Decomposition on Max Halford

The total derivative of a metric tree

maxhalford25@gmail.com (Max Halford) — Tue, 06 May 2025 00:00:00 +0000

A metric tree is a visual way to organize a complex metric. Count gives a good introduction here. Abhi Sivasailam gave a popular talk at Data Council 2023 if watching videos is your thing. Ergest Xheblati is someone to follow if you want to go deeper. There’s also a recent article from Lightdash. Finally, there’s this article by Timo Dechau, but it’s behind a paywall. The concept has a homonym, so beware when you browse for it.

Decomposing funnel metrics

maxhalford25@gmail.com (Max Halford) — Thu, 14 Dec 2023 00:00:00 +0000

Funnel metrics as products

I talked about metric decomposition in a previous article, and how it can be used to explain why metrics change values over time. That article explained how to decompose a sum, as well as a ratio. In this article, I’ll explain how to decompose a product.

revenue = impressions * click_rate * conversion_rate * spend

The decomposition in this article isn’t limited to funnels. It can be applied to any metric that is expressed as a product of factors. For instance, at Carbonfact, we decompose the carbon footprint of a clothing line as so:

Answering "Why did the KPI change?" using decomposition

maxhalford25@gmail.com (Max Halford) — Wed, 09 Aug 2023 00:00:00 +0000

Edit – I published a notebook here that deals with the case where dimension values may (dis)appear from one period of time to the next. The notebook decomposes a ratio, but the logic is also valid for decomposing a sum.

Edit 2 – I’ve stumbled on this article by Shao Zhifei which provides a good derivation of the ratio decomposition formula. I contacted Shao Zhifei on LinkedIn, and he told me they heavily use these formulas at Grab. He also pointed out a typo in the ratio decomposition formula which I have now fixed.