Expectancy and drawdown: measuring edge

Expectancy and drawdown: what you will calculate in this lesson

This lesson explains how to calculate system expectancy, how to set a profitability threshold, and how large a sample needs to be before you can trust the results. It is designed for traders who already record trades in R and want to know whether their setup has an edge or only a positive balance from a good week. After reading, you will be able to calculate expectancy in R, standard error of the mean, required trade count, and drawdown expressed in R.

If you are not yet scoring trades in R, start with the lesson Stop-loss and R-multiple. Without a common unit, the formulas below have nothing to work with.

Why win rate alone is not enough

Win rate is one of two numbers needed to evaluate a system. The other is the ratio of average win to average loss. Both parameters can be combined into one value — the profitability threshold:

profitability threshold = average loss / (average win + average loss)

Above that threshold the system is profitable; below it the system loses. With an average win of +2.5R and an average loss of -1R, the threshold is 1 / 3.5 = 28.6 per cent. A system with a 40 per cent win rate sits clearly above the threshold. The same calculation for an average win of +0.6R and an average loss of -1.5R gives a threshold of 1.5 / 2.1 = 71.4 per cent — and a system with a 70 per cent win rate sits below it, even though it wins more often.

The conclusion is not that high win rate is bad. It is that win rate without average win size and average loss size does not describe a system. Additionally, both parameters must be calculated on results after costs.

Expectancy formula and step-by-step example

Expectancy is the expected outcome of one trade in R units:

expectancy = win rate x average win - loss rate x absolute value of average loss

For system A from the table above:

1. Win rate is 0.40, loss rate is 0.60.
2. Average win is +2.5R, average loss is -1R.
3. First term: 0.40 x 2.5R = 1.00R.
4. Second term: 0.60 x 1R = 0.60R.
5. Expectancy: 1.00R - 0.60R = +0.40R per trade.

For system B: 0.70 x 0.6R = 0.42R and 0.30 x 1.5R = 0.45R, so expectancy is -0.03R. System B wins more often and slowly gives back the deposit.

This same number can be misleading if costs are omitted. If average round-trip cost is 0.06R, expectancy for system B falls to -0.09R. In system A, with 1R = 200 units and cost of 12 units per trade, expected outcome drops from +0.40R to +0.34R. The order is always the same: first subtract round-trip cost, then compare systems. On a Polish account, capital gains tax applies to realised profit — that layer is outside the platform and is covered in the capital gains tax lesson.

Profit factor as the other side of the same calculation

Profit factor is total profit divided by total loss, both in R:

profit factor = sum of positive results in R / absolute value of sum of negative results in R

A value above 1 means a profitable system; below 1 means a losing system. Unlike expectancy, profit factor says nothing about trade count, so both numbers should be given together: a system with profit factor 1.05 over one thousand trades and a system with the same ratio over twenty trades are two different confidence levels. That is exactly the sample size problem covered in the next section.

How many trades are needed to measure expectancy

The spread of results makes the average of a small sample look random. The measure of that uncertainty is the standard error of the mean:

SEM = standard deviation of results in R / square root of number of trades

The approximate confidence interval is mean R plus or minus 1.96 times SEM. With a standard deviation of 1.2R, you get:

The interpretation is practical. After twenty trades, a measured expectancy of +0.20R means the true value almost certainly lies somewhere between -0.33R and +0.73R. The interval includes zero, so you do not know whether the system is profitable or losing. Measurement becomes decisive only at a sample of about 62 trades — with standard deviation 1.2R, that is the smallest number for which the confidence interval for an edge of 0.3R stops including zero.

From the same calculation comes the formula for required trade count. If you want to detect an edge E with standard deviation s, you need:

trade count >= (1.96 x s / E) squared

For E = 0.3R and s = 1.2R, you get (1.96 x 1.2 / 0.3) squared = 7.84 squared = 61.5, or about 62 trades. If the real edge is only 0.1R, the same formula gives 554 trades. That is the most important consequence of this section: the smaller the edge, the longer you must measure it, and there is no way around that by shortening the test period.

You can calculate standard deviation yourself: for each trade, record the difference between its result and the mean, square it, sum those squares, and divide by trade count minus one, then take the square root. The divisor N minus one, not N, gives an unbiased estimate of deviation in a sample, and that is exactly what enters the standard error. Spreadsheets have a built-in function for this, and the lesson on journal metrics describes the formula.

Drawdown in R, not only in percentages

Drawdown is the decline from the peak of the equity curve. It can be measured in R:

drawdown in R = highest running total in R - lowest result after that peak

| Curve point | Running total in R (illustrative) | | --- | --- | --- | | peak | +12R | | trough after peak | +3R | | drawdown | 9R |

This recording has two advantages. First, it does not depend on capital size, so it allows comparing systems. Second, it directly shows how many full stop losses had to be survived — 9R means nine planned losses. With 1R = 1 per cent of capital, that drawdown corresponds to about -9 per cent; with 1R = 2 per cent, about -18 per cent.

The thresholds at which drawdown turns work into a pause and position size reduction are covered in the lesson Daily limit and drawdown. Here the measurement itself matters: record the running total peak and the deepest trough after it, not just the weekly balance.

How long the longest losing streak lasts

A losing streak is not a system failure; it is a property of randomness. Its typical length can be estimated from loss rate and trade count:

expected longest losing streak approx = ln(trade count) / (-ln(loss rate))

That is an approximation, not a guarantee — in a specific sample the streak may be longer. For a loss rate of 55 per cent and one hundred trades, it gives ln(100) / (-ln 0.55) approx 7.7, or about eight losses in a row at some point in the test.

That number is a direct argument for capital planning: eight losses in a row at 1 per cent risk is over 8 per cent of capital, and at 3 per cent risk almost a quarter. How much capital to deposit and when to pause further deposits is covered in the lesson Capital plan.

The table contains only example values calculated from the given formula — each is illustrative.

It is worth pairing this with another number: the probability that a specific trade starts a streak of five losses is about 5 per cent at a 55 per cent loss rate. Individually that sounds harmless, but in one hundred trades there are one hundred such opportunities. The statement my account never has five losses in a row is therefore an assumption, not an observation — and that is exactly why the drawdown limit must be set before the test, not after.

Trade order changes the equity path

Two systems with exactly the same set of results can have different maximum drawdowns if the results appear in a different order:

| Result order (illustrative) | Running total | Max drawdown | | --- | --- | --- | --- | | +2R, -1R, -1R, -1R | 2R, 1R, 0R, -1R | 3R | | -1R, +2R, -1R, -1R | -1R, 1R, 0R, -1R | 2R |

The sum in both cases is -1R, but in the first order the drawdown reaches 3R, while in the second it is 2R. That explains why backtesting is not a promise: it shows one possible path, not the distribution of all paths. A practical exercise is to reshuffle the same trades and calculate drawdown for several variants — if in one of them drawdown exceeds your pause threshold, the system is too fragile despite a good total result.

When statistics says do not trade

Four conditions after which a conclusion about edge is premature:

1. The confidence interval includes zero. As long as you do not know whether expectancy is positive, increasing position size is a gamble, not a decision.
2. You do not know the standard deviation of your results. Without it, you cannot calculate either standard error or required trade count.
3. Costs are not included in the calculation. As long as the cost column is empty, you are measuring expectancy for a version of the system you do not actually trade — and further testing that version adds no information. The starting point is round-trip cost.
4. You average different setups in one expectancy. One average for two setups describes neither of them; separate them by setup definition.

Worksheet: twenty trades to calculate expectancy

Fill in one row per trade in chronological order. The first ten rows are below; add the rest yourself — the minimum sample from the standard error section is about 62 trades.

After filling in, calculate in order: win rate, average win in R, average loss in R, standard deviation, expectancy, and maximum drawdown. Enter the results in the second table:

Only the complete set of these numbers allows a decision: keep the system, change one variable, or end the test. A single expectancy number without the remaining columns leads to conclusions the data do not support.

Common expectancy mistakes

• Calculating from one good week. Expectancy from eight trades is noise. With standard deviation 1.2R, the confidence interval is then wider than the entire edge.
• Omitting costs. Spread, commission, and swap turn positive expectancy into negative after execution.
• Mixing setups in one statistic. If two different setups go into one column, neither has a clean result.
• Ignoring standard deviation. Two systems with the same expectancy can have completely different volatility, and therefore different required sample size and different drawdown.
• Changing rules during measurement. After each plan modification, start a new sample. Combining results before and after the change produces a number that describes neither version.
• Drawing a conclusion from drawdown without reference to sample size. Drawdown calculated on a few dozen trades is just as uncertain as expectancy.

Measurable exercise

1. Take trades from your journal or from a backtest — start with 20, but the threshold from the standard error section is about 62.
2. Record result in R and cost in R for each trade.
3. Calculate win rate, average win, average loss, standard deviation, expectancy, and maximum drawdown.
4. Write one change to your plan and date the version.

Without this sheet, you do not know whether you are improving the setup or just the story about it.

Common questions

How many trades are needed to evaluate a system?

It depends on the standard deviation and on the size of the edge you want to detect. With a deviation of 1.2R and an edge of 0.3R you get about 62 trades, and with an edge of 0.1R more than 550. The practical conclusion: about 62 trades is a minimum, not a goal.

Does negative expectancy on a demo account mean the end?

First check costs, slippage, and whether you traded according to the plan. If the process was clean and expectancy is still negative, change one variable rather than twelve, and start a new sample.

How does drawdown relate to the 1–2 percent rule?

A fixed 1R limits the pace of decline, because every loss has a known size in advance. A daily and weekly limit adds a procedural brake. Together they protect capital, but they do not create an edge — expectancy decides that.

Why calculate the standard error if I already know expectancy?

Because expectancy from a sample is only an estimate. The standard error says how far that number can be from the true value, and it decides whether the conclusion is justified at all. Without it you can see +0.2R over twenty trades and mistake noise for edge.