# Expectancy: the average trade > Compute what an average trade earns after costs from a real trade list, and see why ten trades can tell the opposite story from forty. - Course: [Trading Basics: How It Works, How Not to Lose Everything](https://productovi.com/courses/trading.md) - Module: Can I lose often and still come out ahead? - Lesson 14/32, ~28 min - Source: https://productovi.com/courses/trading/expectancy ## Marc's forty trades **Alex Tutor:** Back on your Pebble practice account, Marc has brought his whole **trade journal**: 40 trades, each risking about 1% of his 10,000 account. Today we squeeze one number out of it. **Dataset (CSV):** [Marc's practice journal, 40 trades](https://productovi.com/datasets/trading/expectancy/m4_marc_trades.csv) Each trade risks about 100 dollars to its stop. net_result is after fees: (exit − entry) × size for a long, (entry − exit) × size for a short, minus fees. - `side`: long (bought first) or short (sold first) - `size`: Units traded - `fees`: Commission and spread for the round trip, dollars - `plan_followed`: Did Marc follow his written plan? - `net_result`: Result after fees, dollars **Nora:** Forty rows. Do I have to add them all up? **Alex Tutor:** Marc did the totals, and you can check any row yourself. Trade 3 is a long: (40.94 − 37.24) × 54 − 4.16 = 195.64, exactly what net_result says. ![Marc kneels and unrolls a long scroll of trade rows dotted with blue and grey pebbles; at its end one blue pebble sits on a small pedestal while Alex and Nora look on.](https://productovi.com/courses/trading/diagrams/m4-l2-scene.png) **Marc:** 16 wins and 24 losses, so a 40% win rate. My wins average 208.91, my losses −105.92. All 40 together: plus 800.41, after 218.36 of fees. > **Marc's journal totals** > > - All 40 trades: 16 wins and 24 losses, a 40% win rate. Average win 208.91, average loss −105.92. > - Net result: +800.41 after 218.36 of fees, so +20.01 a trade after costs. Each trade risks about 1% of his 10,000 account. > - The first 10 trades alone: 2 wins and 8 losses, −405.17. **Alex Tutor:** The number we want is **expectancy**: the average result of one trade after costs. Total net result divided by the number of trades. > **Exercise:** Marc's 40 trades add up to +800.41 after fees. What is his expectancy per trade, in dollars? Two decimals. **Sofia:** Can I get the same number from the win rate and the averages? **Alex Tutor:** Yes. That's the formula version, and it shows where the result comes from. $$ \text{expectancy} = \text{win rate} \times \text{average win} - \text{loss rate} \times |\text{average loss}| $$ *Average result of one trade, after costs* **Alex Tutor:** 0.40 × 208.91 − 0.60 × 105.92 = 83.56 − 63.55 = 20.01. Same answer. Traders sometimes call a positive expectancy an "edge": an average gain per trade after costs. Nothing more mysterious than that. A positive number is the first test a plan must pass, not the last. **Alex Tutor:** Try the formula on a different plan, so you see which numbers move the result. > **Exercise:** A plan on the Harbor 20 Index Fund (HRB) wins 35% of its trades. Its average win is 150 dollars and its average loss is 60, after costs. What is its expectancy per trade, in dollars? **Alex Tutor:** Dollars depend on how much each trade risks. Compare two plans per dollar at risk. > **Exercise:** Plan A on NWF averages +20 dollars a trade with 100 dollars at risk per trade. Plan B on BFE averages +30 a trade with 300 at risk per trade. Which plan earns more for each dollar it puts at risk? ## Before and after costs **Nora:** What would it be without the fees? **Alex Tutor:** Add the 218.36 of fees back to get the gross result, then divide by 40. > **Exercise:** Over 40 trades Marc's net total is 800.41 and his fees were 218.36. What is his expectancy per trade before costs, in dollars? **Marc:** That's why I write fees in every row. A plan with a thin edge can turn negative just from trading more often. **Nora:** Five dollars a trade in fees doesn't sound like much. **Alex Tutor:** Over 40 trades it's 218.36, more than a quarter of Marc's net result. Over a few hundred trades, that's the difference between a plan that works and one that doesn't. **Alex Tutor:** Here's a plan whose costs are bigger than its average gain. What is left after them? > **Exercise:** A plan on Lumen / Crown (LUM/CRN) averages +4.00 dollars a trade before costs. Fees and the spread cost 5.46 a trade. What is its expectancy after costs, in dollars? ## The first ten **Marc:** Confession: after the first 10 trades I almost quit. Two wins, eight losses, minus 405.17. > **Exercise:** Marc's first 10 trades add up to −405.17. What was his expectancy per trade over those 10, in dollars? **Alex Tutor:** Ten trades can swing either way by luck alone. A losing run of eight in ten is entirely possible for a plan that works, and so is a winning run for one that doesn't. That's why the size stays the same while you collect them. **Sofia:** So which number do I believe, the ten or the forty? **Marc:** I nearly believed the wrong one. > **Exercise:** How many trades should a journal hold before you start to trust its expectancy? **Nora:** So 40 trades means Marc's plan definitely works? **Alex Tutor:** No. It means the plan is worth testing further. Check what could be wrong: these are practice trades in one stretch of the market, a calm period may not repeat, and 40 is still a small number. **Marc:** One more thing that could be wrong: I followed the plan on every trade so far. If I start bending it, these 40 rows stop describing what I actually do. **Marc:** So I'm running another 40 before I call it anything. > **Exercise:** After his first 10 trades, Marc had enough evidence to say his plan doesn't work. **Marc:** The hard part was keeping the size at 1% while it looked broken. **Nora:** I'd have doubled up to win it back. **Alex Tutor:** And that's exactly how a slow start becomes a disaster. > **Exercise:** Nora's journal shows 8 trades and an average of +65 dollars a trade. She says: "My expectancy is 65, three times Marc's." In 2–3 sentences, explain what's wrong with comparing them, with numbers. **Alex Tutor:** So that's expectancy: one number, honestly computed. After costs, on enough trades, with a note on what could be wrong. Anything less is a mood, not a measurement. > **Key ideas** > > - **Expectancy** is the average result of one trade after costs: total net ÷ number of trades. Marc: 800.41 ÷ 40 = +20.01. > - The same from the formula: 0.40 × 208.91 − 0.60 × 105.92 = 20.01. > - Before costs it was 25.47; label any before-cost number as such. > - Fewer than 30 trades is too few to tell: Marc's first 10 said −40.52 a trade. > - Even 40 trades is a first reading. Always check what could be wrong with it. > **Educational, not advice** > > This course explains how trading works; it never tells you what to buy or sell. A positive expectancy on a practice account is not a promise for the future. Most people who trade lose money, and you can lose all of it. For taxes and rules, check with a licensed professional where you live. - Previous lesson: [Win rate and reward-to-risk](https://productovi.com/courses/trading/win-rate-and-payoff.md) - Next lesson: [Drawdown: why losses hit harder than gains](https://productovi.com/courses/trading/drawdown-and-ruin.md) --- Productovi Learning. Free, no sign-up needed to read.