EXPECTANCY: WHY WIN RATE ALONE LIES

A trader who wins 60% of the time can still lose money; one who wins 40% can still come out ahead. The score is expectancy — win rate times payoff, minus the toll. Win rate is a batting average; expectancy is the scoreboard. A .300 hitter who only ever singles can be outscored by a .220 hitter who hits home runs — and a trading account is paid in runs, not in batting average. Every trading conversation you will ever hear quotes the batting average, because it is the number that sounds good. This course keeps the scoreboard: what does one trade earn or cost, on average, after everything? Answer that and the win rate becomes what it always was — one ingredient, interesting only in combination.

EXPECTANCY · STAGE 4 · LESSON 1

THE TAKEAWAYS

• Trader A, worked in full: wins 60% of trades, average win $100, average loss $180. Expectancy = 0.60 × $100 − 0.40 × $180 = $60 − $72 = −$12 per trade. Over 100 trades that is about −$1,200 — from a trader who wins most of the time. ‘Wins most trades’ and ‘loses money’ are the same sentence here, with no contradiction.
• Trader B, worked in full: wins 40%, average win $300, average loss $100. Expectancy = 0.40 × $300 − 0.60 × $100 = $120 − $60 = +$60 per trade — about +$6,000 over 100 trades, while losing six of every ten. The payoff column, not the win column, did the work. Neither trader is exotic; the difference between them is arithmetic, not talent.
• The breakeven win rate falls out of the payoff: needed win rate = average loss ÷ (average win + average loss). Win and lose the same ($100/$100) and you must win 50% just to stand still. Win twice your loss ($200/$100) and 33.3% is enough. Win half your loss ($100/$200) and you need 66.7% — a standard most ‘high win-rate’ selling quietly fails.
• Costs sit inside the formula, not after it. Stage 2 priced a real round trip on the Oct 9 chain (773 call, bid 20.53 / ask 20.68): worst case ≈ $16.30 a contract; filled at the midpoint both ways, ≈ $1.30 in contract fees. A method with +$10 of gross expectancy per trade is a losing method filled at the spread and a winning one filled at the mid. Execution is not separate from the edge — it is part of it.

WORKED EXAMPLE — STEP BY STEP

1. Write Trader A’s line: 60% wins at +$100, 40% losses at −$180. The wins contribute 0.60 × 100 = +$60 per trade on average. The losses take 0.40 × 180 = $72. Net: −$12. Every trade this trader takes costs twelve dollars on average, however exciting the wins feel.
2. Write Trader B’s line: 40% wins at +$300 contribute +$120; 60% losses at −$100 take $60. Net: +$60 per trade. B loses more often than A and ends 100 trades roughly $7,200 ahead of A. If that still feels wrong, that feeling is exactly the bias this lesson exists to retire.
3. Find each trader’s breakeven line: A’s payoff ($100 won vs $180 lost) demands a win rate of 180 ÷ 280 = 64.3% to break even — A’s 60% falls short of it. B’s payoff ($300 vs $100) demands only 100 ÷ 400 = 25% — B’s 40% clears it with room. The breakeven line, computed in advance, tells you which side of zero a win rate lands on before a single trade is taken.
4. Now run the toll through both: if either trader’s method runs on options filled at worst-case friction (Stage 2’s ≈ $16.30 per contract round trip), subtract it per trade: A goes to −$28.30; B to +$43.70. Filled at the midpoint instead (≈ $1.30), A is −$13.30 and B +$58.70. Same methods, same win rates — the spread decided how much of the edge survived.
5. The habit to take forward: every method you ever evaluate gets three numbers before it gets an opinion — its win rate, its average win and loss, and its cost per trade. Two of the three are unflattering in most sales pitches, which is why pitches quote only the first.

WHY YOU CAN’T KNOW YOUR EXPECTANCY YET — THE SAMPLE PROBLEM

Expectancy is estimated from a sample of trades, and small samples lie with a straight face. Lesson 3 does the full arithmetic; the headline is this: a win rate measured over 20 trades carries about ±22 percentage points of pure luck either way (the 95% range for a proportion), so a genuinely break-even method can show 72% winners over 20 trades — and a good one can show 30%. Which means your expectancy, early on, is a hypothesis with wide error bars, not a fact about you. That uncertainty is not a footnote to position sizing; it is the reason for it. The next lesson sizes every trade as if the hypothesis might be wrong — because statistically, it might be.

COMMON BEGINNER MISTAKES

• Judging any method — a guru’s, a friend’s, your own — by its win rate alone. 95% winners can be a losing method; 40% winners can be a fine one.
• Averaging wins and losses from memory. Memory edits both columns in your favour; Lesson 6’s journal exists because expectancy computed from memory is fiction.
• Quoting gross expectancy and forgetting the toll. The spread and fees are paid on every trade, including the winners.
• Treating last month’s expectancy as a permanent property. It is an estimate from a small sample of a changing market — hold it the way Stage 3 holds a trend: in pencil.

CHECK YOURSELF

DO IT — SCORE THREE TRADERS COLD

In your journal, rebuild this lesson’s two scoreboards from the raw ingredients (don’t copy the answers): Trader A (60%, +$100/−$180) and Trader B (40%, +$300/−$100) — expectancy and breakeven win rate for each. Then score a third, the typical beginner shape: 50% wins, average win $80, average loss $120. Its expectancy is −$20 a trade and its breakeven line is 60% — check your arithmetic against those. Three scoreboards, computed cold, is half of Stage 4’s arithmetic gate.