 1:5 | 17% | Reversal territory — 1 in 6 wins still profitable |
💡 The formula: Breakeven WR = 1 ÷ (1 + R:R). At 1:2, you need 33%. At 1:3, you need 25%. At 1:5, you need 17%. The higher your R:R, the less you need to win. This is why Model 2 (reversals at 1:3-5) works despite low win rates.
05 — Edge Calculator
Calculate Your Real Edge
Enter your stats. See gross EV, edge erosion, and net income.
Win Rate (%)
Avg Win (£)
Avg Loss (£)
Trades / Week
Edge Erosion Costs (per trade):
Spread (£)
Commission (£)
Slippage (£)
Mistakes (%)
R:R
1:2.2
BE Win Rate
31%
Gross EV
+£54
Net EV
+£41
Weekly Income
+£331
Monthly Income
+£1435
Edge erosion: £12 lost per trade (23% of gross edge)
06 — The Income Equation
Income = EV × Frequency
Weekly Income = Net EV × Trades per Week
Two levers control your trading income: how much you make per trade (EV) and how often you trade (frequency). You can optimise either one — but never sacrifice EV for frequency (forcing low-quality trades to increase volume).
High EV, Low Frequency
+£50/trade × 3/week = £150/week. Selective, high-quality setups. Less screen time. Better for part-time traders.
Lower EV, High Frequency
+£15/trade × 12/week = £180/week. More setups, smaller edge each. More screen time. Better for full-time traders.
07 — Variance: The Noise Around the Edge
Why Good Strategies Have Bad Months
EV is a long-term average, not a per-trade guarantee. In any small sample (one day, one week, one month), actual results bounce around the EV like a ball on a trampoline. This bouncing is variance.
💡 The Coin Flip Analogy: A fair coin has 50% heads EV. But if you flip it 10 times, getting 7 heads and 3 tails is completely normal — even though 50% would predict 5/5. At 1,000 flips, the ratio will be very close to 50/50. Trading is the same: at 10 trades, anything can happen. At 200 trades, the average converges on the true EV.
10 trades: Wildly unpredictable. A +EV strategy can easily lose money. Tells you nothing.
50 trades: Pattern emerging but still noisy. Might be +£800 or -£200 on a +£25 EV strategy.
200 trades: The average is converging. You can trust the numbers. Variance is smoothing out.
08 — Common Mistakes
4 Edge Killers
09 — Cheat Sheet
Expectancy Quick Reference
EV FORMULA = (WR × Avg Win) − (LR × Avg Loss). Positive = edge. Negative = no edge.
BE FORMULA = Breakeven WR = 1 ÷ (1 + R:R). At 1:2, need 33%. At 1:3, need 25%.
INCOME = Net EV × Trades per week. Two levers: EV size and frequency.
EROSION = Spread + Commission + Slippage + Mistakes. Expect 30-60% erosion from backtest to live.
VARIANCE = Bad months are normal. EV converges over 200+ trades. Trust the maths, not the month.
10 — Test Your Understanding
Expectancy Game
5 scenarios. Calculate, compare, and decide.
Trader A: 62% WR, average win £80, average loss £120. Trader B: 41% WR, average win £280, average loss £90. Who is more profitable per 100 trades?
11 — Knowledge Check
Final Quiz — 8 Questions
Question 1 of 8
What does a positive Expected Value (EV) mean?
Question 2 of 8
A strategy has 45% WR and 1:2 R:R. What is the EV per £100 risked?
Question 3 of 8
What is the breakeven win rate for a strategy with 1:3 R:R?
Question 4 of 8
What are the 4 sources of "edge erosion" that reduce backtest EV in live trading?
Question 5 of 8
Strategy A: EV +£40/trade, 4 trades/week. Strategy B: EV +£15/trade, 14 trades/week. Which earns more per week?
Question 6 of 8
A trader has a 60% WR with 1:0.7 R:R. Is this strategy profitable?
Question 7 of 8
Why is a 70% win rate with 1:0.5 R:R worse than a 40% win rate with 1:3 R:R?
Question 8 of 8
Your strategy has +£25 EV per trade. Last month (18 trades), you made +£120 instead of the expected £450. Should you change the strategy?