Why the next pound is never worth the last

A channel returns £3 for every pound you spend on it. So spend more, and it'll keep returning £3. That's the logic behind a lot of budget decisions, and it's almost always wrong.

Every channel saturates

The first pound you spend on a channel reaches the people most likely to respond. The next reaches people slightly less likely. Eventually you're showing the same ad to the same people for the fifth time, or bidding on searches that barely convert. Each extra pound brings back less than the one before.

Plot sales driven against spend and you get a curve that rises steeply, then bends and flattens. Mix models estimate this curve for every channel. It's called a response curve, or saturation curve.

Average and marginal are different questions

The average return is total sales driven divided by total spend. It tells you how the channel did overall.

The marginal return is what the next pound would bring back, at the level you're spending now. It tells you what to do next.

On a flattening curve, the two can be far apart. A channel can have an excellent average return and a poor marginal one, because you've already bought the cheap, responsive part of the curve. Adding budget there buys the expensive, flat part.

What this means for the budget

• Don't scale on averages. A strong average return justifies keeping a channel, not necessarily growing it.
• Compare channels at the margin. The question isn't which channel did best, but where the next pound goes furthest.
• Look at where you sit on the curve. If you're on the steep part, more spend probably helps. If you're on the flat part, the same money may do more elsewhere.
• Keep the range. Curves are estimated, and the flat end is usually the least certain, because few weeks in your history had spend that high.

A simple test of a budget proposal

When someone proposes moving money into a channel because "it has the best return", ask one question: is that the average or the marginal return, at the new spend level?

If nobody knows, the proposal is a guess about the shape of a curve. Mix models make that shape visible, with its uncertainty, so the guess can become a decision.