NPS FamilyAI Opinion Metrics — μNPS™, λNPS™, ΔNPS™

Three metrics, one methodology stack. μNPS is the human community baseline reconstructed from the public corpus. λNPS is what AI actually says about the brand, measured live across five frontier LLMs. ΔNPS is the signed gap between them — the diagnostic signal that surfaces AI amplification or suppression.

Three NPS-family metrics at a glance.

All three live on the canonical NPS scale of −100 to +100 so they can be compared directly. Expand any section below for the full methodology.

What μNPS measures.

μNPS — mu-NPS — is the modeled reputation score reconstructed from the observable public corpus about a brand. The Greek letter μ (mu) denotes modeled: the score is computed from sentiment-classified signals found in public sources, not from a direct customer survey.

The output is an NPS-style scalar in the range -100 to +100, computed as the weighted share of promoter signals minus the weighted share of detractor signals. A score of +40 means the public corpus is meaningfully net-positive; -20 means detractor signals outweigh promoters even after recency weighting.

μNPS is reconstructed, not surveyed. It approximates what an NPS survey would show if every public mention of the brand were treated as a survey response weighted by source credibility and recency.

The human baseline behind ΔNPS.

μNPS exists to anchor the ΔNPS diagnostic. On its own, λNPS (the machine-expressed reputation captured from AI outputs) is just a number. The actionable question is whether AI systems are amplifying or suppressing the public sentiment that already exists about a brand.

Machine output reads more favorably than the public corpus. Usually a tailwind.

Machine output broadly tracks the public corpus. Neutral signal.

Public corpus is stronger than machine output. Remediable via GEO.

Without μNPS, ΔNPS cannot be computed. Without ΔNPS, optimization work on the AI surface is uncalibrated — you cannot tell whether a +5 λNPS lift came from genuine improvement or from a brand that already had +5 latent in the corpus.

Public-corpus review and mention signals feed the signal table.

μNPS draws on multiple public-corpus sources today. Each source is normalized into a versioned, source-weighted signal table with a sentiment classification (promoter / passive / detractor) and the original publication timestamp.

High-volume, sentiment-rich review sources with structured ratings that map cleanly to promoter / passive / detractor classification.

Complaint registry plus BBB letter-grade. Lower volume than reviews but high signal-credibility, particularly for service-sector and consumer-finance brands.

Product reviews for brands that sell through major retail platforms. Star rating maps to classification; verified-purchase signals are preserved for downstream filtering.

Brand mentions on community discussion platforms. Treated as community sentiment; classification derived from sentiment analysis on the mention text rather than a star rating.

Source coverage will expand. Roadmap candidates: G2, Capterra, Glassdoor (employer), app store reviews, YouTube comment sentiment. New sources land as additional signals — the scoring formula is source-agnostic.

Weighted NPS with exponential recency decay.

μNPS is an NPS-style calculation applied to weighted, time-decayed signals. The base formula:

# μNPS — Weighted NPS with exponential recency decay
#
# μNPS is computed from source-weighted promoter / detractor signals
# with exponential recency decay applied per signal:
#
#   W_promoter  = weighted share of promoter signals
#   W_detractor = weighted share of detractor signals
#
# Final score (range -100 to +100):
#   μNPS = (W_promoter - W_detractor) * 100
#
# Each signal carries a source weight and a recency-decay factor.
# The decay half-life is a tuned, versioned parameter.

Two ingredients distinguish μNPS from a naive review-average:

Each signal carries a source weight drawn from a versioned weight configuration. Weights let us treat a verified BBB complaint differently from a single-line community comment.

Each signal's effective weight is multiplied by an exponential decay factor. The half-life is a tuned, versioned parameter, so older signals count for progressively less and a brand's recent reputation dominates a years-old one.

Decay uses the signal's publication date when available, with a recorded fallback. Signals with neither receive a neutral weight rather than being dropped.

Standard NPS range. Read positive as net-positive corpus.

μNPS uses the standard NPS scale of -100 to +100. Industry benchmarks for surveyed NPS are not directly transferable — μNPS is reconstructed from public sentiment, which is structurally biased toward extreme opinions (people review when they love or hate, not when they're neutral). Treat the bands below as directional, not authoritative.

Pass threshold for AnswerShare client reporting: μNPS ≥ +10 with a sample size of at least 50 weighted signals. Below threshold, the brand's ΔNPS diagnostic is reported with a low-confidence flag.

What μNPS does not measure.

Below 50 weighted signals across all sources, μNPS is reported with a low-confidence flag. A handful of strongly-worded reviews can move the score 20+ points and the result is statistically unstable.

Brands with a major recent event (recall, founder news, viral incident) will see μNPS reweight quickly because of the recency-decay weighting. This is intentional — AI systems also reweight quickly — but means μNPS is not a long-run reputation average.

Coverage currently spans consumer review platforms, BBB, retailer reviews, and community forums. Brands whose customer base does not concentrate on these platforms (e.g. B2B SaaS reviewed primarily on G2, regulated industries) will under-sample. Source roadmap is published above.

Sentiment classification is English-language today. Non-English signals are ingested but classified as passive pending multi-lingual sentiment rollout. Multi-region brands will have an English-skew in their μNPS.

Each brand is resolved to explicit per-source identifiers before signals are pulled. Common-name brands (e.g. 'Apple') require manual curation to avoid cross-brand contamination. Disambiguation is reviewed quarterly.

Promoter / passive / detractor classification is automated. Star-rated review sources use rating thresholds and are near-deterministic; text-only mention sources use a sentiment model and inherit its error rate. Per-source classification accuracy is logged but is not currently surfaced on the client dashboard.

μNPS is reputation reconstruction, not customer satisfaction surveying. It cannot substitute for a real NPS program against an actual customer panel. It can substitute for one when no panel exists or as a directional cross-check when one does.

μNPS is one leg of a three-metric framework.

The three metrics are designed to be read together. μNPS answers “what does the public corpus say?”; λNPS answers “what do production AI systems say?”; ΔNPS isolates the gap, which is the diagnostic signal GEO optimization actually moves.

The λ symbol is intended to denote machine-transformed output behavior rather than latent model state. λNPS measures generated responses under controlled prompting conditions, not internal model beliefs or hidden parameters.

Every score is reproducible from a versioned signal table.

Each μNPS computation is reproducible from a versioned, source-weighted signal table. Every score persists the full breakdown — total weighted signals, per-source weighted counts, the methodology version, and the recency parameters used — so that, given the same signal set and weight-config version, the score is deterministic.

The currently published μNPS is a fixed methodology version. Future revisions land as new versioned weight configurations; prior scores remain reproducible at their original version.

What λNPS measures.

λNPS measures how positively (or negatively) AI assistants frame the brand when answering user queries. It is computed by querying the brand across AI systems — Perplexity, OpenAI, Gemini, Claude, and Grok — with a calibrated prompt set, then sentiment-scoring the resulting citations and framing on a net promoter scale.

Where μNPS captures the modeled corpus baseline, λNPS captures what the answer engines actually generate when a user asks about the brand. The two are designed to be directly comparable on the same −100 to +100 scale.

λNPS is the AI half of the NPS family.

The AnswerShare NPS framework has two anchor measurements. μNPS captures the human-community baseline, reconstructed from observable corpus signals. λNPS captures the AI-mediated answer-engine baseline — the sentiment a real user encounters when asking an LLM about the brand.

The two diverge when AI grounds on different sources than the corpus reflects, weights different attributes, or interprets the brand through a domain lens that differs from public sentiment. That divergence — surfaced as ΔNPS — is the actionable signal: it tells you whether the answer engine is amplifying or suppressing what the corpus already says.

Without λNPS, you can audit your corpus but cannot measure what the user actually sees in the AI response. With it, the gap becomes observable and addressable.

Live retrieval from 5 production LLMs.

Each λNPS run queries the five LLMs that make up the AnswerShare measurement panel. Prompts are NPS-calibrated brand-perception queries; responses are sentiment-classified by a separate classifier model so the generator and the rater are independent.

Retrieval-grounded answer engine. Live web grounding gives a current-day view of the brand.

Frontier general-purpose LLM. Broad training corpus, conservative framing tendencies.

Search-grounded LLM. Heavy weighting on Google index signals during generation.

Frontier general-purpose LLM. Tends toward strict-rubric scoring; deductions are common.

Added 2026-05-26 to complete top-five conversational AI panel coverage.

Grok was added to the panel 2026-05-26 to complete coverage of the top-five conversational AI engines by user reach.

Per-LLM NPS, then 5-model median.

For each of the five LLMs the brand is queried with the structured prompt set. Each response is classified as Promoter, Passive, or Detractor by the classifier model. Per-LLM NPS is computed on the standard scale:

# Per-LLM
NPS_engine = %Promoter - %Detractor             # range: -100 to +100

# Across the 5-engine panel
lambda_NPS = median(NPS_perplexity, NPS_openai, NPS_gemini, NPS_claude, NPS_grok)

# Outlier-drop rule (AnswerShare 5-model median convention)
# Drop a clear outlier before taking the median.

The headline λNPS is the median across the five per-LLM NPS values, following the AnswerShare 5-model median convention with outlier-drop (a clear outlier is dropped before the median is taken).

Where λNPS can mislead if read naively.

Live LLM retrieval can lag fresh corpus changes by days to weeks. A brand that just published a major repositioning may still see legacy framing in lambda-NPS responses until indices catch up.

Common brand names (e.g., 'Apex', 'Aurora') force the prompt set to include disambiguators (industry, geography, domain). Disambiguator choice can shift sentiment by several points.

When an LLM refuses to answer a brand question (safety filter, low confidence, unknown entity), the response is classified as Passive, not dropped. This prevents a refusal from inflating a small-sample NPS.

Brands with sparse corpus signal produce higher inter-engine variance. The outlier-drop rule mitigates but does not eliminate this; low-volume brand reports should include the spread alongside the median.

The classifier that scores Promoter / Passive / Detractor is a different model from the one that generated the response. This avoids self-grading bias but introduces a separate classifier-calibration concern that is monitored per release.

Same scale as μNPS — designed for cross-comparison.

λNPS uses the standard net promoter scale of −100 to +100, identical to μNPS. The two are intentionally co-scaled so that ΔNPS (λNPS − μNPS) is a meaningful single number.

Worked examples: λNPS of +60 with μNPS of +40 yields ΔNPS = +20 (AI is more favorable than the corpus). λNPS of −20 with μNPS of +30 yields ΔNPS = −50 — AI is substantially more critical than the public corpus, which is the canonical GEO problem ΔNPS exists to detect.

λNPS is the AI-side measurement. ΔNPS is derived from it.

λNPS is the primary measurement of AI-mediated brand perception. It is one of the two inputs to ΔNPS, the diagnostic signal that surfaces divergence between the corpus baseline and the answer engine output.

mu_NPS    = modeled corpus reputation              (what the corpus says about you)
lambda_NPS = machine-expressed reputation          (what AI says about you)
delta_NPS  = lambda_NPS - mu_NPS                   (the amplification / suppression gap)

# Sign convention (2026-05-26)
# positive delta_NPS  = AI amplifies your corpus    (good)
# negative delta_NPS  = AI underperforms corpus     (bad)
# near-zero          = corpus and AI broadly aligned

λNPS™ — domain-correct notation.

The λ symbol is borrowed from probability theory and queueing theory, where it conventionally denotes a retrieval or sampling rate. That makes the μ / λ / Δ family domain-correct math notation: μ denotes the modeled corpus mean, λ denotes the retrieval/generation rate at which sentiment is sampled from the answer engines, and Δ denotes the difference between the two.

The λ symbol is intended to denote machine-transformed output behavior rather than latent model state. λNPS measures generated responses under controlled prompting conditions, not internal model beliefs or hidden parameters.

λNPS, μNPS, ΔNPS, and AnswerShare are trademarks of AnswerShare. The notation conventions are described in full in theAnswerShare whitepaper.

ΔNPS is the signed gap between machine-expressed and modeled-corpus reputation.

ΔNPS (delta-NPS) is computed as the simple arithmetic difference:

λNPS is what AI systems say about your brand when prompted under controlled conditions (live retrieval, machine-expressed reputation). μNPS is the reputation reconstructed from your observable public corpus (reviews, citations, press, social signal -- the human-grounded baseline). ΔNPS isolates the diagnostic information between them: the gap is where AI's perception of you diverges from the corpus that should ground it.

The λ symbol denotes machine-transformed output behavior rather than latent model state. λNPS measures generated responses under controlled prompting conditions, not internal model beliefs or hidden parameters.

SEO measures whether you appear. GEO measures whether you're cited. ΔNPS measures whether AI thinks better or worse of you than humans do.

ΔNPS is the AnswerShare-distinctive measurement. Every brand is now being re-represented by AI systems millions of times per day in answer-engine results, chat outputs, recommendation surfaces, and agentic workflows. The question is not whether you appear -- it is whether the AI version of your brand is better or worse than what humans currently think.

That gap is a leading indicator. As AI-mediated discovery overtakes human-mediated discovery (and the trajectory is unambiguous), the perception humans form will increasingly be the perception AI projected first. A brand with strongly positive ΔNPS is being amplified by AI relative to its human reputation; a brand with negative ΔNPS is being undersold by AI even when humans speak favorably.

Do you appear in search? Measures presence in candidate result sets.

Are you cited in AI answers? Measures retrieval & parse success.

Is AI's view of you better or worse than humans'? Measures the perception gap.

Sign and magnitude both carry meaning.

AI cites and frames the brand more favorably than the human community does. Often indicates that bot-facing surfaces -- clean-room HTML, JSON-LD, methodology pages, structured citations -- are better than human-facing brand assets, or that competitors are weaker on those surfaces. This is the “AI moat” outcome GEO infrastructure is designed to produce.

Synonymous in the literature with λ-amplification.

AI and humans broadly agree. The corpus baseline is being faithfully reflected in machine output. Neither pathology nor opportunity; the AI is doing its job as a transparent intermediary on this brand.

AI cites and frames the brand less favorably than humans do. Likely causes: weak GEO infrastructure (bots can't reach or parse your good content), citation gaps (AI is grounding on third-party sources you don't control), stale-negative grounding (AI weighting older critical sources over current positive ones), or schema/disambiguation collisions with a worse-performing brand of the same name.

Synonymous with λ-suppression. This is the highest-urgency ΔNPS state: humans like you, AI does not, and AI is increasingly the gatekeeper.

Arithmetic difference of two canonical-scale inputs.

ΔNPS is intentionally simple. Both inputs are measured on the canonical NPS scale (−100 to +100), so the difference lives on a −200 to +200 scale. In practice ΔNPS observations cluster in a much narrower band; extreme gaps are validated, not interpreted, and warrant re-running both inputs before reading anything into them.

# 1. Produce mu-NPS (modeled corpus reputation)
#    Ingest public corpus signals for the brand: reviews, citations, press,
#    social mentions, third-party rankings. Score on the canonical NPS scale
#    of -100 to +100 using the AnswerShare corpus pipeline.
#
#    Output: mu-NPS in [-100, +100]
#
# 2. Produce lambda-NPS (machine-expressed reputation)
#    Run the controlled prompting battery (5 prompts x 5 engines = 25 LLM
#    responses per brand) under matched temporal and disambiguation
#    conditions. Score each response on the canonical NPS scale, aggregate.
#
#    Output: lambda-NPS in [-100, +100]
#
# 3. Compute the difference
#    delta-NPS = lambda-NPS - mu-NPS
#
#    Output: delta-NPS in [-200, +200], typically observed in a much narrower band
#
# 4. Validate before interpreting
#    Extreme gaps are validated, not interpreted: re-run both inputs, check
#    brand disambiguation parity, confirm corpus and retrieval are temporally aligned.

Both inputs are −100 to +100, so the absolute difference can in principle reach 200. In practice this is vanishingly rare.

Cross-cohort ΔNPS measurements concentrate well inside the theoretical range. Extreme gaps are interpretive red flags more often than signal — they are validated, not interpreted.

ΔNPS inherits the noise of both inputs.

Because ΔNPS is a derived metric, any noise or measurement defect in μNPS or λNPS propagates into ΔNPS — often amplified, since errors that pull the two inputs in opposite directions sum constructively in the difference.

ΔNPS only makes sense when μNPS and λNPS each have sufficient signal. Low-volume corpus or sparse machine output produces a noisy difference that can flip sign with small perturbations. Validate sample sizes on both sides before drawing conclusions.

Because ΔNPS sums the variance of both inputs (errors in opposite directions reinforce), the confidence interval on a ΔNPS measurement is wider than on either input alone. A brand with thin corpus presence and thin AI representation will show high-variance ΔNPS even when nothing has changed.

If μNPS is computed on the corpus for one entity and λNPS is computed on AI output that conflates that entity with a similarly-named one, ΔNPS measures disambiguation drift, not perception gap. Both pipelines must apply identical entity-resolution before scoring.

AI training data and retrieval indices lag the live corpus by weeks to months. A μNPS computed on this week's corpus and a λNPS computed against an AI whose grounding is six weeks stale will report a gap that reflects temporal mismatch, not genuine divergence. Best practice: align the corpus snapshot to the retrieval index date when possible, or report the lag explicitly.

When ΔNPS is within the noise floor of the underlying measurements (typically ±5 to ±10 depending on input volume), a sign change between consecutive runs is not meaningful. Treat near-zero ΔNPS as 'aligned' regardless of which side of zero it lands on.

No pass/fail threshold — ΔNPS is signed and interpretive.

Unlike GEO scores or delivery benchmarks, ΔNPS does not collapse to a binary verdict. The sign tells you direction (amplification vs. suppression); the magnitude tells you intensity. The orientation bands below are diagnostic guidance, not pass/fail gates:

Strong-positive ΔNPS is the explicit goal of well-executed GEO — it is the measurable form of the “AI moat” the discipline promises.

ΔNPS is a derived metric — the two primary measurements are upstream.

ΔNPS cannot exist without μNPS and λNPS. Both must be well-grounded and produced under matching brand-disambiguation and temporal-alignment conditions before the difference is interpretable. Read each primary metric's methodology before relying on ΔNPS for any strategic decision:

Related diagnostic terms used when decomposing ΔNPS movement over time: λ-drift (machine sentiment changing without corpus change), λ-divergence (different AI engines disagreeing on the same brand), and λ-suppression / λ-amplification (the two signs of ΔNPS).

ΔNPS is an AnswerShare-distinctive composite, not a public-domain NPS variant.

Net Promoter Score itself is a survey-based human-reported metric in the public domain. AnswerShare's NPS family — μNPS, λNPS, and ΔNPS — is a measurement framework that adapts the canonical NPS scale into the AI-discovery era. The three metrics are jointly produced under a single methodology stack (corpus ingestion, machine prompting under controlled conditions, difference reconciliation) that does not exist outside AnswerShare's tooling.

The notation is deliberate and follows domain-correct mathematical convention. We chose Greek letters specifically because they carry the right academic connotation and avoid the ambiguity of earlier “mNPS” naming that invited misinterpretation as a claim about internal model state:

Population mean in statistics. Here it denotes the modeled reputation reconstructed from the observable public corpus — the human-grounded baseline.

Rate parameter / language-model shorthand. Here it denotes machine-expressed output under controlled prompting — the AI's sampling of the brand.

Universal mathematical notation for change or difference. Here it denotes the directional gap between machine and corpus reputation.

The trademark protects the joint framework, not the individual symbols. “ΔNPS” as a defined composite metric — signed difference of two specifically-produced inputs on a canonical scale, interpreted under the methodology described on this page — is the AnswerShare-distinctive contribution. Anyone is free to compute “the gap between AI output and human sentiment” through other means; this is the canonical measurement.

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