What is a saturation curve?

A saturation curve, or response curve, is the relationship a marketing mix model estimates between spend in a channel and the sales that spend produces. Spend runs along the bottom, sales up the side. The curve rises steeply at low spend, because the first units reach the customers easiest to convince, and flattens as spend grows, because later units reach harder ones. Past a point, more money buys very little more.

Every channel gets its own curve. TV typically flattens late because its reach is huge; paid search gives a lot early and then stops, because there are only so many people searching.

The curve is usually a Hill function with a saturation point per channel: the spend level at which the channel has delivered half of what it can. The model estimates the shape from the history, starting from a prior that is often fitted to the platform's own conversion and impression data, and refines it against sales. The result is a posterior for each curve, so the curve comes with a band, not just a line.

Two readings come off the same curve. Average return is total sales from the channel divided by total spend over the period: the number the platforms report. Marginal return is the slope at today's spend: what the next unit earns. The two are different for every channel, and the difference is what reallocation is built on.

Budget decisions belong on the margin. A channel with a strong average and a flat slope is the one to stop increasing, even when it looks like the best performer; a channel with a modest average and a steep slope is where the next unit should go. Moving spend from flat curves to steep ones, until the marginal returns are roughly level, is what gives typically 5 to 15% more effect from the budget you already have.

The curves are also what make a test plannable. From the curve the model can compute how much extra spend it takes to learn something about a channel, and what that test costs against the optimal plan. The curve for every channel can be inspected in the Odins platform at any time.

A curve is estimated from the range of spend the history actually contains. Far outside that range, say triple the highest level ever spent, the model is extrapolating and the band gets wide. That is a reason to test, not a reason to trust the point estimate.

Most tools estimate one curve per channel and hold it fixed for the whole modeling window. In reality a channel can work differently in November than in July. Where the data supports it, the curve can be allowed to follow the year; see time-varying saturation.

• 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.
• Marginal ROAS: What the next unit of spend in a channel earns at today's level. The number a budget change actually asks for.
• ROAS: Return on ad spend: revenue per unit of spend. Useful, as long as you know which ROAS you are looking at.
• Time-varying saturation: Letting a channel's response curve follow the year, so November and July are not forced to share one curve.
• Budget optimization: Finding the split and the total where the next unit works hardest, under the constraints the business has.
• Pulse test: Vary one channel's spend over time, on and off or up and down, so the model can see how it responds.

Go one level deeper: Allocate budget across channels. How the model works. Or go back to all terms in the glossary.