What is Adstock?

Adstock, also called the carryover effect or advertising decay, describes how the effect of advertising persists and fades after the ad runs. An adstock transformation turns a media time series into an accumulated, decaying "stock" of advertising pressure, so that a model can credit sales in later periods to earlier spend.

Where the concept comes from

The term was introduced by Simon Broadbent in his work on how TV advertising builds and loses effect over time (Broadbent, 1979). Distributed-lag and carryover effects have since become a standard part of econometric market response models (Hanssens, Parsons & Schultz, 2001) and of modern Bayesian marketing mix models (MMM) (Jin et al., 2017).

The idea is that advertising builds a stock of awareness and consideration that does not disappear the moment a campaign stops. It shows up in three ways:

• Delayed response: a consumer sees an ad today but buys days or weeks later.
• Accumulation: repeated exposures add to the stock left by earlier ones.
• Residual awareness: brand recall persists after the flight ends.

The geometric adstock formula

The simplest and most common form is geometric adstock, a recursive exponential decay:

Adstock(t) = Media(t) + λ × Adstock(t−1)

Where:

• Media(t) = media activity in period t (spend, impressions or GRPs)
• λ (lambda) = the retention rate or carryover rate, between 0 and 1
• Adstock(t−1) = the adstock value in the previous period

λ is the share of the previous period's advertising stock that carries over into the current period. A higher λ (closer to 1) means a longer-lasting effect; a lower λ (closer to 0) means the effect fades quickly. The actual decay per period is 1 − λ. Some sources call λ the "decay rate", which is confusing, because a higher value then means slower decay.

A convenient way to express λ is the half-life, the number of periods until half of the effect is gone: half-life = ln(0.5) / ln(λ).

Worked example

Assume a daily model with λ = 0.8. An advertiser spends 100 dollars on Google Performance Max on Monday and nothing afterwards. The adstocked value is 100 on Monday, 80 on Tuesday (80% of Monday's effect), 64 on Wednesday and 51.2 on Thursday. The half-life is ln(0.5) / ln(0.8) ≈ 3.1 days.

Saturation (diminishing returns) is sometimes treated as part of the adstock transformation. Here it is treated as a separate but related step: the adstocked media series is passed through a shape function, such as the Hill function used by Jin et al. (2017), to produce an advertising response curve.

Common types of adstock functions

1. Geometric adstock

Exponential decay at a fixed rate, controlled by a single parameter (λ). The peak effect is in the period of the spend.

2. Delayed geometric adstock

Adds a delay parameter so the peak effect can occur some periods after the exposure, which suits media such as TV or out-of-home that take time to influence purchases. This form is described by Jin et al. (2017).

3. Weibull adstock

Uses a two-parameter Weibull curve (shape and scale), which allows a time-varying decay rate. The probability density variant also allows a delayed peak (Robyn documentation).

4. Negative binomial adstock

Uses a two-parameter negative binomial distribution as the lag weights, which can also capture a delayed peak and a long tail.

Adstock in marketing mix modeling

Adstock is a core component of marketing mix modeling. It helps to:

• Credit sales to the right periods, channels and campaigns, instead of only the week of the spend.
• Measure incrementality more accurately by accounting for delayed responses. For example, many Black Friday campaigns start before the event itself.
• Plan budgets and timing with an understanding of how quickly each channel's effect builds and fades.

There are two general ways to include adstock in an MMM:

• As a pre-calculated transformation: the adstock is computed with fixed parameters before the data enter, for example, a regression model. This keeps the model simpler and faster but requires strong assumptions about λ.
• As estimated parameters: especially in Bayesian MMMs, the adstock parameters are learned from the data together with the media coefficients. This requires a robust model formulation and sensible priors to avoid problems such as poor convergence (Jin et al., 2017).

The choice of media metric also matters. Attributed conversion value from an ad platform may already contain part of the carryover effect, depending on the platform's attribution window and implementation.

Estimating adstock parameters

• Statistical estimation: Bayesian regression with priors on λ, or hyperparameter search across candidate models.
• Experiments: holdout and geo tests with a post-test observation window show how long the lift lasts after the campaign ends. Results can be used to calibrate the MMM; see calibrating marketing mix models with experiments.
• Market research: brand tracking studies show how quickly awareness decays.

Data and validation requirements

• Sufficient history: Sellforte recommends a minimum of 1–2 years of data, so that carryover can be separated from seasonality. See what data you need for MMM.
• Granular time series: daily data helps capture short carryover and events such as seasonal sales.
• Channel-specific parameters: search and retargeting usually carry over for a shorter time than TV or brand video, so a single λ for all media is rarely appropriate.
• Validation: out-of-sample tests and sensitivity analysis on λ show how much the results depend on the carryover assumption.

Key takeaways

• Adstock models the carryover of advertising effects; λ is the retention rate, and a higher λ means a longer effect.
• Geometric adstock is the simplest form; delayed, Weibull and negative binomial forms allow a delayed peak.
• In MMM, adstock is combined with a saturation function, and its parameters are best estimated from data and calibrated with experiments.

Related terms

• Incrementality
• Bayesian statistics
• Hierarchical Bayesian modeling
• Frequency
• Return on advertising spend (ROAS)
• Response curve

Further reading on Sellforte

• What is marketing mix modeling?
• Advertising response curves: what are they and why do you need them?
• Why diminishing return curves are crucial insights in marketing planning
• Calibrating marketing mix models with experiments and attribution data

References

1. Broadbent, S. (1979). One way TV advertisements work. Journal of the Market Research Society, 21(3), 139–166.
2. Hanssens, D. M., Parsons, L. J., & Schultz, R. L. (2001). Market response models: Econometric and time series analysis (2nd ed.). Kluwer Academic Publishers. https://doi.org/10.1007/b109775
3. Jin, Y., Wang, Y., Sun, Y., Chan, D., & Koehler, J. (2017). Bayesian methods for media mix modeling with carryover and shape effects. Google Inc. https://research.google/pubs/pub46001/
4. Meta Open Source. (2025). Robyn: Semi-automated marketing mix modeling (R package documentation, adstock transformations). CRAN. https://cran.r-project.org/package=Robyn

Authors

Dr. Paavo Niskala is a Principal Engineer at Sellforte. With PhD in the field of computational plasma physics, he has over 10 years of experience in designing and building complex data-intensive systems. Paavo has especially focused on using data science in critical business applications, such as Marketing Mix Modeling, which helps businesses make better marketing decisions. Follow Paavo in LinkedIn.