Adstock

What is Adstock?

Adstock is a concept introduced by statistician Simon Broadbent in 1979 to describe the accumulated and decaying effect of advertising on consumer memory and purchasing behaviour. Rather than assuming that advertising only influences sales in the week it airs, adstock recognizes that exposure to an ad creates an impression that lingers — and gradually fades — over subsequent time periods.

In practical terms, adstock transforms raw weekly advertising spend or GRP data into a variable that reflects the stock of advertising present in the market at any given time. This transformed variable is then used as an input in Marketing Mix Models, ensuring that the model captures the full impact of advertising — including its delayed effects — rather than just its immediate week-on-week relationship with sales.

Adstock in Ekimetrics' models: Ekimetrics calibrates adstock parameters channel-by-channel and market-by-market within its Marketing Effectiveness solution. Decay rates are estimated from data rather than assumed — making our MMM outputs significantly more accurate than models using default adstock values.

See our measurement approach →

‍

The adstock formula

The standard geometric adstock transformation is written as Adstock(t) = Spend(t) + λ × Adstock(t-1). Spend(t) is the raw media spend or GRP in the current period, λ (lambda) is the decay rate ranging from 0 to 1, and Adstock(t-1) is the adstock value carried over from the previous period. A lambda of 0.5 means half of the advertising effect carries over into the next period.

The lambda parameter is the most critical variable. A high lambda (close to 1) indicates slow decay — meaning the advertising effect persists for many weeks. This is typical of brand-building campaigns, TV, or out-of-home advertising. A low lambda (close to 0) indicates rapid decay — typical of paid search or promotions, where the effect is concentrated in the immediate response window.

‍

Half-life and channel benchmarks

The half-life of an adstock is the number of periods it takes for the accumulated effect to decay to 50% of its original value. It provides a more intuitive way to communicate decay rates than lambda directly, and is calculated as Half-life = log(0.5) / log(λ). For example, a lambda of 0.7 gives a half-life of roughly 1.9 weeks, while a lambda of 0.9 gives roughly 6.6 weeks.

In practice, half-life benchmarks vary significantly by channel and market. Digital channels (paid search, display) typically have half-lives of 1–3 days — their effect is concentrated and short-lived. TV and radio often carry half-lives of 2–8 weeks. Out-of-home and sponsorships, which build brand associations gradually, can have half-lives exceeding 10 weeks.

These are benchmarks, not rules. The right decay rate for a given brand and market should always be estimated from data rather than assumed. Applying an incorrect adstock can dramatically misattribute the contribution of media channels — overestimating channels with rapid decay and underestimating those with slow decay.

Why default adstock assumptions are dangerous: Many MMM implementations use industry-standard lambda values rather than estimating them from data. This shortcut systematically overvalues digital channels (which report more immediate, trackable conversions) and undervalues TV and brand spend (whose effects are diffuse and delayed). Ekimetrics' approach to adstock calibration estimates decay rates empirically — producing ROI estimates that better reflect the true long-term value of each channel.

Learn about our methodology →

‍

Adstock variants

The geometric adstock described above assumes that the carryover effect decays at a constant rate each period. In reality, advertising effects often follow more complex patterns — with a delayed peak before decay, or an S-shaped response curve. Two variants address this:

Distributed lag adstock allows the peak effect to occur one or more periods after the initial exposure, rather than at the point of exposure. This is common for campaigns that require multiple exposures before they influence purchase behaviour.

Weibull adstock uses a more flexible functional form that can accommodate both the delay to peak effect and the shape of the decay curve. It is computationally more expensive but produces better fits in markets with complex advertising dynamics — and is increasingly the standard in state-of-the-art MMM implementations.