The maths around the index — statistical methods in SEO

The Local Digital Visibility Index is scored with deliberately simple arithmetic — ratios, weighted sums, a clamp. No model, no fitting, nothing you cannot check with a published dataset (JSON or CSV) and a spreadsheet. That is a design decision, not a limitation: a ranking that people can be judged by has to be one they can recompute and dispute.

So these entries are not what produces the score. They are the layer either side of it. Once you have four quarters of data, separating a real move from noise is ANOVA and time-series analysis. Reconciling five AI engines that disagree about whether they cited a firm is an evidence-combination problem, which is Dempster-Shafer theory. And several of them — k-nearest neighbours, PCA, Boltzmann machines — describe what is running inside the ranking systems the index measures from the outside.

Each entry defines the method, gives a short mathematical sketch, and links both ways: across to the pillar whose data it would interrogate, and to the Knowledge Base articles that apply it in practice.

Which method reads which pillar

Not how the pillar is scored — how you would analyse it once scored.

Pillar	Weight	Methods that apply to it
Speed & CWV	20%	Time-series analysis, ARIMA
Technical	20%	Coordinate descent, control vector parameterisation
Local presence	20%	k-nearest neighbours, discriminant analysis
Visibility	15%	Regression, ANOVA, PCA
AI search presence	15%	Dempster-Shafer, Bayesian inference, Bayesian outcome prediction
Content & trust	10%	Kolmogorov complexity, probability theory

Six further entries below are general method write-ups that no pillar currently maps to. They carry no pillar block.

What’s in here

Probabilistic + statistical inference

• Bayesian inference (overview) — base rates + evidence under uncertainty.
• Bayesian inference applied to SEO outcomes — the same maths, framed as a ranking-prediction problem.
• Probability theory — the underpinning before the rest of this section makes sense.
• Dempster-Shafer theory — evidence combination when sources disagree.

Classification + clustering

• k-nearest neighbours — non-parametric classification by proximity.
• Discriminant analysis — linear separation of categories.
• Principal component analysis — dimensionality reduction.

Regression + variance

• Regression analysis — fitting a curve to ranking factors.
• ANOVA — comparing variance between groups.

Time series

• Time-series analysis — pattern recognition over time.
• ARIMA — autoregressive forecasting.

Optimisation

• AdaGrad — adaptive subgradient methods.
• Adam optimisation — adaptive moment estimation.
• Coordinate descent — one-variable-at-a-time minimisation.
• Ant colony optimisation — swarm metaheuristic.

Reinforcement learning

• Actor-critic algorithm — policy + value-function pairing.
• If-then rule prediction — rule-based outcome prediction.

Other

• Boltzmann machines — energy-based neural networks.
• Kolmogorov complexity — minimum description length.
• Control vector parameterisation — optimal control formulation.

Why this is here

Scoring 79 businesses and publishing the result as a ranking is only defensible if the method is inspectable. The methodology states the scoring rules, the pipeline is the code that applies them, and the data is CC BY so the numbers can be checked. These entries sit alongside that: the wider statistical toolkit for anyone who wants to take the published data further than we have.

See the topical map for how this cluster interlocks with the Knowledge Base and the Local Indices. The consultancy behind it is PYC.