Marketing & Media Mix Model - Understanding Trends in MMM Predictions

The Prediction Line section of our Marketing & Media Mix Model dashboard shows how a target variable, say form fills, varies as a function of marketing budget. Each point on the plot represents the predicted number of form fills (y-axis) for a given budget (x-axis) assuming that budget is split optimally between all marketing channels. While we expect the trend to show an increase in form fills as the budget is increased, there is no way to know the exact form of the trend before seeing the data.

Although we can’t know the exact trend a priori, we can make reasonable assumptions. The concept of a point of diminishing returns from economics is highly applicable in this situation. It’s expected that as you continually increase your marketing budget, there will be a point at which each increase in budget will provide fewer form fills, purchases, etc. than the previous increase of the same size. This trend is typically modeled using a sigmoid function.sigmoids.png

Figure 1: Examples of Sigmoid functions. For diminishing returns, we typically use only the range where x > 0.

At ChannelMix, we choose to fit a logarithmic function to the trend. While the logarithm isn’t strictly a sigmoid function, it has the same desired characteristics of a sigmoid function while being a more broadly known and understood function. When choosing our logarithmic trend, we assume a few things. 

  1. When the marketing budget is $0, there will be 0 occurrences of the target variable. While this isn’t strictly true, we are assuming that marketing efforts have a significant effect on the action of interest.
  2. There will be a point of diminishing returns. At some point, money spent on marketing is going to start decreasing in efficiency and never recover.
  3. Most people are sitting somewhere in the middle of this curve. Marketers are good at their jobs and use their experience to make good decisions with their marketing budgets. But it’s a tough job and there’s always room for improvement with the help of a Marketing & Media Mix Model.


Figure 2: A scaled natural  logarithm function. We adjust the normal natural logarithm such that when x = 0, y = 0.

Because we are assuming the trend before seeing the data, it is certain that the logarithm will not fit all trends perfectly. The logarithmic fit is intended to be used as a reference against which the actual trend can be compared. From this, many conclusions can be drawn.

Figure 3 shows a situation where the logarithmic trend clearly does not fit the data. In this example, the model is predicting the number of interactions based on the marketing budget. Clearly, the number of interactions is heavily influenced by the marketing budget which completely makes sense. The more opportunities for someone to interact with marketing content, the more interactions that will occur. 


Figure 3: An example of when the logarithmic trend is a poor fit for the data. In this example, the target variable, interactions, is highly dependent on the budget. Increases in budget lead to large increases in the number of interactions up until the saturation point around $100,000.

The reason the logarithm doesn’t fit here, despite the data showing the general trend we expect, is due to the large increase in interactions at low budget followed by a rapid saturation at around 600K interactions. This is telling us two things. First, interactions are even more dependent on budget than our general assumption. And second, there is a hard upper limit on the number of people interested in interacting with this marketing content.

This is just one example of a trend between marketing budget and a target event and how conclusions can be drawn from the similarities and differences between data and the logarithmic fit. Every target event for every business will have a slightly different trend. By analyzing the shape of this trend, marketers can gain insight about where they are on the curve and where they want to be. 

Maybe you’re at the point where a 50% increase in budget will provide a 50% increase in target events. Maybe you’re spending $100K on marketing when you could get roughly the same number of target events with $80K. Understanding these trends provides great potential for optimizing your marketing budget.


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