Not Every Measurement Adds Up: Additive, Semi-Additive, and Non-Additive Facts

Opening Scene

An astronomer reviewing a month of observation logs can confidently sum up total observation time across every single night — thirty individual nightly durations add up to one genuinely meaningful monthly total. But summing a star’s recorded temperature across those same thirty nights produces a number with no real meaning at all; averaging makes sense there, summing doesn’t. And a star’s total known lifespan can’t be meaningfully summed or averaged across observation sessions at all — it’s simply the same fixed fact, restated each time. Three different measures, three genuinely different rules for how they can be legitimately combined.

Additive, semi-additive, and non-additive facts capture this exact same crucial distinction.

In Plain English

An additive fact — like a sales quantity or a duration — can be correctly summed across every dimension it’s associated with. A semi-additive fact — like an account balance — can be summed across some dimensions (across accounts) but not others (across time, where a balance should be averaged or taken as the latest value instead). A non-additive fact — like a ratio, a percentage, or a temperature — genuinely can’t be meaningfully summed across any dimension at all, and requires a different kind of aggregation, like averaging or a recalculated formula.

The Old Way

Understanding a measure’s real additivity has always been essential to designing a fact table and its downstream reports correctly, well before any of this could be automated:

Additive facts are the easiest and most common case, correctly summable across every dimension — sales quantity summed by product, by region, by month, all producing genuinely meaningful totals.
Semi-additive facts, most classically an account balance, can be summed across some dimensions but not time, where the correct aggregation is usually the latest value or an average, not a sum — summing a balance across twelve months of the same account produces a meaningless number.
Non-additive facts, like a percentage or a ratio, genuinely can’t be summed at all; they typically need to be recalculated from their underlying additive components at whatever level of aggregation is being reported, rather than aggregated directly.

Getting this right has always meant explicitly documenting each measure’s additivity as part of the fact table’s design, since assuming a measure is additive when it isn’t is a genuinely common and quietly damaging mistake.

What’s Changing (and Why AI Is the Reason)

AI-assisted additivity classification can automatically analyze a measure’s actual behavior across dimensions and correctly classify it as additive, semi-additive, or non-additive, reducing a source of genuinely common human error. Rather than a modeler relying on intuition or a measure’s name alone, AI-assisted analysis of how a value actually behaves when aggregated across different dimensions can confirm its true additivity classification with real evidence.
AI agents generating aggregation queries need to correctly respect a measure’s additivity to avoid producing a confidently wrong number, particularly for semi-additive and non-additive facts where the naive sum looks plausible but is actually incorrect. An agent asked to “total account balances by quarter” needs to understand that summing across time doesn’t make sense for a semi-additive balance, applying the correct alternative aggregation instead.
AI-assisted metric documentation can capture and surface each measure’s additivity rules directly alongside the metric itself, closing a gap where this crucial context often only lives in a modeler’s memory or scattered institutional knowledge. This connects directly to the semantic layer concepts covered in this site’s semantic-layers-metrics-stores topic, where a shared, documented definition of “how this metric aggregates” prevents exactly this class of quietly wrong calculation.

The Metaphor, Fully Extended

Observatory Element	Additivity Concept
Summing total observation time across every night in a month	An additive fact, correctly summable across every dimension
A star’s recorded temperature, meaningless to sum across nights but sensible to average	A semi-additive fact, summable across some dimensions but not others
A star’s fixed, unchanging known lifespan, restated rather than combined across sessions	A non-additive fact, requiring a completely different kind of aggregation, not summing
An astronomer double-checking which of these three rules genuinely applies to a given measurement	AI-assisted additivity classification confirming a measure’s true aggregation behavior with real evidence
A reference card beside each measurement in the log stating exactly how it can and can’t be combined	AI-assisted metric documentation surfacing each measure’s additivity rules alongside the metric itself

For Beginners: What to Actually Do

Practice asking, for any measure in a fact table, whether it can genuinely be summed across every dimension, some dimensions, or none at all — the answer isn’t always obvious from the measure’s name.
Get comfortable with the classic semi-additive example — an account balance, summable across accounts but not across time — since it’s the pattern most likely to trip up an unwary analyst.
Before summing any unfamiliar measure, check explicitly whether it’s actually additive, or whether averaging or a recalculated formula is the genuinely correct approach instead.
Notice that non-additive facts like ratios and percentages almost always need to be recalculated from their underlying components at whatever level is being reported, not aggregated directly.

For Practitioners and Leaders: The Deeper Layer

Use AI-assisted additivity classification to systematically confirm each measure’s true aggregation behavior with real evidence, rather than relying on intuition or naming conventions alone.
Design query generation and semantic layer tooling to correctly respect each measure’s documented additivity, particularly for AI agents generating aggregation queries automatically.
Invest in AI-assisted metric documentation that surfaces additivity rules directly alongside each metric, closing the gap where this context often only lives in scattered institutional knowledge.
Treat additivity misclassification as a genuinely high-severity risk, given how confidently wrong — rather than obviously broken — the resulting numbers tend to look.

Quick Recap

Additive facts can be summed across every dimension; semi-additive facts can be summed across some dimensions but not others, most classically time; non-additive facts can’t be summed at all and require recalculation.
Documenting each measure’s true additivity has always been essential to avoiding quietly wrong aggregations, well before this could be automated.
AI-assisted additivity classification can confirm a measure’s true behavior with real evidence, and AI-assisted metric documentation can surface these rules directly alongside each metric.
AI agents generating aggregation queries need to correctly respect additivity rules to avoid producing confidently wrong numbers, particularly for semi-additive and non-additive facts.

Where This Fits in the Series

Article 13 covered what happens when two stars share a planet. This article covered whether a measurement actually adds up. Article 15 looks at charting a whole constellation — fact constellations and galaxy schemas.