Sleep Health Score v3.5

A continuous, multi-domain soft-cap evaluation model mapped specifically to commercial smartwatch limitations and clinical boundaries.

What this system does

  • Evaluates sleep across 5 primary clinical domains simultaneously.
  • Applies continuous soft-cap multipliers to penalize severe physiological bottlenecks.
  • Bridges the gap between PSG stage categories and standard wearable compression streams.
  • Includes automatic architectural fallbacks for missing wearable continuity metrics.

What it does NOT do

  • It is not a diagnostic device or a replacement for clinical sleep studies (PSG).
  • It does not utilize sudden, rigid binary thresholds that unfairly punish moderate fluctuations.
  • It does not assume high scores when a critical physiological domain is dangerously compromised.

The Mathematical Spec: Weighted Base & Soft-Caps

Traditional algorithms often map sleep quality using average values or strict binary cutoffs. If sleep efficiency drops to 89.9% instead of 90%, they may execute a harsh penalty. The Sleep Health Score v3.5 addresses this by combining a top-level **Weighted Base Aggregation** (normalized to handle missing metrics) with **Continuous Soft-Cap Multipliers** scaled via linear interpolation.

Mathematical Architecture (SHS v3.5)

1
Top-Level Weighted Aggregation
The base score $SHS_{base} \in [0, 100]$ aggregates 5 dimensions: Duration ($D$, 30%), Continuity ($C$, 20%), Architecture ($A$, 25%), Circadian Timing ($T_{circ}$, 15%), and Regularity ($R$, 10%). It automatically renormalizes to accommodate missing data streams:
$$SHS_{base} = \left( \frac{\sum_{i \in \mathcal{A}} w_i \cdot S_i}{\sum_{i \in \mathcal{A}} w_i} \right) \cdot 100$$
2
Continuous Soft-Cap Degradation
To prevent high scores when a critical physiological sleep domain is dangerously compromised, the final score applies the continuous `dynamicMultiplier` which represents the single worst sleep bottleneck:
$$SHS_{final} = \text{clamp}\Big( SHS_{base} \cdot \text{dynamicMultiplier}, \; 0.0, \; 100.0 \Big)$$ $$\text{dynamicMultiplier} = \min\Big( M_{REM}, \; M_{N3}, \; M_{TST}, \; M_{circ} \Big)$$
3
Linear Bounded Interpolation Helper
Each multiplier $M_i$ scales smoothly from normal operation ($M = 1.0$) down to pathological limits using a continuous linear mapping function:
$$\_linear(v, x_{min}, x_{max}, y_{min}, y_{max}) = y_{min} + \left( \frac{\text{clamp}(v, x_{min}, x_{max}) - x_{min}}{x_{max} - x_{min}} \right) \cdot (y_{max} - y_{min})$$

Interactive live calculator (SHS v3.5)

Adjust the inputs below to see how the scoring engine evaluates the sleep domains, handles wearable falls-backs, and applies soft-cap bottleneck penalties in real time.

8.0 hrs (480m)
Use Wearable Fallback (No WASO/Efficiency)
95 %
10 min
20 % (96m)
25 % (120m)
55 % (264m)
23:00 (23.0)
0.4 hrs (24m)
--
Good
Completeness: 100%
Optimal Sleep Quality
No dynamic soft-cap bottlenecks are active. Your composite sleep score represents full anabolic recovery.

Subscore breakdown

Sleep Duration (D) --
Sleep Continuity (C) --
Sleep Stage Depth (A) --
Circadian Timing (T) --
Sleep Regularity (R) --
Dynamic Multiplier Penalty 1.00

Evidence & further reading