Hierarchical Bayesian MMM and Bass Diffusion for a WPP Marketing Science Consultancy
Gain Theory
The Challenge
Gain Theory, a media effectiveness consultancy, wanted to deepen their Bayesian modeling capabilities across several fronts simultaneously. Their team needed to get fluent with modern probabilistic approaches to marketing mix modeling. They had clients in consumer goods and media who needed custom models that could handle multiple markets and incorporate experimental evidence. And they had a genuinely novel problem: predicting how TV show viewership unfolds over time on streaming platforms — how quickly audiences discover a show, how word-of-mouth builds, and what the total addressable audience looks like.
Our Approach
Marketing mix modeling
The core of the engagement was building marketing mix models that work across geographies and markets. These models share structure across regions — so a market with limited data can borrow insight from similar markets — while still capturing local differences. Where clients had run controlled experiments measuring the impact of specific channels, we wove that evidence directly into the models so the estimates reflect both observational patterns and experimental results.
Viewership forecasting
The viewership forecasting work took a different approach entirely. We adapted a framework from diffusion theory — originally developed to model how new products spread through a population — to the problem of TV show audience growth. The model decomposes viewership into early fans who show up regardless, a broader audience that follows through word-of-mouth and social proof, and the total potential audience a show could reach.
Throughout the engagement, knowledge transfer was as important as model delivery. Gain Theory's team worked alongside ours at every stage, building the expertise to extend and maintain these approaches independently.
Results
Gain Theory's team emerged with substantially deeper modeling expertise and a set of production models serving their client base. The viewership forecasting model opened a new analytical offering for their media clients, giving them a principled way to decompose audience growth into its underlying drivers.
Multiple client engagements were delivered successfully, with Gain Theory's team increasingly leading the technical work as their fluency grew.
PyMC Labs Team
- Joe Wilkinson
- Niall Oulton
- Thomas Wiecki
- Bill Engels
- Carlos Trujillo
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