The Trader's Arithmetic · Lesson 1 of 6
Expectancy: The Only Score That Matters
Win rate is the number beginners worship. It is also, alone, completely meaningless.
Ask a beginner how a trading system is doing and they quote its win rate. Ask a professional and they quote its expectancy: the average amount won or lost per trade, across everything. One formula:
Expectancy = (Win% × average win) − (Loss% × average loss)
That subtraction is the entire game. If it is positive, time and repetition are on your side; if negative, no amount of discipline, psychology or capital fixes it — you have a machine for shrinking money, operated carefully.
Watch it destroy the win-rate worship. System A wins 90% of the time: average win 5 pips, average loss 60. Expectancy: (0.90 × 5) − (0.10 × 60) = 4.5 − 6.0 = −1.5 pips per trade. A machine that is nearly always right and steadily going broke — and it describes a very common trading style: snatch tiny profits instantly, let losers run "until they come back". Its owner will tell you, honestly, that they win nine trades in ten.
System B wins just 35% of the time: average win 80, average loss 25. Expectancy: (0.35 × 80) − (0.65 × 25) = 28 − 16.25 = +11.75 pips per trade. Its owner loses most days and feels like a failure at dinner parties. The arithmetic says the failure is funding the retirement.
Our system's exits are fixed at 25 pips of win against 40 of loss — so its breakeven win rate is 40 ÷ (40 + 25) = 61.5%. That number was known, in writing, before the system went live: below 61.5% sustained, the machine is net negative and the record will say so in public. Knowing your own breakeven before you begin is the first grown-up act in trading.
Two warnings before the next lesson. Expectancy is only knowable from a log — without recorded trades it is a guess wearing a formula. And it is only trustworthy at sample size — a dozen trades tell you almost nothing, which is its own lesson later in this course.