Diminishing returns
Diminishing returns means each additional advertising dollar produces less revenue than the one before it. Auctions surface the cheapest conversions first, audiences exhaust, and frequency piles onto the already-converted. Response is therefore concave, and every straight-line revenue projection from current ROAS is wrong on arrival.
The failure this page exists to prevent: a channel returns 4.0 ROAS at $250k/mo, someone models "double the budget, double the revenue" in a spreadsheet, and the plan ships. Auction economics disagree. The first $250k bought the cheapest impressions and the most eager customers; the second $250k must bid higher for people who care less. Realized ROAS on the increment always lands below the average, and the model that predicts by how much is the saturation curve.1
The number that should drive allocation is marginal ROAS: revenue from the next dollar, not the average of all past dollars. Optimizers inside MMM tooling equalize marginal returns across channels, which is simply calculus applied to budgets: at the optimum, the last dollar in every channel buys the same revenue.2 Any budget where marginal returns differ across channels can be improved by moving money from the flattest curve to the steepest.
See the concavity
One 100-unit pulse of spend in week 1, nothing after. The decay rate is the fraction of last week's effect that survives into this week; the half-life is how many weeks until half the effect is gone. TV-like channels sit at high decay, performance channels low. Values here are illustrative, not benchmarks.
Worked micro-example
Channel at $250k/mo returning $1.0M (average ROAS 4.0). The fitted response curve projects $1.55M at $500k, not $2.0M. The incremental $250k earns $550k: marginal ROAS 2.2. At a 45% contribution margin the increment loses money (2.2 x 0.45 = 0.99 < 1). Same channel, same dashboard, opposite decision once the curve is priced in. Figures illustrative.
Source ledger
Every numeric claim on this page resolves to one of these primary sources.
- [1]Meta Robyn feature documentationhttps://facebookexperimental.github.io/Robyn/docs/featuresretrieved 2026-08-02
- [2]PyMC-Marketing documentationhttps://www.pymc-marketing.io/retrieved 2026-08-02