mix shift

Almost every product rate (conversion, average order value, retention, stickiness) is a weighted average over segments: channels, platforms, countries, paywall triggers, new vs returning users. If the weights change, the total changes too, even when no segment's rate moved. That is a mix shift.

$\bar r = \sum_i w_i \, r_i$

where $w_i$ is the share of segment $i$ in the total and $r_i$ is its rate. Moving from period 0 to period 1, the change splits exactly into two parts:

$\Delta \bar r = \underbrace{\sum_i \left(w_i^{1} - w_i^{0}\right) r_i^{0}}_{\text{mix effect}} + \underbrace{\sum_i w_i^{1} \left(r_i^{1} - r_i^{0}\right)}_{\text{rate effect}}$

The mix effect is what the total would have done if every segment kept its old rate; the rate effect is the real change in behavior, weighted by the new mix. When they point in opposite directions, the total can move one way while every segment moves the other: the extreme case is known as Simpson's paradox.

Mix shifts are everywhere in product data: a partner promo brings users who came for a bonus and makes a new version look worse; a seasonal wave of trip users lowers stickiness; a paid campaign in a cheaper market lowers revenue per user. The habit that protects you is simple: before explaining a change in a total, split it by the obvious segments and check whether the weights moved. Report the result mix-adjusted (at fixed weights) as well as raw.