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Expectancy as the core metric

Define expectancy, compute it from winrate and average P&L, and explain why it's the most useful single number in trading.

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Options, Risk Math, and Psychology

Risk Math Deep Dive

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Lesson 39 of 75Options, Risk Math, and PsychologyRisk Math Deep Dive

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Define expectancy, compute it from winrate and average P&L, and explain why it's the most useful single number in trading.

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Expectancy: dollars per trade, on average

Expectancy is the average amount you expect to make per trade, weighted by how often each outcome happens. The formula is short: E = (winrate x avg_win) − (loss_rate x avg_loss). Positive E means the system makes money over many trades. Negative E means it bleeds. Zero means break-even before costs. This single number is more honest than winrate, more honest than recent P&L, and more honest than how a trade 'feels'.

Wick shows a calculator reading +$5 under the expectancy math for a 40% win rate, showing a system can lose most trades and still earn on average.0.40 x $50 - 0.60 x $25+$5
Wick saysWin 40% with $50 wins and $25 losses, and each trade still averages +$5.

Worked example with the $500 account. Say you take trades risking $25 each. Over 50 trades, you win 20 of them with an average win of $50, and you lose 30 of them with an average loss of $25. Winrate = 20/50 = 40%. Plug in: E = (0.40 x $50) − (0.60 x $25) = $20 − $15 = +$5 per trade. Over 50 trades, that's +$250 — a 50% account gain on a system that LOSES 60% of the time. Winrate alone would have made you quit. Expectancy says keep going.

Wick holds two cards: green Sanity says check average dollars per trade, coral Vanity says judge by win rate alone, teaching that expectancy is the honest number.SanityCheck averagedollars per tradeVanityJudge a system bywin rate alone
Wick saysWin rate is vanity and expectancy is sanity, so always run the math.

Two failure modes to watch. First, the high-winrate trap: 80% win, but you let losers run while cutting winners short. E = (0.80 x $10) − (0.20 x $60) = $8 − $12 = −$4 per trade. You'd be CONFIDENT and broke. Second, the lottery-ticket trap: 5% win on huge home runs. E = (0.05 x $500) − (0.95 x $25) = $25 − $23.75 = +$1.25. Technically positive, but the variance will destroy you emotionally long before the math works. Expectancy alone isn't enough — you also need to be able to survive the variance.

Wick watches a scale tip toward 20% losses of $60 each over 80% wins of $10 each, showing the high win rate trap that ends at minus $4 a trade.80% wins$10 each20%losses$60 each?
Wick saysWin 80% of trades and you can still lose if one loss eats several wins.

Recap: E = (winrate x avg_win) − (loss_rate x avg_loss). Positive E means edge. A losing winrate can still print money. A winning winrate can still go broke. Always compute expectancy from your trade log.

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1. You win 30% of your trades. When you win, you make $90. When you lose, you lose $30. What's your expectancy per trade?

2. Which is the more reliable signal that a trading system 'works'?

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