Mix Shift and Simpson's Paradox
By the end of this lesson, you should be able to: explain how a blended average moves when no group inside it changes, split a change into a within-group part and a mix part, recognize Simpson's paradox, and decide which number to report.
What mix shift is
Most metrics you report are blended averages: a conversion rate across all channels, revenue per user across all countries. A blended average depends on two things.
- How each group performs. The rate or value inside each group.
- How big each group is. The mix: what share of users sits in each group.
Mix shift is when the blended number moves because the second thing changed, even if the first didn't. If more of your users come from a low-value group, your average drops, even when every group is doing exactly as well as before.
A real example: Reddit's revenue per user
Reddit reports daily users and average revenue per user (ARPU) separately for the US and for the rest of the world. Here are its numbers for the first quarter of 2025 against the year before.
| Q1 2024 | Q1 2025 | Change | |
|---|---|---|---|
| US ARPU | $4.77 | $6.27 | +31% |
| International ARPU | $1.10 | $1.34 | +22% |
| Global ARPU | $2.94 | $3.63 | +23% |
| International daily users | 41.1M | 58.0M | +41% |
| US daily users | 41.4M | 50.1M | +21% |
Look at the growth rates. US ARPU grew 31% and international grew 22%, but global ARPU grew only 23%, barely more than the slower of the two.
That's mix shift. International users earn much less per person, and they grew twice as fast as US users. So the share of international users rose from about 50% to about 54%. More of the blend now comes from the cheaper group, and that pulls the average down, even though both groups improved.