# Reach and frequency

The use of reach and frequency is a crucial factor in effective ad campaigns, but it is not often considered in current marketing mixed models (MMMs) due to the lack of accurate reach and frequency metrics for some traditional media channels. Typically, MMMs rely on impressions as input, neglecting the fact that individuals can be exposed to ads multiple times, and the impact can vary with exposure frequency. To overcome this limitation, Meridian offers the option to model any media channel's effect based on reach and frequency data, instead of a single execution metric. This approach can potentially yield more precise estimates of marketing impact on business outcomes and aid in optimizing campaign execution through frequency recommendations.

For modeling purposes, the reach and frequency data must be at the same level of geo and time granularity as the sales and controls data.

• The reach data should be the number of unique individuals exposed to the channels' ad within each time period instead of the cumulative number of individuals reached over consecutive time periods.

• The frequency data should be the total number of impressions divided by the reach for each time period.

The media effect is the additive contribution to expected sales. For channels with reach and frequency data, the media effect of the $$n^{th}$$ channel within geo $$g$$ and time period $$t$$ is modeled as follows:

$$\beta_{g,n}^{(rf)} Adstock \left(\left\{ r_{g,t-s,n} Hill \left( f_{g,t-s,n};\ ec_n^{(rf)}, slope_n^{(rf)} \right) \right\}_{s=0} ^L;\ \alpha_n^{(rf)} \right)$$

Where:

• $$f_{g,t,n}$$ is the average frequency
• $$r_{g,t,n}=L_{g,n}^{(rf)}(\overset {\cdot \cdot} r_{g,t,n})$$ is the transformed reach. This is scaled by population and the median value for the channel. For more information, see Input data.

This effect is calculated by first applying the Hill function to the average frequency $$f_{g,t,n}$$ to adjust for saturation effects. The Hill-transformed frequency for each geo and week is multiplied by transformed reach. These values are then weighted by the Adstock function to capture lagged effects of media exposure over time.

The Hill function allows for the media effect to be S shaped as a function of frequency, which means that the optimal average reach for cost effectiveness may be greater than one. The S shaped curve reflects the intuition that there might be an optimial frequency for incremental KPI value per impression. A certain minimum frequency might be necessary to reinforce brand recall, while excessive frequency can result in ad fatigue and diminishing returns.

Reach is assumed to have a linear relationship with sales response holding frequency fixed. Reach is contingent on the definition of the target audience, which can be a combination of different groups, each with its own responsiveness to advertising. By assuming a linear reach effect, you can implicitly assume that reach across different audiences changes proportionally. However, it is possible that as total reach becomes larger, it becomes more difficult to reach additional members of the target audience. In this case, the reach effect can have diminishing marginal returns. Meridian restricts the reach effect to be linear to avoid model overparameterization, parameter non-identifiability, and Markov Chain Monte Carlo (MCMC) convergence issues. Be careful not to extrapolate this linear effect far outside the range of observed reach values observed in the data.

For more information about reach and frequency, see Bayesian Hierarchical Media Mix Model Incorporating Reach and Frequency Data.

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