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