Geometric adstock
Advertising can continue to have an effect after it has run. Geometric adstock models how much of this week's impact remains next week as a fixed proportion that decays over time.
6 min read · Updated September 7, 2026
What it is
Adstock is the carryover of advertising: the part of an impression’s effect that shows up after the week it was bought. Geometric adstock is the one-parameter version. Each week, a fixed fraction λ of last week’s accumulated effect remains, so the effect of a single week’s spend decays as λ, λ², λ³ and so on.
adstock(t) = spend(t) + λ × adstock(t − 1)
The parameter λ sits between 0 and 1. At 0 there is no carryover: this week’s spend works this week only. At 0.9, ninety percent of the effect is still there a week later, and the tail runs for months.
Why it matters for a media plan
Two decisions depend on it.
The first is attribution. If television spend in week 10 sells product in weeks 11 to 14, a model with no carryover hands those sales to whatever was running in weeks 11 to 14, usually search and retargeting. The television line looks weak and the search line looks strong, and the budget follows the error.
The second is pacing. A channel with a long tail can be bought in bursts; its effect fills the gaps. A channel with no tail has to be on when the demand is there. The plan’s weekly pattern comes out of the decay rates as much as out of the totals.
How it works
The useful way to read λ is as a half-life, the number of weeks by which half the effect has gone:
half-life = −ln(2) / ln(λ)
| λ | Half-life | Typical channels |
|---|---|---|
| 0.3 | 0.6 weeks | Search, email, affiliates |
| 0.5 | 1.4 weeks | Paid social, retargeting |
| 0.7 | 2.0 weeks | Display, radio, online video |
| 0.85 | 4.3 weeks | Television, out-of-home |
| 0.9 | 6.6 weeks | Sponsorship, print |
In a Bayesian model the decay is a parameter with a prior. Media physics is well enough known that the prior can be strong: a team expecting a two-week half-life for television puts a Beta prior centred near 0.7 and lets the data adjust it. A weakly informative prior, Beta(2, 2), is the fallback when nothing is known.
The model also needs a maximum lag, the number of weeks after which the tail is cut. Eight weeks is enough for digital, thirteen for a mixed plan, twenty or more only when television or out-of-home dominate. Doubling the lag roughly doubles the fitting time, so it is not free.
Adstock is applied before saturation: the accumulated effect is what saturates, not the raw weekly spend.
How Kuwalyst uses it
Every data-backed plan in the Media Planner runs on a model whose decay rates are stored, per channel, on the model card, along with the prior they started from. The planner’s response curves and its weekly pacing suggestions come out of those rates.
Benchmark-led plans, for brands with no history yet, use decay priors from the benchmark registry by channel type, tagged as benchmarks. The plan states which channels are running on borrowed decay rates and proposes the history or the experiment that would replace them.
Pitfalls
Decay and saturation trade off: a model can explain the same data with a long tail and a low coefficient, or a short tail and a high one. Strong priors on decay, where the physics is known, are what keep the coefficient honest.
The tail is not free money: a long tail means part of this quarter’s sales came from last quarter’s spend. Cutting a slow channel shows up late, which is why the plan should say when the effect of a cut will be visible, not just that it will be.
Weibull without the data: a delayed-peak form needs enough weeks to estimate where the peak is. On short data it fits noise.
Daily data, weekly physics: decay rates are usually quoted weekly. A daily model needs the daily equivalent, λ to the power of one seventh, or it will carry effects ten times too long.