What is time-varying saturation?

Most marketing mix models estimate one saturation curve per channel and hold it fixed for the whole modeling window. Time-varying saturation relaxes that: how strongly a channel works, and where it saturates, are allowed to move through the year. The baseline season is still modeled separately; this is about the marketing response itself.

In the Odins model each channel's saturation can carry a time-varying budget component (how strongly the channel works through the year) and a time-varying half-saturation point (where it saturates). Each follows a yearly pattern by default, and where the data supports it the pattern can evolve across years rather than repeat exactly. It is configured per model and added only after a static model has been trained and verified; with the components left out, the model is static.

A fixed curve makes the whole model worse, because it forces the model to say that search in July and search in November have exactly the same effect per unit of spend. Anyone who has run a peak season knows that is not true: in peak weeks the same money converts more easily, and the channel saturates later. A curve that follows the year lets the plan say which weeks to lean into, and feeds the monthly split in scenario planning.

The claim worth making, and no more: none of the open-source frameworks ships time-varying saturation out of the box. Meridian's curve is fixed per channel for the window, Robyn's coefficients are static, and PyMC-Marketing's time-varying piece is the media baseline rather than the curve. Some commercial vendors document time-varying parameters too; the honest line is that it is supported in the Odins product and used where the data allows, not that it is ours alone.

• Saturation curve: The response curve per channel: how sales respond to spend, and where the next unit stops paying.
• Seasonality: The yearly pattern in demand that the model separates from marketing, so a December spike is not credited to December's ads.
• Diminishing returns: Each extra unit of spend in a channel earns a little less than the one before. Why the average is the wrong number to plan on.
• Scenario planning: Forecasting what a budget would return before committing it, and comparing several futures side by side.

Go one level deeper: Time-varying saturation, in depth. Google Meridian: build vs buy. Or go back to all terms in the glossary.