J-H-H-R vs Continuous Model — Simulated Trajectories

1 — Interactive Simulator

Both models start at the same chronic weekly volume and assume perfect compliance. The cycle is the current sub-80 J-H-R override (3-week cycle, +17% jump, −15% reduce). The continuous model is V_target = V_chronic × (1 + (CEIL − ACWR_msk) / K_struct) × msk_coef.

2 — Trajectory at Default Parameters (30 km/wk, established < 40, no injury)

Three lines: the J-H-R cycle's target volume (what the engine asks for), the J-H-R chronic (what the body absorbs), and the continuous model's chronic. All same starting state, 20 weeks, perfect compliance, msk_coef = 0.85.

3 — Parameter Sensitivity (Continuous Model)

Same 30 km/wk start, 20 weeks, perfect compliance. Each line is a different parameter combination. Use this to read off the right K_struct / CEIL combo for your athlete archetype.

4 — Proposed K_struct-by-Volume Schedule

The current rule says "sub-80 km gets a faster J-H-R cycle." The literature doesn't support a volume-based cycle-length break, but the underlying intuition is sound: at lower absolute volumes, the same percentage growth produces less absolute MSK load, so the tissue can absorb faster. Express that via K_struct (smaller K → faster growth), not via discrete cycle structure.

Plus the age & injury-history modifiers from the main research doc: 40-49 adds +2 weeks to K, 50+ adds +4. Injury history flagged → step one row more conservative.

What this schedule produces across volumes

Each line starts at a different volume and uses the K_struct from the schedule above. Notice the growth percentages are similar across volumes — that's the design intent: the rule produces proportionally similar progression for everyone, with absolute increments scaling with volume.

5 — How the Continuous Model Handles a Missed Week

Athlete trains normally for 7 weeks, gets sick in week 8 (runs only 40% of plan). No reset rule, no establishment-ratio gate — the EWMA dynamics absorb the disruption automatically. The growth rate temporarily increases (more headroom because acute dropped faster than chronic), target volume drops below week 7's level, and the system rejoins steady state by week 12.

6 — The J-H-R Cycle, Honestly

The J-H-R cycle at 30 km/wk gets a runner to 68 km chronic in 20 weeks. That's aggressive, but by our own ACWR thresholds it's not unsafe — peak ACWR is 1.205, well inside the green zone (caution starts at 1.30). Where the cycle pays its bill is in the week-over-week jumps after every reduce week: +37 % returns that exceed Nielsen 2014's 30 % threshold for distance-related injury in novices. Both charts below tell the same story — the cycle's ACWR is fine, its WoW deltas are where the genuine risk lives.

7 — Option C: Hybrid (cycle below 60 km, continuous above)

The hybrid runs the discrete J-H-R cycle while chronic volume is below 60 km/wk (where "low-volume absorbs faster" applies and the cycle's bigger steps are defensible), then hands off to continuous EWMA-headroom control (K = 6) once chronic crosses 60 km/wk. This honours the research at both ends.

How it works

• Upward crossover (chronic crosses 60 km going up): freeze cycle state at the next cycle boundary; continuous mode picks up from current chronic and EWMAs. No "establishment" reset.
• Downward crossover (chronic drops below 60 × 0.95 = 57 km for two consecutive weeks): re-enter cycle with established_level = chronic, cycle_week = 0 (jump). The 0.95 hysteresis prevents mode flapping.
• Most athletes cross the threshold once and stay continuous. The cycle's complexity is bounded to the early-progression phase.

8 — Takeaways

1. The cycle is faster but spikier, not unsafe. J-H-R at 30 km gets to ~68 km chronic in 20 weeks with peak ACWR 1.205 — still in the green zone (caution starts at 1.30). The genuine cost is post-reduce week-over-week jumps of +37 %, above Nielsen 2014's 30 % threshold. The continuous model is slower but smoother; pick your trade-off honestly.
2. The "sub-80 absorbs faster" research is real, and the K schedule honours it. K = 4 below 60 km/wk produces +20 %/20wk. Not as aggressive as the cycle's +127 %, but in the same spirit — and without the post-reduce spikes that exceed Nielsen's threshold.
3. The continuous model fundamentally can't match the cycle's growth. Even K = 2 only gets to +44 %/20wk vs the cycle's +127 %. That's because the cycle anchors V_target to a discrete `established_level` that sits above chronic, while the continuous model anchors to chronic directly. Different bets, both defensible.
4. Option C (hybrid) is the way to get both. Run the discrete cycle below 60 km/wk where the absorption-is-fast argument is strongest, then hand off to continuous control where absolute MSK load makes the EWMA constraint sensible. Adds complexity; revisit only if Option B's slower sub-80 trajectory turns out to under-train motivated athletes.
5. Illness needs no special handling. The continuous math handles missed weeks by definition: lower acute → bigger headroom → smaller target → graceful re-entry. No "65 % reconciliation rule," no cycle reset.
6. Layer 2 (Frandsen L30 single-session cap) is the missing protection in either model. None of these trajectories model session-level spikes — that's the orthogonal axis the L30 rule covers. See main research doc § 3.2.