A Deep dive into Attribution Maths — Part, 3
In our previous article we explored Shapley and Markov models, two examples of Algorithmic Models. Along with Heuristic Models, Algorithmic models use a bottom up approach to attribute conversions among different channels. Using logic and algorithms to attribute conversions to a marketing channel.
They also rely on all touchpoints on the user journey being tracked effectively. This is not possible all the time, especially in large marketing setups. These models are unable to account for a mix of digital channels and traditional media such as radio and TV. They also fail to solve for physical stores and seasonality.
In this article we will discuss how Data Driven models specifically Media Mix Models account for these complexities. We will then take a look at the shortcomings of Media Mix Models and explore how Controlled Experimentations such as RCT can help to overcome those.
Let’s dive even deeper into the the math behind marketing!
Media Mix Modelling (MMM)
The Logic
Marketing Strategies have a tendency to get complicated quickly. From social media and digital ads to radio and TV, Black Friday Sales to Diwali Discounts and Influencers to Brand Ambassadors.
This complexity can make any analyst feel helpless when questioned about the reasons for growth. Marketing becomes a black box with the budget going in on one end and sales coming out the other.
Media Mix Modelling helps untangle the complex web of multi channel marketing. MMM is a data driven model using a statistical approach to measure the impact of various marketing channels on sales and other business outcomes. Its primary goal is to allocate marketing budgets effectively across channels such as TV, radio, digital, print, and out-of-home advertising.
By analysing historical data, MMM determines how different media investments contribute to performance, enabling marketers to forecast outcomes and make informed decisions.
The Maths
MMM leverages regression analysis to estimate the relationship between marketing inputs and outputs. Here’s how the math works:
The model is typically a multivariate linear regression equation. We solve for an outcome variable (e.g., sales or leads) using Marketing spend across different channels and a baseline level of sales without marketing
External factors like seasonality, economic conditions, and competitor actions are included as control variables to ensure accurate attribution of impact.
By calculating the coefficients, MMM identifies which channels deliver the highest ROI and provides actionable insights for budget allocation.
Conclusion
MMM offers a high-level overview of marketing effectiveness, ideal for companies juggling multiple channels. There are two main advantages to this approach
Holistic View: Evaluates all marketing channels and is able to account for a mix of digital channels along with traditional media channels like radio and TV and physical stores.
Budget Planning: The mathematical nature of these models means that we can simulate various spend scenarios to predict potential outcomes.
Even though MMMs can be extremely powerful, there are still a few drawbacks.
Time Lag: They rely on historical data, so insights may not account for real-time changes in consumer behavior or market dynamics.
Limited Granularity: MMMs do not track individual user journeys, focusing instead on aggregate trends.
Data Quality Dependency: Most importantly, MMM results are only as good as the data input; incomplete or incorrect data skews accuracy.
Randomised Controlled Trials (RCT)
The Logic
RCTs are a necessary addition to Media Mix Modelling. Consider a winterwear brand Fungly Sweaters. Fungly Sweaters runs marketing campaigns across multiple channels. The Growth Team at Fungly knows the best time to spend on marketing is just before winter and uses this approach year after year. Resulting in perfect correlation between Ad Spend and Sales.
However this results in perfectly synchronised data which cannot be used for regression modelling.
If instead the Growth Team at Fungly decided to completely randomise their ad spend and went on an all year vacation. That would lead to a completely chaotic marketing setup. This would result in lower slaes but end up giving us perfect data for MMM.
Does that mean that Growth Teams should stop strategising?
No. But there is a way to mix established growth strategies with controlled experimentation.
This is the principle behind RCT. Introducing some experimentation in the form of A/B Tests and Random Controlled Trials to ensure that marketing teams are able to keep finding the best possible levers for growth.
The Maths
RCTs leverage statistical principles to evaluate the significance and magnitude of observed differences between test and control groups. Here’s an outline of the math:
Randomly assign participants into Test and Control groups. This ensures external factors are evenly distributed and the results reflect the marketing intervention’s true effect.
Calculate the average outcome for both groups to evaluate the incremental effect of the campaign.
The Effect of Radio Ads here is 2.4%
Randomised Controlled Trials are the gold standard for causal inference, measuring how an experiment affects conversion by comparing a test group to a control group. By isolating one variable, such as a specific ad campaign, RCTs can provide clear evidence of attribution.
Conclusion
Media Mix Modelling (MMM) and Randomised Controlled Trials (RCTs) are two powerful methodologies in marketing analytics, each offering unique strengths. MMM excels at leveraging historical data to identify trends and optimise resource allocation across channels, while RCTs provide unmatched accuracy in isolating causal effects through experimental rigour.
Together, these approaches complement each other, enabling marketers to balance strategic planning with tactical precision. By integrating the macro-level insights of MMM with the granular causality of RCTs, businesses can craft data-driven marketing strategies that maximise efficiency, effectiveness, and ROI in an increasingly complex advertising landscape.
