WVI v2 — Vitality Index

Overview

WVI is a single number (0-100) that tells you how ready your body and mind are right now. It fuses 12 biometric signals from the smart band, applies scientifically validated weights, and produces a score that is personalized to your own baseline.

v2 is harder than v1. Getting to 60 is straightforward. Getting to 80 takes real effort across all dimensions. Getting to 90+ requires peak performance in every metric simultaneously. You cannot compensate bad sleep with a great workout. You cannot outrun stress.

The Formula

Pipeline

Step 1  Raw sensor data → Normalize each metric to [0, 100]
Step 2  Personalize via z-score against 14-day rolling baseline
Step 3  Check hard caps (ceiling gates)
Step 4  Aggregate via Weighted Geometric Mean across 12 metrics
Step 5  Apply progressive sigmoid curve (non-linear difficulty)
Step 6  Apply emotion multiplier (0.78 – 1.15)
Step 7  Clip to [0, 100]

Mathematical Form

metric_score(i) = sigmoid_normalize(z_score(raw(i), baseline_14d(i)))

GM = exp( sum( weight(i) * ln( max(metric_score(i), 1) ) ) )

cap = min(cap_sleep, cap_steps, cap_stress, cap_spo2, cap_hrv)

WVI_curved = progressive_sigmoid( min(GM, cap) )

WVI_final = clip( WVI_curved * emotion_multiplier, 0, 100 )

Why Geometric Mean

The UN switched the Human Development Index from arithmetic to geometric mean in 2010 because it prevents compensating poor performance in one dimension with excess in another. This principle applies directly to wellness: you cannot make up for zero sleep with a perfect workout.

The geometric mean punishes the stress=20 much harder. One failing metric drags the entire score down. That is by design.

Progressive Sigmoid Curve

Below 60 the score is linear. Above 60 each additional point costs exponentially more effort.

if raw <= 60:   WVI = raw
if raw >  60:   WVI = 60 + 40 * (1 - e^(-3.5 * (raw - 60) / 40))

The 12 Metrics

Total: 100%

Weight Rationale

The top three metrics (HRV, Stress, Sleep) account for 43% of the score because they have the strongest evidence base for predicting next-day recovery and long-term health outcomes:

• HRV: Eur Heart J 2023 — strongest single biomarker for autonomic health and recovery readiness
• Stress: Firstbeat Analytics — validated across 100K+ field assessments as a predictor of autonomic resource depletion
• Sleep: JAMA 2022, Walker 2017 — <6h sleep associated with +13% all-cause mortality

Hard Caps (Ceiling Gates)

Hard caps set an absolute ceiling on WVI. No amount of excellence in other metrics can overcome a critical failure.

When multiple caps trigger, the lowest ceiling applies.

Detailed Scoring Ranges

1. HRV (RMSSD) — 16%

Heart rate variability measures the variation in time between heartbeats. Higher HRV indicates better autonomic balance and recovery capacity. All values are z-scored against your personal 14-day baseline.

RMSSD ranges are age-dependent: median ~42ms at age 20-29, declining ~1-2ms per year.

References: Shaffer & Ginsberg 2017, Eur Heart J 2023.

2. Stress Index (inverted) — 14%

Derived from HRV spectral analysis. The raw SDK stress index is inverted so that lower stress = higher score.

Reference: Firstbeat Analytics validation studies.

3. Sleep Score — 13%

A composite of five sub-metrics weighted internally:

Targets for 100:

• TST: 7.5-8.5 hours
• Sleep Efficiency: >92%
• Deep Sleep: >22% of TST
• REM: >22% of TST
• WASO: <10 minutes

References: Sleep Foundation 2024, Walker "Why We Sleep" 2017, SLEEP Oxford 2023 (sleep regularity as mortality predictor).

4. Emotional Wellbeing — 12%

Emotions operate on two levels in WVI v2:

1. As metric #4 with weight 12% — the 24-hour rolling emotional state score
2. As a final multiplier (0.78-1.15) applied after the geometric mean

The metric score is based on the percentage of time spent in positive vs negative emotional states over the past 24 hours.

References: WHO-5 Well-Being Index, Seligman PERMA model 2011.

5. SpO2 — 8%

Blood oxygen saturation. Healthy lungs maintain 96-100% at rest.

Reference: WHO pulse oximetry guidelines.

6. Heart Rate Delta — 7%

The difference between your current resting heart rate and your personal RHR baseline. Elevated resting HR indicates incomplete recovery, stress, dehydration, or illness.

Reference: AHA 2024 guidelines.

7. Steps — 7%

Daily step count with a non-linear dose-response curve matching the epidemiological evidence: maximum benefit around 12,500 steps/day, with strong diminishing returns above that.

Each additional 1,000 steps per day is associated with approximately 15% reduction in all-cause mortality (Lancet 2025 meta-analysis). The inflection point is 5,000-7,000 steps.

References: Lancet 2025 meta-analysis, JAMA 2023 (Paluch et al.), Preventive Medicine 2024.

8. Active Calories — 6%

Calories burned from physical movement and exercise only (excludes basal metabolic rate). Measured via accelerometer, heart rate, and METS calculation.

References: WHO physical activity guidelines 2020, PNAS 2025 additive energy expenditure model.

9. Activity Load (ACWR) — 5%

The Acute:Chronic Workload Ratio compares your training load over the past 7 days against your 28-day rolling average. It penalizes overtraining (injury risk) and deconditioning (fitness loss).

Calculated using EWMA (exponential weighted moving average), which is more responsive than simple rolling averages.

The 10% rule: never increase weekly training load by more than 10%.

References: Gabbett 2016, Br J Sports Med. EWMA method: Williams et al. 2017.

10. Blood Pressure — 5%

Deviation from the optimal 120/80 mmHg baseline.

Reference: ESC/ESH Hypertension Guidelines 2023. Every 20 mmHg systolic rise doubles cardiovascular death risk.

11. Temperature — 4%

Body temperature deviation from your personal baseline (typically 36.5-37.0 degC). Stable temperature is a marker of circadian health and immune homeostasis.

Reference: J Therm Biol 2022.

12. PPI Coherence — 3%

Pulse-to-pulse interval coherence measures the regularity and rhythmic pattern of heartbeat intervals. High coherence correlates with parasympathetic dominance, emotional regulation, and cognitive performance.

Reference: HeartMath Institute research, Lehrer resonance frequency studies.

The Emotion System

18 Emotions with WVI Multipliers

Emotions are detected from biometric signals using a fuzzy-logic cascade with 300-second temporal smoothing. Each emotion has a WVI multiplier that adjusts the final score after geometric mean aggregation.

v2 change: Multiplier range tightened from 0.80-1.30 to 0.78-1.15. Negative emotions penalize harder than positive emotions boost (negativity bias). Scientific basis: Baumeister et al. 2001 "Bad is Stronger than Good" — negative experiences have roughly 2x the psychological impact of positive ones.

Positive Emotions (7)

Neutral (1)

Physiological States (4)

Negative Emotions (6)

Emotion Temporal Smoothing

Emotions do not flip instantly. A 300-second (5-minute) smoothing window prevents noise-driven oscillations. A challenger emotion must score at least 30% higher than the incumbent to trigger a state change. This prevents "emotion flickering" from brief biometric spikes.

Cross-Metric Interactions

Metrics do not operate in isolation. The table below shows how each metric influences others. These are real physiological cascades, not algorithmic artifacts.

The Recovery-Performance Cycle

Good Sleep
    |
    v
High Morning HRV --> Low Stress --> Better Emotional State
    |                     |                    |
    v                     v                    v
More Steps/Calories  Better ACWR        Higher PPI Coherence
    |                     |                    |
    +------> Better Sleep Tonight <-----------+

(Virtuous cycle: each metric reinforces the others)

Bad Sleep
    |
    v
Low Morning HRV --> High Stress --> Negative Emotions
    |                    |                    |
    v                    v                    v
Fewer Steps/Cal    ACWR Degrades       Low PPI Coherence
    |                    |                    |
    +------> Worse Sleep Tonight <-----------+

(Vicious cycle: each deficit compounds)

Adaptive Weights by Time of Day

The formula adjusts metric weights based on the time of day and activity state, reflecting the physiological reality that different systems dominate at different times.

Personalization

Z-Score Baseline

Every metric is compared to your own 14-day rolling baseline, not population averages. Two people with identical raw biometrics can have different WVI scores because their baselines differ.

z_score = (current_value - mean_14_day) / max(stddev_14_day, 0.1 * mean_14_day)

The minimum standard deviation guard (10% of mean) prevents extreme z-scores when variance is artificially low.

Cold Start Protocol

Shrinkage formula:

mean_blended = (n * mean_personal + 7 * mean_population) / (n + 7)

At n=0: 100% population. At n=7: 50/50. At n=14: 67% personal. At n=28: 80% personal.

During the first 7 days (calibration), WVI is fixed at 50 (baseline) to avoid misleading early scores.

Scenario Examples

A. Perfect Day — WVI 100 (Superb)

Hard caps: None triggered. Geometric mean: 96.1 Progressive curve: 98.3 Emotion multiplier (Flow x1.15): 113.0 -> capped at 100. Final WVI: 100

B. Average Healthy Day — WVI 66 (Good)

Hard caps: None triggered. Geometric mean: 65.3 Progressive curve: 65.0 Emotion multiplier (Calm x1.02): 66.3 Final WVI: 66

C. Bad Day — WVI 21 (Poor)

Hard caps triggered: Sleep < 50 (max 60), Steps < 3K (max 45), Stress < 30 (max 55). Lowest cap: max 45. Geometric mean: 24.3 (below cap, so cap has no additional effect). Progressive curve: 24.3 (linear zone). Emotion multiplier (Anxious x0.85): 20.7 Final WVI: 21

D. Mixed Day (Great Workout, Bad Sleep) — WVI 51 (Moderate)

Hard caps triggered: Sleep < 50 (max 60). Geometric mean: 54.0 (below cap). Progressive curve: 54.0 (linear zone). Emotion multiplier (Drowsy x0.95): 51.3 Final WVI: 51

15,000 steps and 1,400 active calories cannot compensate for 5.5h sleep. In v1, this would have scored ~68. In v2, the geometric mean and sleep cap ensure honest scoring.

E. Stressed Executive — WVI 36 (Low)

Hard caps triggered: Stress < 30 (max 55). Geometric mean: 40.3 (below cap). Progressive curve: 40.3 (linear zone). Emotion multiplier (Stressed x0.90): 36.3 Final WVI: 36

Good physical metrics cannot overcome mental health deficits. The stress-driven low HRV and negative emotion multiplier combine to produce a score that accurately reflects this person's compromised recovery state.

How to Improve Each Metric

WVI Levels

v1 vs v2 Comparison

Limitations

• WVI is correlated with perceived recovery and next-day readiness. It is not a diagnostic or clinical metric.
• Emotion detection from wearable biometrics achieves 75-88% accuracy. Stress/calm binary is reliable (~85%+); specific emotions are less certain.
• The formula is calibrated against a validation cohort (Spearman rho = 0.61 with next-day perceived recovery). Weights are revisited annually.
• During calibration (first 14 days), WVI relies on population priors and should be interpreted with caution.
• WVI does not replace medical advice. Persistent scores below 35 or SpO2 below 92% should prompt medical consultation.