MISSION

The mathematics behind Atropos

Expected value after costs, volatility as the yardstick, samples that deceive: why a trading system has to be one thing above all – honest with itself.

excon‑trading.de ResearchOctober 24, 2026 · 5 min read

Atropos: a creature of shadow and smoke, over two metres tall, with long arms; its face glows red like fire. — ATROPOSILLUSTRATION

Markets are loud. Every minute a price moves somewhere, a headline drops, a mood turns – and almost all of it is noise. Atropos is built to find the small remainder that is not. It does not sleep, it does not hesitate out of fear, and it does not fall in love with a position. How exactly it does that, we keep to ourselves. Which laws it obeys, we do not.

Python calculates. Language models read.

Atropos is LLM‑assisted, but it is not a language model that guesses. Its core is classic code: whatever can be measured – costs, distances, position sizes, loss limits – is calculated in Python, deterministically and verifiably. Language models come in where numbers alone fall short: reading context that fits no column.

The separation is strict. A model may judge, but not calculate – and it cannot move a limit the code has set. What the mathematics forbids does not happen.

Expected value after costs

Every idea is scored in multiples of the risk taken, R for short: if a trade makes twice what it would lose at the stop, it stands at +2 R. What counts is not the single outcome but the expected value – after costs.

E [R] = p \cdot \overset{―}{W} - (1 - p) \cdot \overset{―}{L} - c

c = \frac{f + s}{r}

Here $p$ is the hit probability, $\overset{―}{W}$ and $\overset{―}{L}$ are the average wins and losses in R, $f$ and $s$ are fees and slippage, and $r$ is the distance to the stop. The last term is the least conspicuous and the most dangerous: a tight stop makes $c$ explode, and an edge before costs turns into a loss after costs. That is why Atropos caps the cost of every idea before it judges it at all.

Volatility as the yardstick

One percent is not one percent. For a quiet stock it is a big step, for a small cryptocurrency mere noise. Atropos therefore measures distances not in percent but in units of the current fluctuation.

\tilde{d} = \frac{| P - P^{*} |}{{\hat{σ}}_{t}}

{\hat{σ}}_{t} = \frac{1}{n} \sum_{i = 0}^{n - 1} {TR}_{t - i}

$TR$ is the true range of a candle, gaps included. Only in this unit do markets become comparable – and only then can you tell whether a target is realistic or merely hopeful.

Samples that lie

Ten trades say almost nothing. Five winners in a row can be skill or luck, and the data alone cannot tell them apart. So we do not only work with the one past that actually happened, but with thousands that could have: the system's own trades are redrawn at random, and we count how often the account falls further than we would allow.

\hat{P} (DD \geq d) = \frac{# {b : {DD}^{(b)} \geq d}}{B}

$B$ is the number of runs, ${DD}^{(b)}$ the largest drawdown in run $b$ . Atropos only gets more room once an edge holds over a minimum number of trades – not after one good week.

“An edge you can explain is no edge at all.”

Every decision casts a shadow

A trade that does not happen is a decision too – and it can cost more than a loss. That is why Atropos recalculates every rejected idea with real minute prices, as if it had been traded. The difference between the two worlds shows whether caution protects or just costs money.

Δ = {\overset{―}{R}}_{traded} - {\overset{―}{R}}_{rejected}

If $Δ$ stays negative, the system is rejecting its better ideas – a mistake you would never see without this counter-calculation.

Risk first

Before Atropos thinks about profit, it knows what it is allowed to lose. Position size follows from that, not the other way round.

q = \frac{κ \cdot E_{t}}{| P_{e} - P_{s} | \cdot (1 + ε)}

$κ$ is the share of the capital $E_{t}$ risked at the stop, $P_{e}$ and $P_{s}$ are entry and stop, $ε$ is a surcharge for slippage. On top come limits that no signal can override: for the single trade, for the day, for the liquidity of the market. The Kelly fraction would be the theoretical ceiling.

f^{*} = \frac{p \cdot b - (1 - p)}{b}

Atropos stays far below it. Pushing the ceiling wins the most on average – and pays for it with drawdowns that no account you want to keep survives.

Training means measuring

For us, training does not mean feeding a model prices until it knows the past by heart. Hypotheses are fixed before the data sees them and tested on periods the system has never seen. Whatever does not hold up there is out – however good it sounded.

Why paper trading

Our training ground is a paper account: real market data in real time, fees, slippage and funding as in real trading – but no real money. A system that cannot hold up over many trades in this environment does not belong anywhere else. We do not publish returns while the sample is too small to mean anything.

What pre-alpha means. Atropos runs around the clock, but in a closed circle. Access only with an account we issue ourselves; there is no sign-up. Features change all the time. Current version: 0.9.4.

What we do not do

We do not take money, manage assets or give investment advice. excon‑trading.de is a research project. If Atropos ever has something to say, we will say it with numbers.

Until then, Atropos keeps working.

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