What Are Saturation Curves?
Saturation curves are the MMM transform that describes how marketing response diminishes as exposure scales. The first hundred GRPs of TV produce more incremental lift than the second hundred; the first 10 percent of LLM share of voice gain matters more than the next 10 percent. Saturation curves encode this diminishing-returns behavior so the model fits realistic response surfaces.
Without saturation, the regression would assume linear response: doubling spend doubles outcome. This is wrong for every meaningful marketing channel and produces budget allocation recommendations that send infinite dollars to the highest-coefficient channel.
Why Saturation Curves Matter
The shape of the saturation curve determines budget allocation. A channel with a steep early slope and aggressive saturation should receive moderate budget concentrated at low spend levels; a channel with a gentle slope and slow saturation should receive sustained higher spend. Wrong saturation produces systematically wrong budget recommendations.
For AI search specifically, saturation matters because brand recommendation in AI assistants saturates quickly. Once a brand is consistently in the top three for a category, additional visibility produces smaller incremental lift. The saturation curve should reflect this; modelers using paid-search saturation priors typically over-recommend AI investment.
Common Functional Forms
Hill function: Three-parameter form (alpha, gamma, K) that flexibly captures both gradual and aggressive saturation shapes. The default in most modern Bayesian MMM frameworks because of its expressiveness.
S-curve: Sigmoid form with two parameters (slope and inflection). Useful when the channel has a threshold below which effect is minimal and above which it accelerates before saturating. Common for upper-funnel channels with awareness thresholds.
Diminishing returns: Simple log or power transformation. Less flexible than Hill or S-curve but appropriate when data is sparse and the analyst wants a stable form with few parameters.
In Practice
Setting saturation priors requires either domain knowledge or enough data to identify the curve. For AI search, the half-saturation prior (the exposure level at which response is half of the asymptote) is typically set in the middle of the observed AI visibility range. This produces a curve that captures the operational reality: moderate AI visibility increases produce meaningful lift; large increases past the operational range produce diminishing additional lift.
The single biggest error is setting saturation priors too weak (essentially linear response), which causes the model to recommend infinite budget for high-coefficient channels and breaks the budget optimization step.
How Presenc AI Helps
Presenc AI publishes category-specific saturation guidance for the AI visibility variable, derived from cross-customer analysis of AI search response curves. The guidance gives modelers a defensible starting prior rather than a vague default, which improves first-refit quality and reduces iteration time on the AI channel.