> ## 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.

# Sensitivity analysis

> Monte Carlo simulations across ROI inputs to show confidence ranges instead of single-point estimates.

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.

***

## What gets simulated

Each ROI input has a distribution, not a point value. The defaults Observatory ships with:

| Input                     | Distribution                 | Why                                                        |
| ------------------------- | ---------------------------- | ---------------------------------------------------------- |
| **Volume**                | Normal, ±20%                 | Adoption typically lands within 20% of forecast.           |
| **Manual hours per case** | Normal, ±15%                 | Real measurements vary; 15% covers the noise.              |
| **LLM cost per call**     | Normal, ±10%                 | Provider pricing and prompt tuning swing it.               |
| **Replacement ratio**     | Beta(α=8, β=2)               | Centred high, with a long tail toward partial replacement. |
| **Discount rate**         | Triangular(0.07, 0.10, 0.13) | Treasury-tied, but uncertain.                              |

You can override any of these per agent or per project.

***

## 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 $4.6M is unfalsifiable. A 90% band of $2.9M–\$6.1M is something a board can plan around.

***

## Running an analysis

<Steps>
  <Step title="Open ROI → Sensitivity">
    Pick the project or VOU to analyse.
  </Step>

  <Step title="Confirm or adjust input distributions">
    The defaults are reasonable starting points. For mature deployments with measured variance, tighten them.
  </Step>

  <Step title="Pick the iteration count">
    1,000 iterations is enough for most use cases. 10,000 for board-grade reports. Anything beyond is overkill.
  </Step>

  <Step title="Run">
    Results appear in under a minute. They persist as a `SensitivityRun` so you can compare two analyses side by side.
  </Step>
</Steps>

***

## 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.

***

## When to present this

<CardGroup cols={2}>
  <Card title="Quarterly business reviews" icon="calendar">
    Pair the p50 with the p10–p90 band. Discuss what's driving the spread.
  </Card>

  <Card title="Investment committee" icon="briefcase">
    A 90% confidence floor that's still positive is the strongest case you can make.
  </Card>

  <Card title="Post-mortems on miss" icon="magnifying-glass">
    When actuals come in below p50, the tornado tells you which assumption was wrong.
  </Card>

  <Card title="Pre-implementation sign-off" icon="signature">
    Show the p10 — if the worst case is unacceptable, scope or delay.
  </Card>
</CardGroup>

***

## Related resources

<CardGroup cols={2}>
  <Card title="Financial ROI" icon="chart-line" href="./financial-roi">
    The point-estimate calculation sensitivity builds on.
  </Card>

  <Card title="Value Outcome Units" icon="objects-column" href="./value-outcome-units">
    Sensitivity bands also apply at the VOU level.
  </Card>
</CardGroup>