The IMPRS Measurement System, V32

01Scope and positioning

IMPRS V32 is a deterministic scoring function that maps observed audience-behavior metrics for a brand account to a single brand health score, reported on a 350-900 scale with a five-pillar decomposition. This paper documents the formula as shipped: signal inventory, normalization, weighting, composite construction, the display transform, and the validation methodology and results that license the published claims.

The epistemic stance matters as much as the mathematics. We are proposing a measurable definition of brand health, not asserting a discovered truth. The definition is falsifiable by construction: the formula is sealed, every validation figure is forward-in-time and carries a sample size and 95% confidence interval, and a prospective log grades the system on data it has never seen. Where the evidence is thin, this paper says so in the same type size as where it is strong.

02Axioms as formal premises

Seven axioms define the measurement target and the admissibility rules for evidence. They are premises, not conclusions: the system is designed so that if the axioms hold, the score is meaningful, and if they fail, the validation record is where the failure will show up.

Axiom 1 selects revealed preference over stated preference and excludes survey instruments from the signal set. Axioms 2 and 3 place brand health in the same class as creditworthiness: a latent construct estimated through behavioral manifestations. Axiom 4 imposes the normalization requirements of section 05. Axiom 5 licenses index construction. Axiom 6 makes predictive validation against external outcomes, here subsequent revenue growth, the acceptance criterion rather than internal consistency. Axiom 7 forbids stochastic components, human adjustment, and generative models anywhere in the scoring path.

03System architecture

The engine tracks 117 metrics per account, split into two structural families that feed a dual composite:

• Part 1, audience to brand: 68 metrics across the five pillars. How audiences respond to the brand: save rates, story exits, carousel completion, sound reuse, retention checkpoints, reaction splits, quote volume, and the financial revealed-preference set. Part 1 feeds the Brand Health Index (BHI), the current-equity signal.
• Part 2, brand to audience: 49 metrics across six domains. How the brand is actively growing its audience: posting cadence and frequency efficiency, audience growth attribution, cross-platform synchronization, ad-to-organic correlation, traffic source diversity. Part 2 feeds the Growth Momentum Score (GMS), the trajectory signal.

Data platforms are Instagram, Facebook, TikTok, YouTube, and Twitter/X for organic signals, plus Meta, Google, TikTok, and X ad platforms. Revenue integrations (Stripe, Shopify, Xero, QuickBooks) supply the revealed-preference Sentiment set. The structural split between the two parts is fixed by design rather than driven by data richness, so platforms with more generous APIs cannot inflate a score: every brand is measured on the same structural basis.

Pillar order in the decomposition is the IMPRS acronym: Impact, Momentum, Presence, Reach, Sentiment. Computation proceeds: raw metrics, then metric normalization against tier and platform benchmarks, then pillar scores, then coverage shrinkage, then the BHI and GMS composites, then the blended composite with bounded bonuses, then the display transform. Each stage is specified below.

04Signal categories

Each pillar is a family of metrics with a fixed capacity, the maximum number of metrics the pillar can draw on, which also anchors the coverage arithmetic of section 06. Representative signals per pillar:

Capacities are the per-pillar metric ceilings used in confidence and coverage computation. Sentiment's active ceiling is 3 (the financial revealed-preference set) while the NLP validation gate is closed; the full 14-metric ceiling activates only if comment classification passes its pre-committed validation criterion (section 10).

Several derived metrics are grounded in standard constructions rather than ad hoc heuristics. Traffic source and demographic diversity use normalized Shannon entropy (Shannon 1948). Audience concentration uses the Herfindahl-Hirschman Index. Posting frequency is scored as distance from an empirically supported optimal band of 1.8 to 4.0 posts per week (Pechmann and Stewart 1988). Facebook reaction sentiment uses a three-way split in which ambiguous reactions are never collapsed into positive. Ad-to-organic correlation carries a hard minimum-sample gate of n at least 10 before it contributes at all.

05Normalization

Raw platform metrics are incomparable across account sizes and platforms: a 2% engagement rate is elite for a Fortune 500 brand and weak for a nano creator. Every metric is therefore normalized against a benchmark table keyed by audience tier (tiny, nano, micro, macro, mega, brands, fortune500, agencies) and, where behavior differs by platform, by platform-specific expectations for that tier. Benchmarks cover expected engagement, posting frequency floors, reply rates, unfollow tolerances, and story completion.

For example, expected average engagement descends from 8% for tiny accounts through 3.5% for micro and 1.2% for mega accounts to 0.1% for Fortune 500 brands, with agencies benchmarked at 3%. A metric scores against what an account of its size on its platform should achieve, which is what makes the final score size-independent: the validation tests of section 11 would fail for any score that merely tracked scale.

06Coverage shrinkage

Real accounts have missing data: a platform not connected, an API field not granted, a metric with no events yet. Rather than dropping pillars or imputing values, every pillar score is shrunk toward the neutral midpoint of 50 in proportion to how much of its metric capacity is actually observed:

Full coverage leaves the score unchanged; half coverage pulls it halfway to neutral; a pillar with 2 of 12 metrics is pulled 83% of the way to 50. The estimator is deliberately conservative: sparse data cannot produce extreme pillar scores in either direction, and connecting more data increases the weight of the account’s own behavior rather than changing the rules. The same mechanism handles partial financial coverage in Mode-2 Sentiment (section 10).

07Weighting

Pillar weights are segment-specific and empirically calibrated, not asserted. The calibration history runs through the simulation suite documented in the engine changelog: pillar-level lagged Spearman correlations with next-year revenue set the initial weights, and successive iterations were accepted only when they improved hold-out performance. The per-account-type weights in V32:

ACCOUNT_TYPE_WEIGHTS, V32. *Sentiment does not participate in this base weight vector: it enters the composite exclusively through the Mode-2 additive channel at weight 0.20 when a revenue integration is connected (section 10), and at weight 0 otherwise.

Weighting rationale, from the calibration record: small-business Reach was raised from 0.08 to 0.40 after grid search showed word-of-mouth amplification is a primary small-business revenue driver; B2B Presence and Reach were cut to 0.05 each because both were anti-predictive for that segment; creator Momentum is weighted at 0.45 to let the delta signal dominate (section 08).

On top of the base vector, four segments carry directly validated composite parameters (V29 exact-grid calibration) that control the within-BHI pillar shares, the momentum share of GMS, and the BHI/GMS blend:

COMPOSITE_PARAMS_V29. B2C intentionally has no override: candidate parameters failed the worst-fold improvement gate, so the segment keeps the V28 path byte for byte. Segments without an entry use the legacy transform, in which the base P/R/I weights are re-ratioed (0.15/0.35, 0.45/0.35, 0.40/0.30) and re-normalized within BHI.

Changing any of these values requires re-running the full simulation suite and re-sealing the formula as a new version. There is no runtime tuning surface.

08The composite

The composite blends two engines computed from the shrunk pillar scores.

Brand Health Index (BHI): the equity signal

The maturity modifier is a stagnancy correction for large, established accounts: when Presence is high (P’ at least 65) while Momentum is low (M’ below 45), the composite would otherwise reward accumulated scale that is no longer earning attention. The modifier discounts BHI by up to 15%:

Growth Momentum Score (GMS): the trajectory signal

The effective momentum term M_eff is mode-dependent, in priority order:

• Creator delta mode. When a previous-year momentum score exists, M_eff is the year-over-year delta centered at 50: M_eff = clamp(50 + (M’ - M’_prev), 0, 100). Absolute momentum anti-correlates with creator growth because of the maturity curve, so velocity replaces level.
• Creator year-1 neutral mode. A first-year creator with no prior momentum receives M_eff = 50, a neutral value, and the score anchors on Impact until a baseline year exists. This is surfaced in the product as establishing baseline.
• Lagged blend mode. When financial data and lagged snapshots are present, M_eff = 0.40 M’(t) + 0.35 M’(t-7d) + 0.25 M’(t-14d), reflecting the 3-to-14-day lag between social velocity and transaction outcomes.
• Absolute mode. Otherwise M_eff = M’.

Blend, bonuses, and the internal score

The bonus term aggregates stability, acceleration, and cross-platform consistency credits, and the compression guard caps it at the distance to 90: bonuses cannot lift an account into the elite band on their own, the base composite must do the work. The internal 0-100 score grades at fixed thresholds (90 elite, 70 strong, 50 moderate, 30 developing), with the elite cut calibrated so that roughly the top decile of observations qualifies.

09The display transform

The internal score is linear on 0-100; users see a credit-style 350-900. The transform is a single affine map, defined in exactly one place in the codebase, and it is the only scaling formula in the system:

Because the map is affine, pillar contributions remain legible on the display scale. Each pillar contributes points above the 350 floor in proportion to its weight, so the 550 available points are allocated by economic importance:

A pillar weighted 0.25 can contribute at most 137 display points; one weighted 0.10 at most 55. Display grade bands are contiguous: Critical 350-499, Developing 500-649, Moderate 650-749, Strong 750-849, Elite 850-900.

10Sentiment: the Mode-2 additive design

Sentiment is the most redesigned pillar in the system’s history, and the current design is deliberately narrow. The governing principle: only revealed preference scores. What audiences do with money is admissible evidence of belief; what they type in comments is not, because comment-volume proxies encoded market-wide activity rather than brand-specific belief and measured near zero against outcomes. The retired proxies (reply depth, UGC mention rate, DM volume) were removed rather than down-weighted.

The engine distinguishes four sentiment modes, resolved in strict priority order:

In Mode 2 the composite becomes 0.80 times the BHI/GMS blend plus 0.20 times the shrunk sentiment score, as in section 08. Three design decisions deserve explicit statement:

• Single channel. Earlier versions ran sentiment through two channels at once, a 10% additive pillar plus a multiplier of up to plus or minus 20% on the BHI composite share, for an effective influence of roughly 12-24% depending on segment. V32 retired the multiplier entirely and consolidated that envelope into one auditable number, 0.20 additive. The weight was chosen to stay inside the already-shipped influence envelope, not to expand it.
• Any coverage scores, shrunk. In Mode 2 the 0.20 weight is never zeroed for partial data. An account with one of the three financial metrics scores at full weight with the score shrunk toward 50 by the coverage formula of section 06, identically to every other pillar.
• Pre-committed gates. Comment classification re-enters the scoring set only if, on real classified data, ablating sentiment costs the model at least 0.020 in correlation, a criterion committed before the data exists. Separately, any elevation of the 0.20 weight toward the 25-30% band requires production Mode-2 outcome validation first. Neither threshold can be moved after seeing results without a new sealed version.

11Validation methodology

The validation question is fixed by axiom 6: does the score, computed from one period’s behavior, predict meaningful external outcomes in the next? The design:

Panel

122 companies with public revenue histories, nine industries, six years (2019-2024), stratified into six tiers: agencies (15 firms), Fortune 500 and large brands, consumer brands, B2B brands, small businesses, and creators (25 accounts, 2021-2024). The panel is sealed: formula iterations were tested against it with hold-out validation each time, and walk-forward validation across the 122 companies grades each signal only on outcomes that follow it in time.

Forward-only protocol

Every association measures a signal computed in year N against revenue realized in year N+1. Same-year fit is never presented as forward evidence. Ground truth is subsequent revenue growth, realized brand equity, chosen because it is external, size-independent once expressed as growth, and unforgiving.

Measurement metrics

• Level correlation. Spearman rank correlation between the score and next-year revenue growth.
• Growth ordering (OOA). For every same-year pair of accounts within a tier, did the higher score grow faster the following year? 50% is no skill.
• Large-gap ordering. The same test restricted to pairs the score clearly separates, where a health measure should be most reliable.
• Cohort separation. The share of panel years in which the top-scoring half of a tier outgrew the bottom half, with the median growth gap.

Movement analysis: delta versus level

The lead-lag suite compares the information content of score changes against score levels. Pooled across the panel, score movement was associated with next-year revenue movement at Spearman rho +0.395, against +0.160 for the score’s level, and +0.563 for consumer brands, the strongest movement association in the panel. A falling score preceded a decline 1.44x more often than the base rate, and top score-movers outgrew bottom score-movers by +25.6 points the following year. This delta dominance is why the product is built around score movement.

Direction claims: balanced accuracy and skill over base rate

Revenue rises in most company-years, so raw direction-match flatters everyone: a predictor that always says up looks 71% accurate on this panel. Two rules are therefore mandatory for every directional claim. First, direction accuracy is reported as skill over the base rate, under which the always-up predictor scores zero. Second, where a single accuracy number is given for movement association, it is balanced accuracy with symmetric up and down recall, so the association must hold in both directions, not just in bull years; for consumer brands this balanced accuracy was 68.1%. Raw accuracy alone is never the claim.

Benchmark reconstruction

The comparison index is a rebuild of Brand Finance’s published Brand Strength Index component categories, marketing investment (30%), stakeholder equity (35%), business performance (35%), z-scored within year and run on the identical panel. It is a benchmark rebuild, not Brand Finance’s proprietary index, and the reconstruction was handed trailing revenue as an input, which should help it. The roughly forty lines of reconstruction code are committed, and an independent rebuild of both sides is openly invited.

12Validation results summary

The full per-tier record, with every confidence interval and the honest caveats attached to each tier, lives on the research hub and is the canonical presentation. The headline structure:

All figures retrospective, forward-only, sealed V32 formula. Skill and balanced-accuracy framing per section 11; raw direction accuracy is never reported alone.

Two published corrections are part of the record and are stated here as they are on the hub: earlier suite figures for the large-brand tier had agency holding companies mixed into the stratum, and the slightly lower pure-brand numbers are canonical; and an earlier creator movement result (+0.447) was driven by first-year baseline transitions, disappeared in predictive mode, and was retracted before publication. No creator movement result is claimed.

13Assumptions and limitations

• Single-panel iteration. The formula was iterated across twelve versions on one sealed panel with hold-out testing each time. This is a rigorous backtest, and it is still one dataset: repeated iteration can produce optimistic results before external data arrives. The prospective log is the control for this.
• Small strata. Agencies (n=15) and creators (n=25) have wide intervals, and single-year direction calls in those tiers carry modest skill. The defensible agency claim is ordering, who is stronger and which way they are heading, not point forecasts.
• Cross-tier ordering inverts. A large score gap across tiers usually separates a macro account from a nano account, and small accounts grow faster off a small base. Comparisons are valid within a tier only; this is a published limitation, not a footnote.
• Creator down-calls are suppressed. Gated direction calls inverted for creators on the panel, so the production engine issues no creator down-calls at all, including for creator clients on agency rosters, until the live panel re-tests the claim.
• Mode-2 sentiment awaits production outcome data. The 0.20 additive weight is bounded by the previously shipped influence envelope, and its own outcome validation happens prospectively as revenue-connected accounts accumulate. Its weight cannot rise before then.
• Revenue growth is a proxy for realized brand equity. It is external and unforgiving, but it is affected by forces the score cannot see: pricing changes, distribution deals, macro shocks. The macro-regime guard in the forecasting layer widens intervals in rate-compression regimes for this reason.
• Benchmark comparison is against a reconstruction. The proprietary index itself is unobservable to us; claims are scoped to the rebuild of its published component categories, and part of the rebuild’s weakness is structural, since any size-dominated index anti-correlates with future growth.

14Reproducibility and versioning

Axiom 7 is enforced mechanically. The scoring function contains no randomness, no clock dependence within an audit window, no learned components that drift, and no generative model anywhere in the calculation path. Identical inputs produce the identical score to the reported precision, on any machine, at any time. AI systems in the product operate strictly downstream of the number: they explain it and recommend actions.

The formula is sealed under a versioning contract: every change to the mathematics, weights, thresholds, or normalization creates a new version number, and validation results stay permanently attached to the version that produced them. V32 evidence is V32 evidence; a future V33 must earn its own on the same protocol before it ships, and versions are never retroactively merged. The Developer Specification states the operational side of this contract: the single scoring path, input assumptions, edge-case behavior, and the reproducibility guarantee as an engineering interface. The business-level narrative of this system is in the Whitepaper.