Threshold Band Map¶
Visual model — instantiates Counterfactual Proximity Signal Calibration
Places cases into named proximity bands — far miss, close miss, threshold crossing, close escape — so distance to the line is visible at a glance.
A Threshold Band Map is a picture. It takes a population of cases and lays them out relative to a meaningful threshold, partitioned into a few named bands — far miss, close miss, threshold crossing, close escape — and it can shade those bands by the value at stake so that severity and proximity are read together. Its defining move is spatial and categorical: it does not measure how close any single case came (it consumes that) and it does not decide what to do about any band (that is a policy). It renders the shape of the whole population's relationship to the line — where the mass sits, whether a cluster is bunched just short of crossing, how the just-missed and just-crossed compare — in a form a human can take in at a glance. It is comprehension, made visual.
Example¶
An election analyst maps every race in a legislative chamber against the 50% line. The horizontal axis is margin — distance from the tipping point — and cases are sorted into bands: safe (won or lost by double digits), comfortable, close (inside a few points), and photo-finish (decided by a fraction of a point either way). Each band is shaded by stakes — races that would have flipped chamber control are drawn in a hot color, ordinary seats in a cool one. The finished map shows at a glance something no vote tally conveys: a dense cluster of hot-colored, photo-finish races on the losing side of the line — a handful of chamber-deciding seats that came within a hair of going the other way. That single image reframes the night: not "we lost the chamber" but "the chamber turned on four coin-flip seats," which is a completely different lesson for where to focus next cycle. The map places and shades; it draws no conclusion the eye cannot see for itself.
How it works¶
The map is built by partition and overlay. It defines the band boundaries — the cut-points on the proximity axis that separate far miss, close miss, crossing, and close escape — and assigns every case to a band, giving the population a categorical shape. It then overlays the value-delta frame as a second visual channel (color, size), so a case's band shows how close while its shading shows how much was at stake, letting a viewer see the dangerous quadrant — close and high-value — without reading a number. It takes the raw proximity scores as input rather than computing them, and it renders rather than decides. Everything about it is optimized for a human reading the distribution's shape.
Tuning parameters¶
- Band boundaries — where the cut-points between far/close/crossing/escape fall. Moving them changes which cases look alarming; boundaries should map to real changes in meaning, not round numbers.
- Number of bands — how many categories the proximity axis is cut into. More bands show finer structure but clutter the picture; fewer read cleanly but blur distinctions.
- Value-delta encoding — which visual channel carries stakes (hue, size, opacity) and its scale. Sets whether the "close and costly" cases pop or hide.
- Symmetry of the map — whether just-missed and just-crossed (or almost-win and almost-loss) are shown mirrored around the line, making the two sides of the threshold directly comparable.
When it helps, and when it misleads¶
Its strength is pre-attentive comprehension: a well-built band map surfaces a cluster of close, high-stakes cases in an instant, where a table of scores would bury it. Its failure mode is the clustering illusion and the tyranny of the boundary — bands impose hard categorical lines on a continuous proximity axis[1], so a case a hair inside "close miss" looks meaningfully different from one a hair outside it, and the eye readily invents a real gap where only a cut-point exists. A vivid band can also draw disproportionate attention simply because it is drawn boldly. The guarding discipline is to keep the underlying continuous scores available beneath the bands, to place boundaries where the meaning actually shifts rather than at convenient marks, and to resist reading a categorical break into what is really a smooth gradient.
How it implements the components¶
threshold_band_partition— it defines the named proximity bands and their cut-points and assigns every case to one, giving the population a visible categorical structure.value_delta_frame— it overlays the value at stake as a second visual channel so proximity and severity are read together rather than separately.
It does NOT implement proximity_metric_or_ordering — computing how close each case actually came is Near-Miss Distance Scorecard's job; this map consumes those scores and only partitions and renders them. Nor does it implement learning_update_boundary, the band-to-bounded-response mapping owned by Near-Miss Response Tier.
Related¶
- Instantiates: Counterfactual Proximity Signal Calibration — supplies the visual partition that makes the archetype's proximity bands comprehensible at a glance.
- Consumes: Near-Miss Distance Scorecard supplies the per-case proximity scores the map partitions into bands.
- Sibling mechanisms: Near-Miss Distance Scorecard · Near-Miss Response Tier · Counterfactual Value-Delta Table · Almost-Reward Annotation · Close-Call Review Protocol · Counterfactual Plausibility Filter · Proximity Signal Backtest · Regret-Weighted Decision Log · Salience Overweighting Check
Editorial Notes¶
Form Classification¶
Form family: Interface, Display & Cue
Rationale: Threshold Band Map is defined in the frozen evidence as: Places cases into named proximity bands — far miss, close miss, threshold crossing, close escape — so distance to the line is visible at a glance. Its operative deployed or enacted form is therefore Interface, Display & Cue.
Nearest alternative: Representation, Specification & Plan — Representation, Specification & Plan can support this mechanism, but the evidence centers the concrete operation described above rather than the alternative family's defining operation.
Review outcome: Adjudicated after independent review; medium confidence.
Origin Attribution¶
Primary origin: Statistics & Experimental Design
Origin pattern: Cross-disciplinary synthesis
Present-day reach: Universal
Rationale: Threshold band map derives most directly from statistics' measurement, sampling, inference, and experimental-design tradition; its defining operation is to places cases into named proximity bands — far miss, close miss, threshold crossing, close escape — so distance to the line is visible at a glance.
Related originating lineages:
- Data Science & Analytics — Data science's telemetry, modeling, profiling, and monitoring tradition provides a formative adjacent lineage for the same threshold band map operation.
- Human-Computer Interaction — Human-computer interaction and interface design supplies a parallel or contributing lineage for the mechanism's defining operation: places cases into named proximity bands — far miss, close miss, threshold crossing, close escape — so distance to the line is visible at a glance.
- Mathematics — Mathematical modeling, proof, and abstract-structure practice supplies a parallel or contributing lineage for the mechanism's defining operation: places cases into named proximity bands — far miss, close miss, threshold crossing, close escape — so distance to the line is visible at a glance.
Review resolution: Both blind reviewers independently select statistics_experimental_design as the primary historical origin for the concrete operation—Places cases into named proximity bands — far miss, close miss, threshold crossing, close escape — so distance to the line is visible at a glance. The queued differences concern alternate origin disagreement, origin mode disagreement, domain reach disagreement, encyclopedia synthesis disagreement, not the primary lineage. I retain every alternate that either reviewer explains, without a numeric cap, and choose origin_mode=cross_disciplinary_synthesis because the reviewers' combined evidence identifies material construction from multiple disciplines. domain_reach=universal records later portability rather than multiplying historical origins; confidence=high is the conservative shared evidentiary level, and encyclopedia_synthesis=true preserves either reviewer's affirmative synthesis finding.
Encyclopedia synthesis: The exact catalogued form synthesizes established practice rather than reproducing a single standard historical label.
Review outcome: Reconciled after independent review; high confidence.
References¶
[1] MacCallum, R. C., Zhang, S., Preacher, K. J., & Rucker, D. D. "On the Practice of Dichotomization of Quantitative Variables". Psychological Methods 7(1), 19–40 (2002). Shows that dichotomizing a continuous variable imposes an artificial cut point and treats observations on opposite sides as categorically different. registry ↩