Additive and Multiplicative Decomposition
By the end of this lesson, you should be able to: tell whether a metric is a sum of parts or a product of drivers, split a change in either kind into the contribution of each piece, and explain why the obvious split of a product leaves a leftover term that logs remove.
Two shapes a metric can have
To find which piece of a number moved, you break it apart. A metric can break apart in two ways.
A sum of parts. Total revenue is US revenue plus international revenue. Total orders are orders from each city added together. The pieces are separate groups.
A product of drivers. Ride volume is the number of riders times how many rides each one takes. Ad revenue is the number of ads shown times the price of each ad. The pieces are different factors of the same group.
Splitting a sum: just add the changes
For a sum, splitting a change is easy. The change in the total is exactly the sum of the changes in the parts.
Reddit reported its revenue for the first quarter of 2025 by region. US revenue was $313.9 million, up 57%. International revenue was $78.5 million, up 82%. Working back to the year before gives these numbers.
| Region | Q1 2024 | Q1 2025 | Change | Share of growth |
|---|---|---|---|---|
| US | $199.9M | $313.9M | +$114.0M | 76% |
| International | $43.1M | $78.5M | +$35.4M | 24% |
| Total | $243.1M | $392.4M | +$149.3M | 100% |
The two changes add up to the total change exactly. International grew faster in percent, 82% against 57%, but the US contributed about three times as many dollars, because it started much bigger.
That's the main rule for sums: rank the parts by how much they added, not by their growth rate. A small part can grow quickly and still barely move the total.