Diagnosis: how to read ad data honestly before you act

For any KPI that is a sum or ratio of sums over a segmentation, the between-period delta decomposes exactly into definition-change + mix + within-segment rate + volume terms, once an interaction-allocation convention is fixed. Causes must act through these terms.

Multiple changes landing coincidently on one unit are point-identified only jointly: the unit's series yields one confounded contrast. Individual attribution requires external structure, temporal separation, an untouched control segment, randomization, or exclusion restrictions.

The more surprising a reported KPI movement, the more likely it is a measurement or pipeline artifact than a real market event.

KPI aggregates over many independent buyers move as drift plus noise; code, config, and platform-policy changes switch atomically. Absent a known discrete market event, a step discontinuity implicates a system change dated to the step.

Measurement pipelines fail asymmetrically toward undercounting: dead components emit nothing, while overcounting requires an active defect (duplication, replay, bots). Conversion collapse with stable spend, clicks, and sessions is presumptively tracking loss.

When budget is chosen using any signal of demand and spend affects outcomes, outcome-spend covariation cannot separate demand from budget policy; separation requires variation independent of the budget rule (exogenous demand signals, natural experiments).

A zero reading assigns near-equal likelihood to no-demand, no-exposure, and event-dropping measurement failure; alone it identifies no cause. Silence becomes evidence of absence only after exposure and instrument health are independently verified, with strength scaling with expected volume.

Time-additive ad metrics are defined only over a stated window: a valid sum requires rows that exactly partition that window, no gaps, overlaps, or mixed coverage. Partial coverage may be reported as-is or as a labeled estimate, never as the period total.

Conversion counts produced under different definitions (events counted, attribution, dedupe) are different measurands; any comparison spanning a definition change confounds measurement with demand unless the change is modeled, bridged, or shown null.

A directly witnessed, locally decidable fault is established by one observation regardless of unmeasured dimensions; an unqualified all-clear is a universal claim requiring evidence on every dimension. Signal absence under partial coverage licenses neither verdict.

Under one consistent counting rule, a defined subset's count cannot exceed its superset's over identical scope and window; any inversion is a counting fault, not behavior. Absent a shared rule, a nonzero cross-system gap alone proves nothing.

For time-based observational attribution, an advertiser-initiated intervention recorded nowhere at execution time can never later be excluded or separated as a confounder: the outcome series maps many-to-one over intervention histories, so unlogged history is unrecoverable.

Alerts protect only through triggered responses. A capacity-limited operator sustainably responds only while precision times avoided loss exceeds handling cost; below that threshold response extinguishes, so a noisier, more-sensitive monitor protects strictly less than a quieter one.

Click-path conversions are sessions times per-source CVR, summed; ad levers act only through delivered-session volume and composition (including ad-set expectations); site-side changes touch every source; a binding downstream capacity cap zeroes marginal conversions from added traffic.

Under unmodeled stochastic parameter drift with noisy observations, windowed-estimator error is sampling variance (falling in window length) plus staleness error (rising in it); the MSE-optimal lookback is finite and interior, shrinking with drift rate, growing with event sparsity.