Expectancy arithmetic: what a trade is worth before it happens.

The formula

Two probabilities, two magnitudes, one number.

Expectancy is (Win% × AvgWin) − (Loss% × AvgLoss), expressed in R. Nothing exotic hides inside it — the power is in what it forces you to measure honestly: a real hit rate from recorded trades, not remembered ones, and real average magnitudes net of fees, slippage, and friction. A system printing +0.31R per trade with 200 trades of evidence is a machine with a rated output. A green month with no expectancy behind it is weather. The arithmetic is trivial; sourcing honest inputs for it is the entire discipline.

Gross versus net

The edge that survives friction is the only edge you own.

MARS computes expectancy gross and net because the gap between them is its own diagnostic. A strategy can carry positive gross EV and negative net EV — profitable in theory, a slow leak in practice — and the operator would never see it in a P&L column. Fee drag, spread cost, and slippage are subtracted per trade, per branch, so the number that reaches the scorecard is the number the account actually experiences. Reporting only the gross figure would make the system flattering in exactly the situations where an operator most needs it to be blunt.

The sample behind the number

An expectancy figure without a sample size is an opinion in decimal form.

Expectancy is an estimate, and every estimate carries an uncertainty band that shrinks with evidence. Twenty trades can produce a +0.4R reading that is almost entirely noise; the same reading over three hundred trades is a rated output. This is why MARS refuses to display an expectancy figure without the trade count beside it, and why thin samples are flagged rather than quietly averaged into the scorecard. The discipline it enforces is unglamorous but decisive: the correct response to an attractive number on forty trades is to keep trading the system unchanged, not to size up around it.

Conditional expectancy

One blended number can hide two opposite systems.

A book that reports +0.28R overall may contain a branch at +0.6R and another at −0.1R, and the blend conceals both facts. MARS therefore computes expectancy conditionally — by branch, by session, by regime, by risk tier — because the aggregate is a summary rather than a diagnosis. The operational consequence is direct: the repair for a weak blend is almost never ‘trade better’, it is to find the conditional slice that is dragging and either fix its management or stop deploying into it. Conditional EV is what makes that surgery possible instead of guesswork.

• Never read a blended EV without its conditional breakdown.
• A negative slice inside a positive blend is a repair target, not noise.
• Session and regime slices expose costs that branch slices miss.

Expectancy against realised P&L

A good system can lose for a long time without anything being wrong.

The two numbers answer different questions and will disagree for extended stretches. Expectancy describes what a trade is worth on average before it is taken; realised P&L describes what a particular finite sequence of trades happened to deliver. A system with genuine positive expectancy can post a losing quarter purely through ordering, and a system with no edge at all can post a winning one. This is the gap that destroys most discretionary traders — not because they lack an edge, but because they abandon one during the stretch where the two numbers disagree. Treating expectancy as the master metric and P&L as a lagging consequence is what makes it possible to hold a system through the disagreement, which is the only condition under which the edge ever gets to pay.

Why it governs

Every other metric in MARS exists to audit this one.

Drawdown asks what expectancy costs to harvest. RAPF asks whether the profit behind it is quality or luck. Monte Carlo asks how it distributes across thousands of futures. Structural diagnostics ask whether it is drifting. The five-metric hierarchy is not a dashboard of equals — it is one master number under permanent cross-examination, which is exactly what turning expectancy into alpha requires.