The short answer
Sensitivity analysis changes one input at a time to show how a model responds. It can identify fragile assumptions before a budget decision. It does not assign probabilities to outcomes unless those probabilities come from a separate defensible model.
Start with a transparent baseline
Illustrative baseline: order rate 2%, AOV $100, and CPC $0.50. ROAS is 0.02 × $100 ÷ $0.50 = 4×. Assume a 40% contribution margin before ads and $1,000 of spend. Modeled revenue is $1,000 × 4 = $4,000, leaving $4,000 × 0.40 − $1,000 = $600 after ads.
Change one input
| Changed input | ROAS calculation | Result |
|---|---|---|
| Order rate 1.5% | 0.015 × 100 ÷ 0.50 | 3× |
| AOV $80 | 0.02 × 80 ÷ 0.50 | 3.2× |
| CPC $0.625 | 0.02 × 100 ÷ 0.625 | 3.2× |
Check the cost margin separately
ROAS can stay at 4× while contribution margin falls. At an illustrative 25% pre-ad margin instead of 40%, the same $4,000 revenue leaves $4,000 × 0.25 − $1,000 = $0 after advertising. This is why sensitivity limited to the revenue ratio can miss a major economic risk.
Combine assumptions only deliberately
A lower AOV could occur alongside a higher order rate after a discount. Inputs may move together. One-at-a-time scenarios are helpful for understanding direction, but they are not a full forecast. A combined scenario should state each changed input and why that combination is plausible.
Choose the next measurement
If small changes in an uncertain input erase contribution, prioritize better evidence for that input. For example, confirm the fee schedule or inspect mature conversion data before relying on the baseline. Keep a downside case visible and avoid labeling the most attractive scenario “expected” without evidence. The purpose is to make uncertainty usable in a decision, not to hide it behind a precise output.
Choose the next input to verify
- Gather: List CPC, order rate, AOV and margin with the evidence behind each baseline assumption.
- Produce: Change one input at a time, then document any combined downside scenario separately.
Decision boundary: A scenario range has no probability attached unless you have a defensible probability model.
Next reading
Examples are illustrative, not client results or benchmarks. The calculations use the inputs shown; real-world decisions depend on your records and assumptions. Report a correction.