Why some channels reward breadth and others require commitment

Many budget allocation strategies assume that every channel follows the same pattern: the first dollar is the most productive, and each additional dollar yields a slightly lower return.

The charts below show what that pattern looks like.

The log shape means that the first dollar is the most productive, and each subsequent dollar is worth a little less. When every channel looks like that, the game plan is to spread the budget to as many channels as possible and equalize the marginal CPAs to maximize profit.

But not every channel looks like that. Some have a warm-up region where the early spend is the least efficient, not the most. On those channels, the logic above breaks, and so does the “test small, scale the winners” playbook that most of the industry runs on autopilot. 

The difference comes down to one question about the channel: Is the response curve C-shaped or S-shaped?

The answer can change how you approach channel testing and channel measurement, including any MMM analysis. Moreover, Google has been incorporating more S-shaped campaign types, and after its Google Marketing Live announcements, this trend seems set to continue.

The two shapes — and the only part that matters

The response curve plots output (conversions, revenue) against input (spend). This generally results in two types of curves in marketing.

• C-shaped (concave): Diminishing returns from the very first dollar. A log or power curve. Picture the top-left quarter of a circle: steep at the start, flattening as you go.
• S-shaped (sigmoid): A slow, inefficient start, then an inflection point where it gets steep, followed by a flattening into saturation. A logistic curve.

The response curve itself isn’t what you allocate against. You allocate against the marginal curve, the derivative, which answers the question: “What did the next dollar buy me?” That’s where the shapes diverge in a way that matters.

• For a C-curve, marginal return is highest at the first dollar and falls in only one direction. Marginal CPA rises from the first dollar onward. If conversions are a*ln(s), marginal conversions per dollar are a/s, so marginal CPA is s/a, climbing in a straight line as you scale. There’s no warm-up. The cheapest conversion you’ll ever buy is the first one.
• For an S-curve, marginal return starts low, rises to a peak at the inflection point, then falls. Marginal CPA is U-shaped. It’s expensive at the start, bottoms out around the inflection point, then climbs into saturation.

That region of increasing marginal returns is the whole story. It’s the difference between a channel where small budgets are productive and one where they are wasted.