Synthesize Training Intensity Distribution (TID): time-in-zone + Polarization Index — the engine knows how MUCH you train but is blind to the easy/hard MIX, the single most actionable lever in endurance science

[bepcyc]

The one-line gap

WattWise measures how much you train (TSS, CTL/ATL/TSB) and how hard a single session was (intensity_class, IF, hr_load_zonal). It has no number for how your training time is split across easy / moderate / hard over a week or a block. That split — the Training Intensity Distribution (TID) — is the most-studied and most-coachable lever in endurance science, and right now the coach literally cannot answer the most common coaching question on earth: "Is my easy/hard balance right?"

Why this is the critical missing metric (not just another nice-to-have)

Training load is intensity x duration collapsed into one scalar. That collapse is the whole point of TSS — and also its blind spot. Two athletes with an identical CTL of 70 can be on opposite ends of adaptation and injury risk:

• Athlete A: 80% easy aerobic, 20% hard intervals — polarized, the distribution that repeatedly wins for VO2max and highly-trained performance.
• Athlete B: most sessions in the moderate "grey zone" just under threshold — the single most common mistake in amateur endurance training ("black-hole" / junk-miles training): too hard to recover from, too easy to drive top-end adaptation.

Same load. Same PMC chart. Same form. Completely different coaching verdict. Today WattWise renders A and B as indistinguishable. The PMC tells you the size of the stimulus; TID tells you its quality — and quality is where the real advice lives.

This also unlocks forecasting that works: the research is now specific about which distribution produces which adaptation (polarized: best VO2max gains, esp. in shorter blocks and trained athletes; pyramidal: most effective for many runners and base phases; ~75–80% low-intensity + ~15–20% high-intensity as the productive band). With TID measured, the coach can say "to peak your VO2max for the event in 8 weeks, your current threshold-heavy mix should shift polarized" — a real, testable prescription, instead of only describing past load.

The metric set (one logical bundle)

A rolling-window distribution, computed per sport, anchored to the athlete's existing thresholds:

1. Time-in-zone fractions over a window (7/28-day, and per block) using the standard 3-zone physiological model:
   • Z1 — below the first threshold (LT1/VT1 / aerobic threshold)
   • Z2 — between the two thresholds ("threshold / grey zone")
   • Z3 — above the second threshold (LT2/VT2 / FTP / CP)
2. polarization_index — Treff et al. (2019): PI = log10( (Z1 / Z2) x Z3 x 100 ), where a TID is polarized when PI > 2.00; higher = more polarized. One honest number that integrates all three zones.
3. lit_hit_ratio — the low-intensity vs high-intensity split (the "80/20" coaches actually talk about).
4. tid_archetype — a typed classification: polarized / pyramidal / threshold / grey_zone, with the math, not a guess. (Polarized condition, Treff: 0 <= z2 < z3 < z1.)

Why it is derivable from data we already store — today

This is not a new sensor; it is a synthesis of streams already in the record, and most of the machinery exists:

• hr_load_zonal already bins per-second HR samples against athlete zone boundaries (analytics/trimp.py) — time-in-zone is the same binning, kept as durations instead of collapsed into a weighted scalar.
• intensity_class already cut-points IF against fixed thresholds (analytics/np_if_tss.py).
• The fitness signature already stores the anchors: cp_w / ftp_w, threshold_hr_bpm, max_hr_bpm, zone boundaries + weights are already a first-class concept.
• Sport-agnostic by construction, matching the existing applicability rules: power zones for cycling, pace or HR zones for running, HR for swimming/rowing/xc-ski, and — degrading honestly — an RPE/zone fallback for strength and sensor-less sessions (reusing the srpe_load path from Collect session-RPE (sRPE) + synthesize a perception:output divergence signal — the engine's load model is blind to every session without power/HR (all strength work, most swimming), and we're already dropping the RPE fields our own sources send us #27). Pace/HR three-zone TID is exactly how the running and skiing literature reports it, so we stay comparable to the papers.

Fits the project's honesty contract

• No anchors, no number. TID requires zone anchors (CP/FTP, or LTHR/threshold-HR, or threshold pace). When the athlete has none, return Unavailable with the typed reason — never a fabricated split.
• Fidelity tag. A power-derived TID is raw_stream; an HR-derived one is lower fidelity; an RPE-derived one is SUBSTITUTED. Same fidelity ladder the rest of the engine already uses.
• Groundable & citable. Each fraction / index is a deterministic function of (streams, zone anchors), so it earns a normal citation — the grounder can verify a coach claim like "68% of last month was Z1" against the record, instead of scrubbing it as an unknown metric.

Distinct from the existing record (checked)

• Synthesize a Durability / Fatigue-Resistance profile: every prediction today is built on FRESH fitness (CP/FTP/pace), which systematically over-predicts long events — the work-conditioned decline is the single missing input, and it is fully derivable from streams we already store #26 durability / fatigue-resistance — how power decays within a long effort (the fatigue axis). TID is how intensity is distributed across sessions. Orthogonal axes.
• Collect session-RPE (sRPE) + synthesize a perception:output divergence signal — the engine's load model is blind to every session without power/HR (all strength work, most swimming), and we're already dropping the RPE fields our own sources send us #27 sRPE / perception:output — adds a load source for sensor-less work; TID consumes it as one optional input but is about distribution, not load magnitude.
• Grounding treats prescriptions as descriptions: the gate can only verify the future against 7×CTL maintenance, rewrites goal-directed targets in place (a taper week is "corrected" UPWARD), and the approval gate ships that rewritten body as the "grounded plan" #25 prescription-by-simulation — a different kind of thing, and not a dependency in either direction (this caused confusion on first read; see the note on #25). Grounding treats prescriptions as descriptions: the gate can only verify the future against 7×CTL maintenance, rewrites goal-directed targets in place (a taper week is "corrected" UPWARD), and the approval gate ships that rewritten body as the "grounded plan" #25 is a verification mechanism for future plans — it grounds a prescription by forward-simulating it, instead of "correcting" it against the past. Synthesize Training Intensity Distribution (TID): time-in-zone + Polarization Index — the engine knows how MUCH you train but is blind to the easy/hard MIX, the single most actionable lever in endurance science #76 is a descriptive metric of the easy/hard mix you have already done. They compose but ship independently: Synthesize Training Intensity Distribution (TID): time-in-zone + Polarization Index — the engine knows how MUCH you train but is blind to the easy/hard MIX, the single most actionable lever in endurance science #76 would give Grounding treats prescriptions as descriptions: the gate can only verify the future against 7×CTL maintenance, rewrites goal-directed targets in place (a taper week is "corrected" UPWARD), and the approval gate ships that rewritten body as the "grounded plan" #25's simulation envelope one more thing to check a plan against — extending its per-session "intensity anchoring" leg to a whole-block distribution target (e.g. a build block grounds only if its prescribed sessions add up to a polarized PI). Grounding treats prescriptions as descriptions: the gate can only verify the future against 7×CTL maintenance, rewrites goal-directed targets in place (a taper week is "corrected" UPWARD), and the approval gate ships that rewritten body as the "grounded plan" #25 is not blocked on Synthesize Training Intensity Distribution (TID): time-in-zone + Polarization Index — the engine knows how MUCH you train but is blind to the easy/hard MIX, the single most actionable lever in endurance science #76; Synthesize Training Intensity Distribution (TID): time-in-zone + Polarization Index — the engine knows how MUCH you train but is blind to the easy/hard MIX, the single most actionable lever in endurance science #76 is not part of Grounding treats prescriptions as descriptions: the gate can only verify the future against 7×CTL maintenance, rewrites goal-directed targets in place (a taper week is "corrected" UPWARD), and the approval gate ships that rewritten body as the "grounded plan" #25.
• Per-ride TSS resolver missing from CanonicalEvidence.metric_value: a per-activity TSS claim cannot ground #47 per-ride TSS — a single session's load scalar. TID is a multi-session distribution.
• hr_load_zonal / intensity_class — a zone-weighted load scalar and a per-activity label. Neither exposes the distribution, a window-level index, or an archetype.

No prior open or closed issue proposes a time-in-zone distribution, a polarization index, or a TID archetype.

Proposed slice (no code in this issue)

1. AnalyticsService.intensity_distribution(athlete, sport, window) -> time-in-zone fractions + polarization_index + lit_hit_ratio + tid_archetype, same purity / fail-closed envelope as siblings, reusing the hr_load_zonal binning and the signature's zone anchors.
2. MetricName members + capability resolvers + metric aliases ("intensity distribution", "easy/hard split", "polarization", "80/20") so retrieval can name them and grounding can cite them.
3. docs/METRICS.md entries (definition, formula, honest ranges with sources, when Unavailable).
4. Golden + property tests at the service seam (a known polarized vs grey-zone fixture must classify correctly; PI math must match Treff worked examples; fail-closed without anchors).

Selected sources

• Treff et al. (2019), The Polarization-Index, Front. Physiol. — https://pmc.ncbi.nlm.nih.gov/articles/PMC6582670/ (PI formula, PI > 2.00 cutoff)
• Comparison of Polarized vs other TID, systematic review + meta-analysis, Sports Medicine (2024) — https://link.springer.com/article/10.1007/s40279-024-02034-z
• Polarized TID effect on VO2max and work economy, systematic review (2024) — https://pmc.ncbi.nlm.nih.gov/articles/PMC11679080/
• Recent advances in TID theory for cyclic endurance sports (2025), Front. Physiol. — https://www.frontiersin.org/journals/physiology/articles/10.3389/fphys.2025.1657892/full

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@bepcyc — flagging this as the highest-leverage metric gap I can find, and I'd value your read before anyone builds it. Two calls I'd want your opinion on: (a) scope — ship the 3-zone TID + PI first and treat per-session "black-hole" detection as a follow-up, or build both together? (b) zone model — anchor zones to CP/FTP and threshold-HR we already store (pragmatic, available today), or hold out for a proper dual-threshold (LT1/LT2) model where data allows? (Audit + proposal only — no code changed for this issue.)