What is Adstock?

Adstock (also known as carryover effect or advertising decay) is a marketing measurement concept that quantifies how advertising effects persist and diminish over time after an advertisement is shown. Rather than assuming advertising impact stops immediately when a campaign ends, adstock models recognize that advertising continues to influence consumer behavior for weeks, months, or even years after exposure.

How Adstock Works

Adstock operates on the principle that advertising creates a "stock" of awareness, consideration, or positive sentiment in consumers' minds that doesn't disappear instantly. This stock gradually decays over time, similar to how a product's inventory depletes or how memory fades.

The adstock effect manifests in several ways:

• Delayed response: Consumers may not purchase immediately after seeing an ad but may be influenced to buy weeks or months later
• Reinforcement: Repeated exposures build upon previous advertising impressions, creating cumulative impact
• Residual awareness: Brand recall and recognition persist beyond the campaign period

The Adstock Formula and Decay Rate

Adstock is often modeled using an exponential decay function that also helps to illustrate the basic concept:

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

Where:

• Media(t) = current period's media activity
• λ (lambda) = adstock decay rate (0 to 1)
• Adstock(t-1) = previous period's adstock value

The decay rate determines how quickly advertising effects diminish:

• Higher decay rate (closer to 1) = longer-lasting effects
• Lower decay rate (closer to 0) = shorter-lasting effects

As a simplified example, let's assume the decay rate is 0.8. If an advertiser invests 100 dollars on Google Performance Max on Monday, the effect of advertising on Tuesday is assumed to be 80% of the effect on Tuesday.

In some sources, the saturation effect is also considered to be part of the adstock transformation but here it is considered to be a separate but related concept.

Common types of Adstock Models

1. Geometric Adstock

The standard approach, using exponential decay at a fixed rate over time based on a single decay rate parameter.

2. Delayed Geometric Adstock

Similar, but with the maximum effect occurring after a short delay as determined by an additional delay parameter.

3. Weibull Adstock

Uses a flexible decay curve with two parameters based on the Weibull distribution, allowing for both delayed and accelerated effects.

4. Negative-Binomial Adstock

Employs the negative binomial distribution with two parameters for greater flexibility, capturing delayed peak and varied decay patterns.

Adstock in Marketing Mix Modeling (MMM)

Adstock is a fundamental component of Marketing Mix Modeling (MMM), where it helps:

• Attribute sales correctly to media investments across time periods, channels, and campaigns
• Optimize budget allocation by understanding long-term vs. short-term media effects
• Measure incrementality more accurately by accounting for delayed responses (for example many Black Friday campaigns start before the actual event)
• Plan campaign timing based on how effects build and decay

There are two general approaches in incorporating adstock transformation in MMM:

• As a pre-calculated transformation: To avoid making the model more complex and computationally intensive, the adstock effect can be calculated before the data is input into e.g. a regression model. This requires strong assumptions.
• As a modelled parameter: Especially in Bayesian marketing mix models, the adstock parameters are often learned from the data together with the regression coefficients. This often requires robust formulation of the model and sensible priors for the parameters to avoid problems with for example model convergence.

The implementation also depends on which media metric is chosen as the basis for the model feature for each marketing activity. For example attributed conversion value may have some of the carryover effect already built-in depending on the technical implementation of the ad platform attribution system.

Measuring Adstock Parameters

Determining the right adstock parameters can include:

Statistical Analysis

• Regression modeling to identify optimal decay rates, including Bayesian regression
• Cross-correlation analysis between media and sales data
• Hyperparameter optimization when running multiple models
• Analysis of attribution data (e.g. newsletter data)

Market Research

• Brand tracking studies to measure awareness decay
• Consumer surveys on purchase timing and influences
• Panel data analysis for individual-level insights

A/B Testing

• Holdout tests to measure lift duration
• Geo-experiments comparing different adstock assumptions
• Incrementality studies across various time horizons

Best Practices for Adstock Implementation

Data Requirements

• Sufficient historical data (minimum 1-2 recommended)
• Granular time series (daily is preferred to correctly capture for example seasonal sales)
• Comprehensive media tracking across all channels

Model Validation

• Out-of-sample testing to verify predictive accuracy
• Cross-validation across different time periods
• Sensitivity analysis on decay rate assumptions

Business Application

• Regular parameter updates as market conditions change
• Channel-specific adstock rates for different media and campaign types
• Integration with budget planning and forecasting processes

Common Challenges and Solutions

Challenge: Determining Optimal Decay Rates

Solution: Use statistical methods combined with business judgment, validate with holdout tests.

Challenge: Different Decay Rates Across Channels

Solution: Apply channel-specific adstock parameters based on media and campaign characteristics

Challenge: Increasing Number of Parameters in Statistical Models

Solution: Combine adstock modeling with attribution analysis for comprehensive measurement

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.