Brand Strength, Positioning and AI Recommendation, with Five Formulas to Test

This digest answers the brand-strength question: does a stronger, more clearly positioned brand get recommended more often by AI engines, and through what mechanism? The category-ownership question, how a brand wins by moving to questions it can lead, is answered in PS-04. This digest reviews the published evidence on that question: twelve academic papers, seventeen industry studies and four case studies, read in primary form except where marked second-hand. It then sets out five testable formulas, adapted from established marketing science, that would let LBOX measure the relationship directly. The short answer is that brand strength matters, through two separate paths, but the kind of strength that matters is narrower than most marketers assume, and nobody has yet shown it causally.

Sources: research notes RN-07A (academic), RN-07B (industry and case studies) and RN-07C (marketing-science models), 6 Oct 2026, held in research-notes/ in the lbox.com repository. Figures were read in the primary source by the research pass unless marked second-hand. A second independent check of the headline figures was completed for Zhen et al. and the Ahrefs correlation study. The second check on Malthouse et al., Tannenbaum and Jack et al. is pending, because their arXiv pages could not be fetched a second time this session.

Evidence tags: [LBOX] measured in LBOX research; [Test] a single LBOX run; [External] someone else's published claim, named in the sentence; [Hypothesis] a reasoned mapping not yet tested. Principle codes (AZ-01 to AZ-24) refer to PS-00.

1. What the evidence says

Four findings hold across independent sources, and one claim that LBOX has been making does not.

Survey brand equity is a weak predictor of AI recommendation. The most direct academic test, Malthouse et al. (Northwestern and Boston University, arXiv 2609.16304, Sep 2026), asked six frontier models for brands in five categories across 2,400 answer lists with web search off. Brand salience from a large commercial brand-equity survey predicted recommendation weakly and inconsistently, and well-known brands such as L.L.Bean, Craftsman, Black+Decker, Braun and Philips were named in none of the category-only answers [External]. Advertising spend had no significant relationship with recommendation prominence (coefficient −0.14, p = .17, n = 82 brands) [External].

Attention and third-party presence are the strong correlates. In the same study, Google search interest was the strongest predictor of recommendation prominence (fractional logit coefficient 1.06, p < .0001; raw correlation with the square root of mean reciprocal rank .63) [External]. Ahrefs' study of 75,000 brands found branded web mentions correlate with AI mentions at 0.664 for ChatGPT, 0.709 for Google AI Mode and 0.656 for AI Overviews (Spearman), well above branded search volume (0.352 to 0.466) and domain rating (0.266 to 0.326) [External; vendor]. Seer Interactive, the only industry study that corrected for running hundreds of tests at once, found mentions in "best of" articles correlate with ChatGPT mentions at about 0.69 across 62 brands [External; vendor].

Redundancy across independent sources is associated with selection. Zhen et al. (arXiv 2607.15771) audited four Chinese AI search engines across 632,256 brand candidates. Only 8.3% of brands that appeared in cited pages made it into the answer. The selection rate rose from 2.1% for a brand named in one cited source to 59.9% for a brand named in eleven or more, and that count correlated with total brand frequency at only r = 0.04 [External; vendor, checked twice]. Being named by many different sources was associated with selection even after controlling for how often the brand was named overall. The study is correlational and does not compare predictive power head to head.

Positioning decides which questions retrieve a brand. The brands Malthouse et al. found absent were not unknown to the models. Craftsman rose from 0% of answer lists on category-only prompts to 35.4% on needs-based prompts and 81.3% on prompts using its own positioning language; L.L.Bean rose from 0% to 5.4% and 88.5% (240 lists each) [External]. The engines knew the brands. Ordinary buyer wording did not call them up. This is the clearest evidence yet for AZ-15 Buyer Wording, and it rests on two brands.

The correction: three names is not established. PS-00 described the shortlist as usually about three names. Published counts disagree widely. One BrightEdge analysis reports an average of 5.84 brands per ChatGPT answer, 5.44 for Google AI Mode and 4.37 for Perplexity; another BrightEdge analysis, as reported by Search Engine Land, gives 2.37 for ChatGPT, 1.59 for AI Mode and 6.02 for AI Overviews [External; vendor, both read second-hand]. A Search Engine Land analysis of 12 B2B software prompts run 100 times each found about ten brands per ChatGPT answer [External; read second-hand]. LBOX's three-name figure came from counting top-three slots in the EV test [Test], which measured what we chose to count. List length varies by engine, category and study, and is itself a measure LBOX should record. Whether buyers act mainly on the top few names is a separate, untested question. PS-00 AZ-01 is revised accordingly.

2. The evidence, source by source

2.1 Academic and preprint studies

Source	Design and n	Key finding	Causal?	Conflicts
Malthouse et al., arXiv 2609.16304 (Sep 2026)	Audit; 6 models, search off; 5 categories; 2,400 lists; 82 brands in the regression	Search interest strongest correlate (1.06, p < .0001); ad spend not significant; positioning cues lift absent brands to 81 to 89%	Correlational for brand metrics; prompt contrasts experimental but n = 2 brands	None declared
Pfrommer et al., EMNLP 2024 (arXiv 2406.03589)	Controlled swaps of product names with page content fixed	The product name alone moves rank; GPT-4 Turbo leaned mostly on prior knowledge of the name	Causal	None
Allouah et al., arXiv 2508.02630 (Dec 2025)	Randomized trials in a mock marketplace; 8 categories; up to 1,000 runs per category; 6 buyer models	An "Overall Pick" badge raised selection from a 10% baseline to 19.9 to 42.6%; a Sponsored tag lowered it; +0.1 rating lifted it to 15.4 to 20.3%; front-loading the category term in titles gained up to 80 points of share in one category	Causal for badges, ratings and titles; brand identity not randomized	Two authors at a commercial AI firm
Zhen et al., arXiv 2607.15771 (2026)	Audit of 4 Chinese engines on 8 interfaces; 614 queries × 3; 632,256 brand candidates	8.3% of cited brands reach the answer; 2.1% to 59.9% by number of citing sources; comparison and ranked-list passages select at 22.9%	Correlational	Commercial authors, no statement
Tannenbaum, arXiv 2609.23162 (Sep 2026)	Field panel of 34,960 unbranded runs on GPT and Gemini; 75 projects; June to Sept 2026	Mention rate 2.8 to 3.8% without own-domain evidence, 49 to 58% with it; within-prompt odds ratio 15.3 (GPT) and 29.7 (Gemini); established competitors named in 28 to 30 of 40 runs that cited nothing	Correlational	Declared: author runs an AI search vendor
Jack et al., arXiv 2605.27440 (May 2026)	Controlled prompt experiment; about 12,000 runs; 2 providers	Cosmetic rewording kept 0.288 of the recommended set (Jaccard); adding a constraint kept 0.135; same-prompt reruns kept 0.50 to 0.61	Causal for wording	Authors at an AI marketing company
Kandpal et al., ICML 2023	Retraining study on entity co-occurrence	Recall of a fact depends on how often the two entities appear together in training text	Causal	None
Mallen et al., ACL 2023 (PopQA)	Benchmark across entity popularity	Popular entities answered well from memory; retrieval mainly helps the long tail	Correlational	None

Popularity-bias studies of LLM recommenders for films, music and books (three papers, reviewed in RN-07A) find real but moderate bias toward popular items. They support the direction of AZ-02 and AZ-04 without measuring brands.

2.2 Industry studies

Source	n and method	Key finding	Weaknesses
Ahrefs (Dec 2025)	75,000 brands; ChatGPT, AI Mode, AI Overviews; Spearman	Web mentions 0.656 to 0.709; YouTube mentions 0.712 to 0.740; branded search 0.352 to 0.466; domain rating 0.266 to 0.326	No control for brand size; Ahrefs measured both sides with its own tools
Seer Interactive (Mar 2026)	62 brands; ChatGPT; about 350 tests with false-discovery correction, 21 survived	Domain authority about 0.75; "best of" mentions about 0.69; Wikipedia mentions negative in B2B (−0.631); paid search spend no relationship	Small n; contradicts Ahrefs on backlinks
SparkToro and Gumshoe (Jan 2026, read second-hand)	About 3,000 runs by about 600 volunteers; press reports disagree on whether that was 12 prompts or 2,961	The same brand list repeats in under 1 run in 100; leaders still appear in 60 to 90% of answers	Rank tracking from single runs is unreliable
AirOps (Oct 2025)	21,311 brand mentions, B2B software	85% of mentions attributed to third-party pages, 13.2% to the brand's own site; most third-party pages are lists, comparisons and reviews	Descriptive only
Seer and Trustpilot (May 2026)	804,000 responses	Brands with fuller review profiles had 9.5× more co-mentions	Partner-funded; headline metric close to circular

These agree with LBOX's own classification of 28,492 citations, where own sites were 5.1% and other companies' sites, editorial and retail made up most of the rest [LBOX]. The two independent datasets point the same way: what others publish about a brand dominates what engines repeat (AZ-03).

2.3 Case studies

No published case study shows a positioning or category change followed by a measured change in how AI answers describe or rank the brand, with a baseline, a control and repeated runs.

Case	Change	Reported result	Why it is not evidence yet
SearchPilot with Omio	Clear brand selling points added to matched test pages	+18% LLM referral sessions against a control group	Measures traffic, not answer content; the only design with a control
Profound with Optro (formerly AuditBoard)	Rebrand plus 31 articles	"70% improvement" in citation share	No baseline, window or definition
Profound with Ramp	Category pages	Visibility 3.2% to 22.2%	No control; vendor metric
GR0 with AdQuick	Narrowed to "billboard advertising"	+48% LLM traffic	No control; link building ran in parallel

2.4 Repeated figures that do not hold

As repeated	What the source shows
"Brand mentions beat backlinks 3 to 1"	A ratio of two correlation coefficients (0.664 ÷ 0.218) written by secondary authors. It does not measure relative importance, and Ahrefs never claimed it
"Wikipedia is 48% of ChatGPT citations"	47.9% of the top ten cited domains in Profound's data; the overall share is 7.8%
"Brand search volume is the strongest predictor, .334"	Primary analysis not found
"AI visitors convert 23×"	One website over 30 days

3. Scientific assessment

What is causal. Product names, randomized badges, ratings, category terms in titles and prompt wording all move AI choices in controlled designs. Brand strength itself has never been manipulated. Every link between real-world brand strength and AI recommendation is cross-sectional.

What is consistent. Independent sources agree on direction. Third-party presence, especially across many different sources and in comparison or list formats, correlates with AI mention in Ahrefs, Seer, AirOps, Zhen and LBOX's own citation data. Stated brand equity and paid media do not.

What conflicts. Backlinks correlate weakly with AI Overview mentions in Ahrefs (0.218) and strongly in Seer. Malthouse et al. report news coverage as significant in their unpenalized regression (p = .032) and close to zero under ridge and lasso estimation. Both remain unresolved.

What threatens validity. Fame produces both web mentions and AI mentions, and no industry study controls for company size, revenue or age, so reverse causation and confounding are live. Same-prompt reruns reproduce only half to three fifths of the recommended set and cosmetic rewording reproduces less than a third, so any study that runs each prompt once measures noise. Coefficients shift with every model release, so findings carry a short shelf life. The large field datasets come from vendors whose data cannot be audited.

The two-path mechanism. The evidence supports a model with two routes into an answer. A brand can be named from the model's memory, where it has been learned in connection with a category or a need (Kandpal, Pfrommer, Malthouse, and Tannenbaum's citation-free competitor mentions). A brand can also be named because it appears in the evidence the engine retrieves for that question (Tannenbaum's own-domain odds ratios, Zhen's source redundancy, Allouah's badges and titles). Positioning plausibly works on both routes [Hypothesis]: it may decide which needs the brand is remembered for, and whether third-party pages describe the brand in the words buyers use. Malthouse et al. raise this as an implication and do not test it.

4. Five formulas to test

None of these has been applied to AI answers in published work, as far as RN-07C could find. Each is [Hypothesis] until LBOX runs it. All five share one measurement design.

4.1 Common measurement design

• Fix the competitive set from outside the answers (market share lists, analyst lists) before running prompts, so brands that never appear are counted as absent.
• Group buyer questions into situation clusters (when, where, with whom, for what need), with about ten paraphrases each, so a cluster measures a need rather than one wording.
• Run each prompt in fresh sessions, with search on and search off logged as separate engine variants.
• Collect about 100 answers per cluster and engine. A proportion near 50% then carries a 95% interval of about ±10 points; at 40 answers it is about ±15.

Base measures: answer penetration (share of unbranded answers naming the brand), mean reciprocal rank (prominence, zero when absent), volunteered share (the brand's share of all brand mentions), network size (number of clusters where the brand is named in at least 20% of answers), run stability (share of runs naming the brand on prompts where it ever appears), descriptor consistency (similarity of the words used for the brand across engines and runs) and third-party share (the brand's share of brand mentions in cited pages it does not own).

4.2 F1: The size benchmark

Established buying research shows that small brands suffer twice: fewer buyers, who also buy a little less often. Across decades and dozens of categories, purchase frequency × (1 − penetration) stays roughly constant within a category, and the Dirichlet model predicts each brand's penetration from its share alone.

Applied to AI answers, each prompt plays the role of a buyer and each run a purchase occasion. With S fitted per category and engine and n answer slots per prompt:

P(brand named at least once on a prompt) = 1 − Π (S − α + i) / (S + i), for i = 0 to n − 1, where α = volunteered share × S

Prediction. Small brands appear on fewer prompts and appear less reliably on the prompts where they do appear. A brand named on more prompts than its share predicts holds a sharper position than its size; a brand below the line is spread thin.

Why it matters. It turns positioning into a residual. For the first time a client can see whether its AI presence is above or below what its size alone would give it.

Test. One category, 200 unbranded prompts, 20 runs per engine. Fit S, predict penetration on held-out prompts, and compare fit against the human-buying benchmark (correlation above 0.6, average error under 20%).

Falsified if brand penetration on held-out prompts is not predicted by share at all, which would mean prompt wording dominates size.

4.3 F2: AI mental market share

Mental availability research measures how many buying situations a brand is linked to. Mental market share is the brand's share of all brand-to-situation links; network size is the number of situations linked to the brand.

AI mental market share = brand-to-cluster links for the brand ÷ all brand-to-cluster links, across situation clusters and runs

AI mental market share ≈ γ × (human mental market share)^θ

Prediction. AI mental market share measured on a battery of 15 to 25 situation clusters predicts volunteered share on held-out prompts. θ above 1 means the engines concentrate attention on leaders more than buyers' memories do; θ below 1 means they flatten it.

Why it matters. If it holds, a fixed situation battery is a cheap, repeatable tracking instrument for any category, and θ answers whether AI search is a rich-get-richer channel.

Test. One category, 20 clusters with 10 paraphrases each, five engines, 40 passes each. For θ, a matched human survey on the same clusters.

Falsified if held-out share is not predicted by the battery, or θ cannot be estimated with a confidence interval narrower than ±0.3.

4.4 F3: Excess third-party voice

Advertising research found that brands whose share of voice exceeds their market share tend to grow, at about half a point of share per year for every ten points of excess voice. The rule rests on observational data and is disputed, so it is the weakest prior here.

For AI answers, the "voice" is what third parties publish about the brand.

Change in volunteered share (next period) = κ × (share of corpus voice − volunteered share)

Elasticity η = ∂ ln(volunteered share) ÷ ∂ ln(share of corpus voice)

Share of corpus voice is the brand's share of category-relevant third-party text: cited third-party pages, branded web mentions, review volume and forum volume, weighted by source type because engines weight earned sources above social ones.

Prediction. AI share drifts toward third-party share. κ is fast for engines that search the live web and close to zero between model releases for engines that do not, with a step at each release. η can be compared with the published mean advertising elasticities of 0.12 short term and 0.24 long term (Sethuraman, Tellis and Briesch, 2011, 751 and 402 estimates) as an order-of-magnitude check on whether earning third-party coverage looks like a stronger or weaker lever than paid media. The two elasticities measure different things, so only the order of magnitude is comparable.

Test. A monthly panel of 50 or more brands in three categories across five engines for twelve months, with brand fixed effects and model-release markers. A cross-sectional version can run now.

Falsified if κ is indistinguishable from zero for search-on engines over six months.

4.5 F4: The retrievability gap and the positioning residual

Malthouse et al.'s positioning result suggests a direct diagnostic.

Retrievability gap G = answer penetration on prompts built from the brand's own positioning language − answer penetration on real buyer-need prompts for the same need

L.L.Bean's figures give G = 88.5 − 5.4, about 83 points [External]. A large gap means the engine knows the brand but buyers' words do not reach it, which calls for a vocabulary fix in third-party sources more than an awareness campaign.

The positioning residual removes size effects from how engines describe a brand. From branded probe answers, build a brand × descriptor count table O, compute the expected count E from row and column totals, and score each cell:

Z = (O − E) ÷ √E

A positive Z on the brand's intended descriptors means the engines hold the intended position after allowing for the fact that big brands get more of every descriptor.

Prediction. G falls, and Z on intended descriptors rises, when third-party pages start describing the brand in buyer vocabulary.

Test. Before and after measurement around a content and source programme, with matched control brands that received no work.

Falsified if G and Z move equally in treated and control brands.

4.6 F5: The two-path mention model

Tannenbaum's fitted stage model, generalized, gives a practical decomposition of where a mention comes from:

P(mention) ≈ P0 + (1 − P0) × P(brand's evidence retrieved) × P(selected | retrieved)

P0 approximates the memory path: the probability the engine names the brand without retrieving its own pages. In Tannenbaum's data this prior mixes model memory with third-party retrieval, so search-off runs are needed to separate the two. The second term is the retrieval path. Zhen's source-redundancy gradient suggests that P(selected | retrieved) rises with the number of independent sources that name the brand.

Prediction. Established brands have high P0 and are named often even when nothing about them is retrieved. Retrieval still raises their mention rate: in Tannenbaum's data, high-prior states rose from 32.0% to 82.0% on GPT and from 28.7% to 86.2% on Gemini with own-domain evidence [External]. Challengers have low P0, and their mentions depend almost entirely on being in the retrieved evidence, named by several independent sources.

Why it matters. It tells a client which path to work on. A challenger with low P0 should spend on third-party presence for specific questions, and a leader with high P0 should spend on keeping its credentials current.

Test. For each brand and cluster, compare search-off runs (an estimate of P0) with search-on runs, and log which cited sources named the brand.

Falsified if search-off and search-on mention rates are equal for challengers.

4.7 Order of work

1. F1 first. It needs only prompt runs, one category can run in a week, and it gives every client a size-adjusted benchmark.
2. F2 next, as the candidate tracking instrument.
3. F5 alongside both, since search-on and search-off runs come from the same design.
4. F4 as the before-and-after metric for client work, with controls.
5. F3 last, because it needs a twelve-month panel.

5. What can be said now, and what cannot

Supported by more than one independent source, and safe to state internally with attribution:

• What third parties publish about a brand is among the strongest measured correlates of AI mention, and owned pages are a small share of what engines cite.
• Paid media spend shows no measured relationship with AI recommendation (Malthouse et al.; Seer for paid search).
• Prompt wording changes the recommended set substantially, so any measurement needs many paraphrases and many runs.

Supported by a single source, to be stated only with that source named:

• Being named by many different sources is associated with selection beyond how often the brand is named overall (Zhen et al., Chinese engines, vendor).
• Survey brand equity is a weak predictor of AI recommendation (Malthouse et al., 82 brands, search off).
• Brands the engines know can still be absent when buyers' words do not match how the brand is described (Malthouse et al., two brands).

Not supported, and not to be stated as findings:

• That improving any of these signals causes more AI recommendations.
• That a rebrand or category change moves AI answers.
• That AI answers hold a fixed number of names, three or otherwise.
• Any per-brand coefficient beyond the model versions it was measured on.

6. What changes in LBOX

• PS-00 AZ-01 no longer gives a fixed list length. It records list length as a measure and keeps "top three" only as a hypothesis about where buyers' attention goes.
• Pre-flight should report the size benchmark (F1) and the retrievability gap (F4) per cluster, and fix the competitive set before it runs.
• Studio briefs should aim for redundancy: the same brand facts and descriptors carried by several independent third-party sources, in comparison and list formats where they are honest.
• Measurement in every tool should move to the common design in 4.1: situation clusters, paraphrases, about 100 answers per cluster and engine, search on and off recorded separately.

7. Guardrails

• Every finding in section 2 is [External] and correlational unless marked otherwise. None goes to clients as established.
• Vendor studies are labelled as vendor studies wherever they are cited.
• The formulas are [Hypothesis] until LBOX runs them with stated n.
• Truthful work only. No fabricated reviews, badges, list placements or endorsements, even though Allouah et al. show badges move AI choices.

8. Research queue

Continuing the numbering from PS-03 (items 19 and 20).

21. F1: does share predict prompt penetration in AI answers as it predicts penetration in buying, and how far do positioned brands sit above the line?
22. F2: does a situation-cluster battery predict held-out volunteered share, and is θ above 1?
23. F3: what is the elasticity of volunteered share to third-party mentions, by engine?
24. F4: does a third-party vocabulary programme close the retrievability gap against controls?
25. F5: how much of each brand's mention rate comes from memory, measured by search-off runs?
26. How long are AI answer lists by engine and category, and where do buyers' clicks and follow-up questions concentrate within them?
27. Does the backlink conflict between Ahrefs and Seer resolve when brand size is controlled?