Hold segment weights fixed when a blended retention rate moves

A blended retention rate can improve because the campaign reached a different mix of segments. This lab holds two segment rates constant while changing their weights. It isolates the arithmetic of composition; it does not explain why the mix changed or whether buying caused it.

Define the calculation before using it

Enter two segment retention rates and the share of the first segment in each reporting period. Calculate each blended rate as the weighted sum of the two segment rates. Keep the segment definitions stable and use complete, mutually exclusive populations. The exercise is deliberately simple so the contribution of the weights remains inspectable.

Work through the synthetic example

With segment rates of 30% and 10%, moving the first segment’s share from 20% to 80% lifts the blended rate from 14% to 26% without improving either segment. The twelve-point change is entirely compositional in this synthetic construction. A buyer should inspect segment-level movement before attributing the aggregate change to a new creative.

Use the artifact and preserve its assumptions

Open the editable calculator to change the inputs and inspect the sensitivity view. The CSV records synthetic inputs and expected outputs; the JSON fixture keeps the equations available for reproduction. These calculations have been checked against the stated example. No measured campaign data is included.

The sensitivity rows vary only mixAfter by 20% below and above the entered value. They are scenarios, not confidence limits or a forecast distribution. A row outside the model’s constraints is labelled rather than turned into a plausible-looking result. Save the chosen inputs with the decision so another reader can distinguish a changed assumption from a changed formula.

Evidence and limits

Google’s export schema separates the reporting date, UTC timestamp and event parameters. The worksheet uses simplified aggregate inputs; it does not claim that an export already contains a correctly reconciled cohort. See Google Analytics BigQuery Export schema, especially “event_date, event_timestamp, event_value_in_usd and event_params fields”.

Two segments rarely capture every confounder. This is a standardisation illustration, not a causal adjustment or a claim that real segments would retain fixed performance after a large budget change.

Background: UA metrics explained: CPI, ROAS, LTV and payback and Reading an MMP dashboard without fooling yourself. These existing articles provide context; the present calculation does not verify every archived claim.