Expectancy and sample size

You now have a setup, a filter and an invalidation. The question is whether the combination makes money, and the honest answer for a long time is: you do not know. This lesson is about what "knowing" would take, so that you neither abandon a working setup after a bad week nor trust a broken one after a good one.

Expectancy, briefly

The risk management course covered this in full. The one-line version:

Expectancy (R per trade) = win rate × average winner (R) − loss rate × average loser (R)

A setup with a 40% win rate, average winner 2.2R and average loser 1R has expectancy 0.4 × 2.2 − 0.6 × 1 = 0.28R per trade. Positive. A setup with a 65% win rate, average winner 0.8R and average loser 1R has 0.65 × 0.8 − 0.35 × 1 = 0.17R. Also positive, and it feels much better to trade, because it wins more often. The first is better.

Nothing on the plan should be evaluated on win rate alone. It is the number that feels most important and tells you the least.

What to expect from a real edge

Retail setups that survive contact with costs tend to land somewhere between 0.1R and 0.4R per trade in expectancy. Anything above 0.5R sustained over a large sample is rare and usually means the sample is not large or the costs are not counted. If your first twenty trades show 1.2R per trade, the correct reaction is suspicion, not celebration.

Costs matter more than beginners expect. A 0.28R setup with spread and commission equal to 0.1R per round trip is a 0.18R setup. On a tight-stop intraday plan, costs can be 0.2R or more, which is why intraday edges need to be larger on paper to survive.

The sample size problem

Here is a table that every trader should have memorised. It shows, for a setup with a true win rate of 45%, the range of win rates you would actually observe over samples of different sizes, roughly 95% of the time.

After ten trades, a 45% setup can look like a 76% setup or a 14% setup. After thirty, it can still look like a 27% one, which would be a loser at most reward ratios. It takes about a hundred trades before the observed number is within ten points of the truth, and even then, one time in twenty it is not.

Expectancy is worse, because it also depends on the size of the winners, and a couple of 5R outliers in a 20-trade sample will swing it enormously.

Key idea: Twenty trades tell you almost nothing. Fifty tell you whether the setup is probably not terrible. A hundred start to tell you what it is. Do not change a rule on less than thirty, and do not trust a number on less than a hundred.

What this means for the plan

• The plan's REVIEW line specifies a minimum number of trades before any rule changes. Thirty is the practical floor; fifty is better.
• Losing streaks are expected. At a 45% win rate, a run of six losses in a row has roughly a 3% chance on any given trade, which means it will happen several times a year if you take a trade a day. A six-loss streak is not evidence. It is Tuesday.
• Winning streaks are also not evidence. Eight wins in a row feels like mastery; it is a 1.7% event at 45% and it will also happen.
• The way to build a sample faster is not to trade more setups. It is to trade the same setup consistently so every trade counts toward the same sample.

Expectancy expectations, written down

Put a line in your journal, not on the plan, that says what you expect the setup to do, before you have the data. "Expected: 40 to 50% win rate, 1.8R average winner, roughly 0.2R per trade after costs." When you reach fifty trades, compare. If the result is inside the range, keep going. If it is wildly outside in either direction, Module 5 has the checklist for what to look at, and "the setup is broken" is only one of the possibilities.

Try it: Compute the expectancy of your planned setup under three assumptions: pessimistic (win rate 35%, avg winner 1.5R), base (45%, 1.8R) and optimistic (55%, 2R), all with a 1R average loser. Subtract 0.1R for costs in each case. Write the three numbers in the front of your journal. They are what "on track" looks like.

Recap

• Expectancy per trade is win rate × avg winner minus loss rate × avg loser. Evaluate the setup on that, never on win rate alone.
• Realistic retail edges run 0.1R to 0.4R per trade after costs. Higher numbers over small samples are noise.
• Twenty trades tell you almost nothing; a hundred begin to tell you the truth. Do not change rules on fewer than thirty.
• Six-loss streaks are routine at a 45% win rate. They are not evidence.
• Write your expected numbers down before you have data, so that "on track" is defined in advance.