the equation leaves out. Expectancy is the first measurement because it is the one the others are corrections to: sequence, friction, correlation, regime and sample size.
Record AR-PUB-000 · Educational Index
The measurements first.
The opinions later.
A curriculum organised around the things a trading system can actually be measured on: expectancy, drawdown, sequence, friction, correlation, regime and sample size. Fourteen publications are specified across sixteen subject areas. One is written in full on this page; the other thirteen open in place as published outlines — abstract, claims, definitions, engine-drawn figures and the misreadings each exists to prevent — and every one of them says plainly that its full text is still to be written.
01Using the CurriculumAR-PUB-000·01
Most trading education
teaches the entry.
The entry is the part a new trader can see, the part that fits in a screenshot, and the part with the least influence on the outcome. Almost everything that determines an equity curve happens afterwards: how the position is carried, how it is sized, how many are open at once, what they cost, and what the operator does during the third consecutive losing month.
This curriculum is therefore organised by measurement rather than by technique. Every publication is about a quantity you can compute from your own record, and about what that quantity does and does not license you to conclude. None of them is about a setup.
The levels below describe prerequisite knowledge, not difficulty of prose. An Advanced publication is not harder to read; it assumes you already have the vocabulary from the ones before it, and it will be much less useful without them.
Level definitions
What is published today
One publication — Why a single equity curve is not evidence — is written in full and appears further down this page. The other thirteen are published as outlines: open any title in the index and you get the abstract, the claims the publication is responsible for, the terms it defines, two figures generated from the live preview engine, and the specific misreadings it exists to prevent. What an outline does not have is the finished editorial text, and each one says so at the foot of its own record. The reading time shown against a publication describes the finished article, not the outline.
02Publication IndexAR-PUB-101…114
Fourteen publications.
Filter by subject area or by level, then open any publication to read its record: what it establishes, the terms it defines, its figures drawn from the live preview engine, and the misreadings it exists to prevent. The subject list carries all sixteen areas of the taxonomy, including the two that hold no publication yet — selecting one of those returns nothing, which is the accurate answer.
Subject area
Level
Showing 14 of 14 publications
No publication in this selection
Two of the sixteen subject areas — trade flow and concurrency, and data quality and journalling — are part of the taxonomy but hold no publication yet, and several areas hold a single entry at one level only. Clear the filters to see the full index.
Colour marks the level: beginner, intermediate and advanced. Reading time is a specification written when the publication was scoped, not a measurement of anything, and it exists mostly to make the shape of the curriculum visible — the advanced material is longer because it has more prerequisites to hold together, not because it is denser.
Shape of the curriculum
03Suggested SequencesAR-PUB-000·03
Three routes
through the same material.
The index is alphabetical by nothing in particular; these are ordered. Each path starts from a situation rather than a subject, and each step carries the reason it comes where it does. Following a path out of order is possible and usually wasteful — the later steps assume the vocabulary the earlier ones establish.
Figure 3 · Level progression across the three paths
A reading order is a claim about difficulty, so the claim is plotted rather than asserted. Each bar is one step, in order, at the level its publication is filed under. Path 01 climbs without reversing. Path 03 opens at advanced, because a structural decision cannot be deferred until it feels comfortable to make.
Stated level of each publication in path order — a filing level, not a measured difficulty.
Where the paths agree
All three end at a publication about sample size, governance or allocation — subjects that only make sense once the measurements underneath them are trusted. That convergence is deliberate. The common failure in self-directed trading education is reaching the sophisticated material early and applying it to numbers that were never reliable in the first place.
04Subject TaxonomyAR-PUB-000·04
Sixteen subject areas,
and where each one stops.
The taxonomy is fixed so that a publication has exactly one home and a reader knows where to look for a subject before knowing whether it has been written. Two areas are defined and currently unpopulated; they are listed with the rest rather than added quietly later.
| Subject area | What it covers | Publications |
|---|
05Featured PublicationAR-EXP-118
Why a single equity curve
is not evidence.
Almost every trading system a retail operator will ever see is presented as one line rising from the bottom left to the top right. That line is not a lie and it is not a result. It is a single sample from a distribution that nobody showed you, and the distribution is where all the information lives.
The curve you were shown
Consider what an equity curve actually is. It is the cumulative sum of a set of outcomes, plotted in the order those outcomes happened to occur. Two facts follow immediately and neither is obvious from looking at the picture.
First, the endpoint depends only on the outcomes, not on their order. Added in R, the same numbers in any sequence give the same total; compounded under fixed-fractional sizing, each trade multiplies the balance by one factor and multiplication commutes, so the final balance is identical too. If you are being shown a curve to demonstrate profitability, the shape of the line is decoration — the final value is the entire claim, and it could have been stated as one number.
Second, and much more importantly, everything else about the curve depends almost entirely on the order. The deepest decline, the longest period spent below a previous high, the worst run of consecutive losses, the point at which an operator would have stopped trading — all of these are properties of the sequence, and the sequence is the one thing about a historical record that will certainly not repeat.
This is why a curve is not evidence in the way it is usually offered. It answers a question about the past that nobody is really asking, and it is silent on the question everybody is asking, which is what the range of plausible futures looks like.
One curve is one draw
The useful mental model is sampling. A strategy, if it has an edge at all, is a process that generates outcomes from some underlying distribution. A track record is one finite sample from that process, arranged in one particular order. Showing it is roughly equivalent to flipping a biased coin two hundred times, drawing the running total, and presenting the drawing as proof of the bias.
The drawing is real. The bias may well be real too. But the drawing tells you very little about the bias, and it tells you nothing at all about how bad the running total might have looked under a different arrangement of exactly the same flips.
The correct response is not scepticism about the record. It is to ask for the other draws — and because they do not exist, to generate them. That is the entire purpose of resequencing: take the outcome set you actually have, reorder it thousands of times, and look at the distribution of the numbers that depend on order.
What ordering alone does to the worst number on the page
The figure below does exactly that. A single configuration is evaluated once, producing a fixed set of trade outcomes. That same outcome set is then re-drawn across a hundred and fifty seeded orderings, and the deepest decline from peak is recorded for each. Nothing about the strategy changes between runs. No parameter moves. The trades are the same trades.
Distribution of maximum decline across resequenced histories.
Simulated demonstration data. This visualization illustrates proposed product behaviour and does not represent historical, live, or guaranteed trading performance.
The spread is the point. If the record you were shown happens to sit at the favourable end of that distribution — and records that get shown to people tend to — then the drawdown figure quoted alongside it understates the drawdown the same strategy would routinely produce. Not because anyone is being dishonest, but because one ordering was observed and the rest were not.
The three curves below make the same argument in a form that is harder to dismiss. They are the gentlest, the middlemost and the harshest of those hundred and fifty orderings, drawn from the identical set of trades. They finish at precisely the same value, to the decimal — that is arithmetic, not coincidence. Almost nobody would have held all three to the end.
The same outcomes, arranged three ways.
Simulated demonstration data. This visualization illustrates proposed product behaviour and does not represent historical, live, or guaranteed trading performance.
A worked example
Suppose a record contains 240 trades. Ninety-six of them were profitable, giving a hit rate of 40 percent. The average win was 2.4 R and the average loss 1.0 R, and total costs came to roughly 0.06 R per trade. Expectancy is then straightforward.
EVnet = p · W − (1 − p) · L − f
With p = 0.40, W = 2.4 R, L = 1.0 R and f = 0.06 R: gross expectancy is 0.40 × 2.4 − 0.60 × 1.0 = 0.36 R, and net expectancy after friction is 0.30 R per trade. Across 240 trades that is 72 R of accumulated edge — a genuinely good record.
Now measure the uncertainty rather than the result. The dispersion of individual outcomes around that 0.30 R mean is about 1.67 R, which is typical for a distribution containing 2.4 R wins and 1.0 R losses. The standard error of the mean is that dispersion divided by the square root of the sample.
CI95 = EV ± 1.96 · σR / √n
1.67 ÷ √240 = 0.108 R. The ninety-five percent interval around a measured 0.30 R expectancy therefore runs from roughly 0.09 R to 0.51 R. The sign is established; the magnitude is not. The true edge could be a third of what the record shows, or nearly double it, and 240 trades cannot distinguish between those cases.
Two conclusions follow that most operators would not draw from the curve alone. The record is strong enough to justify believing there is an edge, and far too weak to justify sizing as though the edge were 0.30 R. And a plan built on the assumption of 72 R over 240 trades is a plan built on the upper half of a range that includes 21 R.
Note what happened here. Nothing was added except the dispersion — a number that every trade log already contains and that almost no trading report ever quotes. The curve had the information the whole time; drawing it as a line simply threw the information away.
Three things a single curve cannot tell you
Whether the result is repeatable. A curve has no confidence interval attached. Two records with identical endpoints and identical trade counts can differ enormously in how much evidence they contain, and the difference is entirely in the dispersion of the individual outcomes.
How bad it gets. The observed maximum decline is one draw from the distribution in Figure 2. Quoting it as the drawdown of a strategy is the single most common overstatement in retail trading material, and it is usually made in good faith.
Whether you would have held on. The curve shows what happened to the capital. It says nothing about what happened at trade 114, four months underwater, when the operator was deciding whether the system still worked. Every historical curve was, by construction, held to the end.
What to do about it
None of this requires new data. Everything below can be done with a trade log you already have.
Convert every outcome to R before anything else. Currency amounts encode position size, which encodes decisions you made about confidence — and those decisions contaminate every statistic downstream. R strips them out, and it is the unit every measurement on this site uses for exactly that reason.
Report dispersion beside every mean. An expectancy figure without the standard deviation of the outcomes behind it is not a measurement, it is a summary statistic pretending to be one. The two numbers cost the same effort to produce.
Resequence before you trust a drawdown. Shuffle your own outcome set a few thousand times and record the deepest decline each time. The number you should be planning around is somewhere in the upper region of that distribution, not the one your history happened to deliver.
Ask what the sample can support. Before concluding that a change improved anything, work out how many trades would be needed to detect an improvement of that size given your dispersion. The answer is very often larger than the entire record, which is a useful and deflating thing to know early.
Treat the curve as an illustration. It is a perfectly good way to communicate the shape of an experience. It is not a way to establish that the experience will repeat, and it should never be the artefact on which capital is committed.
The reframing is small and it changes almost everything: stop asking whether the curve is good, and start asking what range of curves the same process could have produced. One of them is the one you were shown. The others are the ones you will have to live through.
Published as AR-EXP-118 · Educational Publication · Methodology · Validated · figures generated by the Foundry preview engine from explicit seeds
The vocabulary
is doing real work.
Several words in this curriculum are used more precisely here than in general trading conversation. Drawdown is four measurements, not one. Risk is a defined quantity in R rather than a feeling. Validated describes evidential standing and says nothing about profitability.
The full reference carries thirty-two terms, a metric reference for every quantitative measure used across the site, a notation key and the complete identifier index. If a publication uses a word in a way that seems narrower than expected, it is being used in the reference sense.
Eight terms from the reference
32 terms in total · A–Z with jump links on the reference page
06LimitationsAR-PUB-000·06
What this curriculum
will not do for you.
Four limits, stated at the front rather than in a footer, because each one is a way a reader could reasonably come away with the wrong expectation.
Thirteen of fourteen publications are not yet written
Their subject, level, scope and reading time are specified and will not drift, but the text does not exist. Nothing on this page links to an article page that has not been published, and every unwritten entry carries a level pill saying so at the point of display.
Every figure here is model output
The distributions in the featured article come from the Foundry's deterministic preview engine, which reads no market data. They are correct demonstrations of how sequence risk behaves in a model and they are not measurements of any market, account or strategy.
Measurement literacy is not an edge
Everything taught here helps you evaluate a system honestly. None of it helps you find one. A trader who measures a bad strategy impeccably has a well-documented bad strategy, and the curriculum is quite clear that this is a real and common outcome.
This is education, not advice
Nothing in this section is investment advice, a recommendation, a signal or a statement about what any reader should trade. The Foundry does not provide advisory services and has no plans to. Trading involves substantial risk of loss.
Reading about dispersion is one thing.
Watching it move is another.
Every measurement in this curriculum is exposed as a live control somewhere in the laboratory. The fastest way to internalise why sequence matters is to change one parameter and watch the distribution of outcomes move while the average stays where it was.
14 publications specified · 1 written in full · 16 subject areas · 3 reading paths