> ## 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

**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.

***

## 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

> [card] Quarterly business reviews
>
> Pair the p50 with the p10–p90 band. Discuss what's driving the spread.

> [card] Investment committee
>
> A 90% confidence floor that's still positive is the strongest case you can make.

> [card] Post-mortems on miss
>
> When actuals come in below p50, the tornado tells you which assumption was wrong.

> [card] Pre-implementation sign-off
>
> Show the p10 — if the worst case is unacceptable, scope or delay.

***

## Related resources

> [card] [Financial ROI](https://docs.flowx.ai/6.x/observatory/roi/financial-roi.md)
>
> The point-estimate calculation sensitivity builds on.

> [card] [Value Outcome Units](https://docs.flowx.ai/6.x/observatory/roi/value-outcome-units.md)
>
> Sensitivity bands also apply at the VOU level.


## Related topics

- [Financial ROI](https://docs.flowx.ai/6.x/observatory/roi/financial-roi.md)
- [Value Outcome Units](https://docs.flowx.ai/6.x/observatory/roi/value-outcome-units.md)
- [ROI & value](https://docs.flowx.ai/6.x/observatory/roi/overview.md)
- [Gap analysis & heatmap](https://docs.flowx.ai/6.x/observatory/compliance/gap-analysis-heatmap.md)
- [Agent Builder](https://docs.flowx.ai/6.x/ai-platform/agent-builder/overview.md)


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