Data Science: The Hard Parts

Chapter 3. Growth Decompositions: Understanding Tailwinds and Headwinds

Chapter 2 described some techniques to find better metrics that can drive actions. This chapter deals with a completely different subject: how you can decompose metrics to understand why a metric changed. In corporate jargon these changes are usually associated with tailwinds or headwinds, that is, factors that positively or negatively affect the state of the company.

Why Growth Decompositions?

Data scientists are frequently asked to help understand the root cause of a change in a metric. Why did revenues increase quarter over quarter (QoQ) or month over month (MoM)? In my experience, these are very hard questions to answer, not only because many things can be happening at the same time, but also because some of these underlying causes are not directly measurable or don’t provide enough variation to be informative.¹ Typical examples are things like the state of the economy or the regulatory environment, as well as decisions made by competitors.

Nonetheless, I’ve found that you can use some other source of variations that, when coupled with the following techniques, can give you hints of what’s going on.

Additive Decomposition

As the name suggests, this decomposition is handy when the metric (output) you want to understand can be expressed as the sum of other metrics (inputs). In the case of two inputs, this can be expressed as $y_t=y_{1,t}+y_{2,t}$. Note that I’m using a time subscript.

The decomposition ...