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A Unified Theory of GEO VisibilityDependent Variables and the Denominator Problem

How to match each visibility stage to the right outcome—and why the denominator can completely change the story.

How to match each visibility stage to the right outcome—and why the denominator can completely change the story.

The stage determines the dependent variable

Search activation can be measured as yes or no. Retrieval needs presence or recall at k. Context exposure may use rank, top-k inclusion, or allocated tokens. Citation needs a rate or probability. Prominence may use first position, repetition, or answer share. Fidelity requires claim support. Brand visibility uses mention, position, recommendation, or share of voice. Behavior and conversion require clicks, leads, purchases, or revenue.

The dependent variable defines what a study has actually learned. A citation study cannot automatically claim a conversion effect, and an answer-influence study cannot automatically claim improved retrieval.

The denominator defines the question

Suppose a source is cited in eight of ten search-enabled responses. Its conditional citation rate is 80%. If search activated in only twenty of one hundred total runs, the source appeared in just 8% of all runs.

Same observations, different questions

8 ÷ 10 measures citation after search. 8 ÷ 100 measures end-to-end appearance.

Both values are valid only when their denominator and interpretation are explicit.

A dashboard must preserve its measurement conditions

Every reported rate should identify its denominator, platform, mode, date, location, prompt set, and number of repeated runs where relevant. Without this context, high conditional performance can be mistaken for high overall visibility.

Never interpret an effect without identifying its stage and denominator.

Frequently asked questions

Questions about this topic

What is a dependent variable in GEO?+

It is the specific outcome being measured, such as retrieval presence, citation probability, brand mention, fidelity, referral traffic, or conversion.

What is the GEO denominator problem?+

The same event rate can look very different depending on whether it is divided by search-enabled runs, all runs, retrieved runs, or another eligible set.

Which citation rate should a dashboard show?+

It may show both conditional and overall rates, but each must be clearly labeled with its denominator and measurement conditions.

Source notes

References

Sources are listed in APA 7 style. Preprints are identified as such and should not be treated as peer-reviewed findings unless separately published.

  1. Martinez, O. (2026). Optimizing visibility in generative engines: A critical survey of generative engine optimization (2023–2026) [Preprint]. arXiv. https://doi.org/10.48550/arXiv.2607.14035
  2. Aggarwal, P., Murahari, V., Rajpurohit, T., Kalyan, A., & Narasimhan, K. (2024). GEO: Generative engine optimization. In Proceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining (pp. 5–16). Association for Computing Machinery. https://doi.org/10.1145/3637528.3671900
  3. Zhang, K., He, X., & Yao, J. (2026). From citation selection to citation absorption: A measurement framework for generative engine optimization across AI search platforms [Preprint]. arXiv. https://doi.org/10.48550/arXiv.2604.25707