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Documentation Index

Fetch the complete documentation index at: https://docs.flowx.ai/llms.txt

Use this file to discover all available pages before exploring further.

A single ROI number invites a single objection — “what if your adoption number is wrong?” Sensitivity analysis pre-empts that by running thousands of simulations across the input distributions and reporting confidence bands.

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What gets simulated

Each ROI input has a distribution, not a point value. The defaults Observatory ships with:
InputDistributionWhy
VolumeNormal, ±20%Adoption typically lands within 20% of forecast.
Manual hours per caseNormal, ±15%Real measurements vary; 15% covers the noise.
LLM cost per callNormal, ±10%Provider pricing and prompt tuning swing it.
Replacement ratioBeta(α=8, β=2)Centred high, with a long tail toward partial replacement.
Discount rateTriangular(0.07, 0.10, 0.13)Treasury-tied, but uncertain.
You can override any of these per agent or per project.

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What the analysis produces

Each Monte Carlo run produces:
  • p10 / p50 / p90 for monthly savings, payback, annual ROI, and NPV
  • A tornado chart showing which inputs drive the most variance
  • A histogram of NPV outcomes
The numbers most executives respond to:
  • “Base case (p50) NPV is $4.6M”
  • “There’s a 90% chance NPV is above $2.9M”
  • “There’s a 10% chance NPV is above $6.1M”
A point estimate of 4.6Misunfalsifiable.A904.6M is unfalsifiable. A 90% band of 2.9M–$6.1M is something a board can plan around.

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Running an analysis

1

Open ROI → Sensitivity

Pick the project or VOU to analyse.
2

Confirm or adjust input distributions

The defaults are reasonable starting points. For mature deployments with measured variance, tighten them.
3

Pick the iteration count

1,000 iterations is enough for most use cases. 10,000 for board-grade reports. Anything beyond is overkill.
4

Run

Results appear in under a minute. They persist as a SensitivityRun so you can compare two analyses side by side.

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Reading the tornado

The tornado chart sorts inputs by how much variance they contribute to NPV. Typical result for a mature agent:
  1. Volume — usually dominates
  2. Replacement ratio — second largest
  3. Manual hours per case — meaningful
  4. LLM cost — surprisingly small (cost is small vs savings)
  5. Discount rate — minor
If volume is the dominant driver and you don’t have a tight forecast, that’s where to invest measurement effort, not in tuning LLM cost.

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When to present this

Quarterly business reviews

Pair the p50 with the p10–p90 band. Discuss what’s driving the spread.

Investment committee

A 90% confidence floor that’s still positive is the strongest case you can make.

Post-mortems on miss

When actuals come in below p50, the tornado tells you which assumption was wrong.

Pre-implementation sign-off

Show the p10 — if the worst case is unacceptable, scope or delay.

Financial ROI

The point-estimate calculation sensitivity builds on.

Value Outcome Units

Sensitivity bands also apply at the VOU level.
Last modified on June 2, 2026