// glossary
Saturation Curve.
Diminishing-returns model of channel spend
The saturation curve is the S-shaped MMM output that shows how channel spend doesn't lift sales linearly; after a certain point diminishing returns kick in. It's the heart of budget optimization.
// detail
A model that assumes linear ad effect — 'twice the budget, twice the sales' — is wrong. Reality:
- Low spend: every additional dollar produces high returns (steep curve).
- Medium spend: the elbow approaches; returns slow.
- High spend: saturation — extra dollars produce almost no extra sales (curve flat).
Mathematically, the curve is expressed as a Hill or S-shape:
Effect = β × X^α / (X^α + γ^α)
α and γ control how fast saturation kicks in and at what threshold. Each channel gets its own — the most critical output of an MMM model.
The elbow marks where saturation begins. If your current spend sits left of the elbow you can scale; right of it, additional budget is wasted.
Example: A brand's Google Search saturation curve elbows at $20K/week. Current spend is $19K — just left of the elbow. Going to $22K yields 10% extra sales; going to $30K only adds another 4%. Holding spend at $22K and shifting the rest to Meta (still far from saturation) is optimal.