A marketing mix model’s response curve shows how much extra sales each channel delivers at every level of spend. Two ideas shape that curve. Adstock describes how long a channel’s effect lingers after the money is spent. Saturation describes how quickly each extra dollar starts buying less. Read together, they answer the only budget question that matters: where should the next dollar go? The answer is almost never “the channel with the highest average ROI.”
Adstock: media that keeps working
When a consumer sees a TV spot on Tuesday, they don’t all buy on Tuesday. Some buy that weekend. Some buy two weeks later, when the product catches their eye on the shelf. Adstock is the model’s way of capturing that delay.
It’s usually expressed as a decay rate. Say a model estimates a weekly decay of 0.6 for online video. That means 60% of this week’s effect carries into next week, 36% into the week after, and so on until it fades. A search ad might have a decay close to zero: the click happens, the sale happens, and the effect is gone.
This matters for how you read results. A channel with long carryover will look weak if you judge it on the week it aired. Its real contribution is spread over the following month. If your reporting window is shorter than the adstock, you will undervalue exactly the channels that build demand for consumer brands: TV, video, out-of-home and audio.
Saturation: the curve bends
Saturation is diminishing returns. The first $10,000 in a channel reaches fresh, receptive audiences. The next $10,000 reaches many of the same people again, at higher frequency and often at higher cost. Eventually each additional dollar adds very little.
On a chart, this turns a straight line into a curve that rises steeply, then flattens. Where you sit on that curve today tells you more than the curve’s overall shape. A channel can be excellent in general and still be the wrong place for extra budget, simply because you’re already spending near its ceiling.
Average versus marginal ROI
Here’s where most misreadings happen. Average ROI is total return divided by total spend. It describes the past. Marginal ROI is the return on the next dollar at your current spend level. It describes the decision in front of you.
Because of saturation, the two drift apart as spend grows. A heavily funded channel can have a strong average ROI and a weak marginal one. A lightly funded channel can show the reverse. Budget decisions should follow the marginal number.
A worked example: shifting budget between two channels
Take a hypothetical snack brand spending $200,000 a month across two channels: $120,000 on online video and $80,000 on paid search. Its model reports, for example, these figures:
- Online video: average ROI of $1.80 per dollar. At current spend, the next $10,000 returns about $1.40 per dollar.
- Paid search: average ROI of $2.50 per dollar. But search is close to saturation, so the next $10,000 returns only about $0.90 per dollar.
A team reading average ROI would move money into search. The curves say the opposite. Suppose the brand moves $10,000 from search to video. Pulling back from search costs relatively little, because those last dollars were the least productive. Say that’s $11,000 of lost sales. Adding $10,000 to video gains roughly $14,000. The net effect is a gain of about $3,000 a month, with no change in total budget.
The logic keeps going until the marginal returns of the two channels meet. After a few steps, video’s next dollar gets less productive and search’s last dollar gets more productive. At that point the split is balanced and further moves stop paying off. Planning tools built on media mix modeling run this same calculation across every channel at once, and add confidence ranges so planners can see how certain each estimate is.
Two caveats apply even in this simple case. First, adstock means the video gain arrives over several weeks, so judge the shift on a monthly or quarterly view, not week by week. Second, a model’s curve is only reliable across the spend range it has actually observed. If video has never run above $130,000 a month, the curve beyond that point is an educated guess.
Common mistakes when reading curves
Extrapolating off the edge. Curves are fitted to history. Doubling a budget into territory the model has never seen is a test, not a forecast. Move in steps and re-measure.
Ignoring the uncertainty band. A curve is an estimate with a range around it. If two channels’ marginal returns overlap within their confidence ranges, the model is telling you it can’t separate them yet. That’s a reason to experiment, not to swing budget hard.
Treating channels as independent. Channels interact. Search volume often rises when TV is on air, because TV creates the demand that search captures. Cut TV, and part of search’s curve may drop with it. Good models estimate these interactions explicitly rather than treating each channel in isolation.
Forgetting that curves move. Creative changes, pricing, competition and seasonality all shift response. A curve from last year’s model describes last year’s market. Refresh the model before making big reallocation calls.
What to take into your next planning meeting
Ask for three numbers per channel, not one: average ROI, marginal ROI at current spend, and the confidence range around the marginal figure. Ask how long each channel’s carryover lasts, so you judge performance on the right time window. Then look for the channel pairs where marginal returns differ most. That gap is where a budget shift is most likely to pay off.
Response curves don’t make the decision for you. They make it visible. And once a team starts talking about the next dollar instead of the last one, budget conversations get shorter and much more productive.