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Saturday, 13 September 2014


In this post I share a formal framework for reasoning about advertising traffic flows, is how black box optimisers work and needs to be covered before we get into any models. If you are a marketer, then the advertising stuff will be old-hat and if you are a data scientist then the axioms will seem almost obvious.

What is useful is combining this advertising + science view and the interesting conclusions about traffic valuation one can draw from it. The framework is generalised and can be applied to a single placement or to an entire channel.

Creative vs. Data – Who will win?

I should preface by saying my view on creative is that it is more important than the quality of one's analysis and media buying prowess. All the data crunching in the world is not worth a pinch if the proposition is wrong or the execution is poor.

On the other hand, an amazing ad for a great product delivered to just the right people at the perfect moment will set the world on fire.

Problem Description

The digital advertising optimisation problem is well known: analyse the performance data collected to date and find the advertising mix that allocates the budget in such a way that maximises the expected revenue.

This can be divided into three sub-problems: assigning conversion probabilities to each of the advertising opportunities; estimating the financial value of advertising opportunities; and finding the Optimal Media Plan.

The most difficult of these is the assessment of conversion probabilities. Considering only the performance of a single placement or search phrase tends to discard large volumes of otherwise useful data (for example, the performance of closely related keywords or placements). What is required is a technique that makes full use of all the data in calculating these probabilities without double-counting any information.

The Holy Triumvirate of Digital Advertising

In most digital advertising marketplaces, forces are such that traffic with high conversion probability will cost more than traffic with a lower conversion probability (see Figure 1). This is because advertisers are willing to pay a premium for better quality traffic flows while simultaneously avoiding traffic with low conversion probability.

Digital advertising also possesses the property that the incremental cost of traffic increases as an advertiser purchases more traffic from a publisher (see Figure 2). For example, an advertiser might increase the spend on a particular placement by 40%, but it is unlikely that any new deal would generate an additional 40% increase in traffic or sales.

Figure 1: Advertiser demand causes the cost of traffic to increase with conversion probability

Figure 2: Publishers adjust the cost of traffic upward exponentially as traffic volume increases

To counter this effect, sophisticated marketers grow their advertising portfolios by expanding into new sites and opportunities (by adding more placements), rather than by paying more for the advertising they already have. This horizontal expansion creates an optimisation problem: given a monthly budget of $x, what allocation of advertising will generate the most sales? This configuration then is the Optimal Media Plan.

Figure 3: The Holy Triumvirate of Digital Advertising: Cost, Volume and Propensity

NB: There are plenty of counterexamples when this response surface is observed in the wild. For example with Figure 2, some placements are more logarithmic than exponential, while others are a combination of the two. A good agency spends their days navigating and/or negotiating this so that one doesn't end up over paying.

To solve the Optimal Media Plan problem, one needs to know three things for every advertising opportunity: the cost of each prospective placement; the expected volume of clicks; and the propensity of the placement to convert clicks into sales (see Figure 3). This Holy Triumvirate of Digital Advertising (cost, volume and propensity) is constrained along a response surface that ensures that low cost, high propensity and high volume placements occur infrequently and without longevity.

For the remainder of this post (and well into the future), propensity will be considered exclusively in terms of ConversionProbability. This post will provide a general framework for this media plan optimisation problem and explore how ConversionProbability relates to search and display advertising.