P5 to P95: what the equity fan actually represents.

The construction

A vertical slice, ranked, fifty-two times.

At each week of the simulated year, the engine takes all 50,000 path equities at that moment, sorts them, and reads off the values at the 5th, 10th, 25th, 50th, 75th, 90th, and 95th positions. Connect each rank's values across the weeks and you get the fan. The crucial consequence: no simulated account actually travels along P75. The path sitting at P75 in week 10 is usually a different path from the one there in week 30 — individual futures cross bands constantly, the way a runner's race position changes even as the field's spread is stable. The bands describe the population's envelope at each moment, not any individual's journey through the year.

What the widening means

The fan spreads because compounding amplifies divergence.

The fan is narrow in early weeks and wide by year-end, and the widening is compound arithmetic, not increasing uncertainty about the system. Early on, every path has taken few trades and equity outcomes cluster tightly. As the year runs, fortunate orderings compound their gains while adverse orderings compound inside compressed gates, and the same per-trade edge produces increasingly divergent absolute positions. The governed fan has a signature shape worth knowing: its lower edge falls more slowly than an ungoverned simulation's would — the gate ladder is visibly holding the floor up — while its upper region runs free until it meets the one artificial boundary in the chart.

The flattening

Why the top of the fan goes horizontal — target-capped equity.

Late in the year, the upper percentiles bend flat, and the first-time reader assumes the system's upside somehow saturates. The real cause is bookkeeping: paths that reach the $100K target complete, and their equity is capped at the target thereafter. As more of the fast paths finish — and the benchmark's completers cluster around weeks 15 to 20 — the top of the distribution fills with capped values, and P95 presses against the target line like foam against a lid. The flattening is therefore a success artifact, not a performance ceiling: it marks where the population's leaders have already finished the race the simulation was asked to run.

What the fan is for

Location and expectation-setting — nothing else.

Two legitimate uses. First, location: your live equity at week N, placed against the week-N slice, tells you where among the governed futures you currently sit — the raw material of the whole comparison workflow. Second, expectation-setting before the year begins: the fan is the honest answer to 'what might this year look like?', in distribution form, including the lower bands most planning conveniently omits. The illegitimate uses follow from the construction: the fan cannot forecast your path, cannot tell you you're 'due' for reversion to median, and cannot promise that a P80 start means a P80 finish — band membership is re-earned every week, by you and by all fifty thousand of them.

• Read the fan vertically (where am I in this week's slice?), never horizontally (which line am I riding?).
• The lower bands are the planning numbers. A plan that only survives the upper half of the fan isn't a plan.
• Percentile position is context for the full cross-check battery, not a verdict on its own.

The key idea

The fan is a population portrait you locate yourself inside.

Everything confusing about percentile charts dissolves once the construction is internalized: rankings per week, not routes per account; divergence from compounding, not growing doubt; flattening from completion, not saturation. What remains is the fan's real gift — a full year of governed possibility rendered as geometry, against which one live account's actual journey can be located, week after week, without flattery or panic. That located position is the input to everything downstream; producing it honestly is this chart's entire job.