Expectancy: the average trade

Expectancy is the average result of one trade after costs: the total net result of a set of trades divided by the number of trades. It answers the question a win rate can't: on average, does a trade from this plan add money or take it away?

Marc's practice journal on Pebble holds 40 trades, each risking about 100 dollars (1% of his 10,000 account) to its stop. All 40 together come to +800.41 after 218.36 of fees, so his expectancy is 800.41 ÷ 40 = +20.01 a trade.

Any row can be checked: trade 3 is a long, (40.94 − 37.24) × 54 − 4.16 = 195.64, just as the journal says. The habit matters, because one wrong row shifts the average.

Some traders call a positive expectancy an edge. In this course the word means nothing more than an average gain per trade after costs, above zero over enough trades. A positive number is the first test a plan must pass, not proof that it works.

Expectancy can also be built from numbers you know from Win rate and reward-to-risk:

expectancy = win rate × average win − loss rate × average loss

Here the loss rate is 1 − win rate, and the average loss is taken without its minus sign.

For Marc: 0.40 × 208.91 − 0.60 × 105.92 = 83.56 − 63.55 = 20.01, the same as dividing his total by 40. For a plan on HRB that wins 35% with wins of 150 and losses of 60: 0.35 × 150 − 0.65 × 60 = 52.50 − 39.00 = +13.50 a trade.

The formula shows why the number is positive or negative and which lever moves it: a few more wins, slightly bigger wins or slightly smaller losses. It also ties back to the break-even win rate: expectancy is exactly zero when the win rate sits on that line. Use averages after costs, or the result is a before-cost number and must be labelled that way.

A dollar expectancy depends on how much each trade risks. To compare plans fairly, divide it by the planned risk per trade. The result is expectancy in risk units, where one risk unit is what a trade plans to lose if it hits its stop: 100 dollars for a 10,000 account at 1%, the risk per trade set in module 3.

Marc makes +20.01 a trade on 100 of risk, about +0.2 risk units: on average each trade earns back a fifth of what it puts at risk.

Now two plans. A on NWF makes +20 a trade with 100 at risk, +0.2 units. B on BFE makes +30 with 300 at risk, +0.1 units. B shows more dollars only because it bets three times as much. Per dollar at risk, A is twice as good, and its losing runs cost a third as much.

Risk units also keep the arithmetic stable when the account grows or shrinks: the quality of a plan lives in the units, and the dollars simply follow the size.

Every expectancy has two versions. Before costs adds back the fees, the spread and slippage (Where the money goes: spread, fees and slippage); after costs is what actually reached the account. Only the after-cost number says whether a plan earns.

Marc's 40 trades made +800.41 after 218.36 of fees. Before costs that is 800.41 + 218.36 = 1,018.77, or 25.47 a trade. Costs took 5.46 of every 25.47, more than a fifth of the gross result.

Costs are charged on every trade, win or lose, so they hurt most when the average is thin and the trades are many. Over 40 trades Marc's fees came to more than a quarter of his net result; over a few hundred trades they can decide whether a plan works at all.

The rule is short: quote the after-cost expectancy, and label any before-cost number "before costs". A plan that only works before costs doesn't work.

A small positive expectancy before costs can turn negative after them, because costs are charged on every trade whatever its result.

Take a plan on LUM/CRN that averages +4.00 a trade before costs, with 5.46 of fees and spread per trade. After costs: 4.00 − 5.46 = −1.46 a trade. Over 200 trades that is −292. The trades were often right about direction, and the account still shrank.

That is why plans built on many tiny moves are fragile: the average gain per trade is small, while the cost per trade stays the same. Trading more often multiplies the costs as fast as the gains, so it can't rescue a thin edge, and a cost rise of a dollar or two can wipe one out.

When you judge a plan, put its expectancy before costs next to its cost per trade. If the two are close, the plan has almost no room for error.

An expectancy computed on a few trades swings wildly with luck. Marc's first 10 trades had 2 wins and 8 losses, −405.17 in total: an expectancy of −405.17 ÷ 10 = −40.52 a trade. The same plan over all 40 trades: +20.01. Ten trades told the opposite story from forty.

Nothing about the plan changed between trade 10 and trade 40. Eight losses in ten are entirely possible for a plan that works, and a run of wins is just as possible for one that doesn't. Short samples mostly measure luck.

That has a practical side: while the trades are being collected, the risk per trade stays the same. Marc kept his at 1% through the bad start. Doubling it to "win it back" would have made the early losses far bigger than the plan intended, and the later average would no longer describe one plan. How long losing runs can be has its own lesson later in the course, A losing streak is normal.

This course uses a simple rule: before you trust an expectancy or a win rate, collect at least 30 trades, and more is better. Below 30, the honest label is "too few to tell".

Thirty is not a magic number. It is a floor where the average stops jumping around quite so much, not a point where it becomes certain. Even Marc's 40 trades are a first reading: the next 40 could come out higher or lower.

So when a journal reaches 30 or 40 trades with a positive expectancy, the conclusion is "worth testing further", not "proven". Then look for what could be wrong with it:

• the trades come from one stretch of the market, and a calm period may not repeat;
• the plan was followed on every trade, and bending it would change what the rows describe;
• the costs in the rows match what real trading would cost.

Expectancy turns a journal into one number, but only an honest version of it is worth anything. Four conditions:

1. After costs. A before-cost figure must say so.
2. On enough trades. Fewer than 30 is "too few to tell" in both directions: Marc's first ten trades (−40.52 a trade) did not prove his plan broken, and forty (+20.01) don't prove it works.
3. At a steady risk per trade, so the average describes one plan, not a mix of small and big bets.
4. With a note on what could be wrong: one market stretch, plan discipline, real costs.

A number that misses any of these is a mood, not a measurement.

How it fits together: the win rate, payoff and break-even line from the last lesson combine into expectancy, which counts only after costs and on enough trades. The next lesson, Drawdown: why losses hit harder than gains, shows how the size of each trade can still ruin a positive expectancy.