Chapter 6: From Parameters to Business Impact

The true utility for a business comes from translating these learned parameters into actionable metrics.

• Contribution: The direct output of the Hill function for a given spend level. It’s the absolute impact on the target variable (e.g., sales) attributed to a channel over a period.
• ROI: Calculated as Total Contribution / Total Cost. This is an average metric over the entire spend range. While useful, it can be misleading for future planning.
• Marginal ROI (mROI): This is the holy grail for budget optimization and the most important output for a data scientist to understand. The mROI is the derivative of the Hill response curve. In simple terms, it’s the ROI of the next dollar spent. Because the curve is non-linear, the mROI is not constant; it is highest at low spending levels and decreases as you spend more, eventually approaching zero.

Advanced Structures: Geos, Reach, and Validation

Meridian’s architecture includes several sophisticated features for handling real-world data complexity.

• Geo-Level Modeling: Instead of building one national model, Meridian promotes a hierarchical (or multilevel) Bayesian model. Each geo (e.g., state or DMA) has its own parameters for media effects, but these parameters are assumed to be drawn from a common national-level distribution. This technique, known as partial pooling, allows geos to “borrow statistical strength” from each other. A small geo with noisy data will have its estimates “shrunk” towards the national average, preventing overfitting and producing more stable results. This is a statistically principled way to balance local variation with national trends.
• Reach and Frequency Data: Meridian recognizes that spending is a crude proxy for impact and allows for the inclusion of reach and frequency data. Instead of feeding spend into the adstock function, you can use a more nuanced metric like “impressions among the target audience” or “unique reach.” This can lead to a more accurate modeling of the saturation curve, as saturation is fundamentally a function of audience exposure, not dollars spent.
• Holdout Observations: To guard against overfitting and assess predictive power, Meridian emphasizes using holdout data. A common practice is to train the model on data up to a certain date (e.g., the last 3 months) and then test its ability to predict the observed outcomes in that holdout period. Metrics like Mean Absolute Percentage Error (MAPE) on this out-of-sample data are critical for model selection and validation.

The Final Act: Budget Optimization

The entire framework culminates in budget optimization. The process is elegant and directly driven by the model’s outputs. With the mROI curve calculated for every channel, the optimization algorithm is straightforward:

1. Start with a given budget.
2. Set business constraints like minimum media channel spend or category constraints
3. Set your target KPI goals.
4. Allocate the first dollar (or a small increment of budget) to the channel that currently has the highest mROI.
5. After allocating that dollar, recalculate the mROI for that channel (it will now be slightly lower).
6. Repeat the process, always allocating the next dollar to the channel with the current highest mROI, until the entire budget is exhausted. After each iteration, the process ensures constraints are respected and aims to reach established KPI goals.

This simulation provides a data-driven, forward-looking budget allocation plan designed to maximize the total return on the next period’s marketing investment. It is the practical, monetizable payoff of the entire sophisticated statistical system.