UNDER THE HOOD
A bridge, not a black box
Overall return rate is total returned ÷ total eligible. It’s weighted by the size of each segment, never an average of segment rates.
We use a symmetric midpoint decomposition to separate changes in audience mix from changes in within-segment return rates. The two contributions reconcile to the overall change.
Read the math & limitations
For each segment: mix = (current weight − baseline weight) × average return rate. Within = (current rate − baseline rate) × average weight. Both averages use the two comparisons equally. Add the terms across segments.
This splits the interaction equally between the two orderings. It’s a convention, not the only possible allocation. Results depend on your segmentation and upstream definitions. Monthly windows can have different lengths, and the method does not control calendar effects.
Segment mix terms can be large and offset. They are not independent operational causes. No causal effects, confidence intervals, significance claims, or forecasts are inferred. A person may appear in both comparison populations.
Zero eligible people in any paired segment allows an overall summary only. We don’t invent the missing rate, drop the segment, or force a decomposition.
Method: symmetric_rate_mix_v1