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.

Additionally:

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:

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.

## Differences between assumed frequency for ROI and for optimization

There are differences between the assumed frequency for ROI and for optimization. You can adjust the assumed frequency for optimization if needed.

As discussed in ROI, mROI, and response curves, ROI measures the return of investment of a channel as it was executed during the time window for which the MMM has data. How a channel was executed includes how impressions are allocated across geos and time, and also includes the historical frequency of that channel.

Optimization assumes that future campaigns will be executed at the optimal frequency, since frequency is something often in an advertiser's control, especially for digital channels. If the optimal frequency is different from the historical frequency, a channel's performance in optimized budget allocation might not match the channel's historical performance according to ROI. This can be exacerbated if the current frequency is far from the optimal frequency.

If future campaigns won't be executed at the optimal frequency, you can use the optimization option to change the assumed frequency. This can be helpful for channels that cannot be executed at a specific average frequency.