How Crusd Works.
The Science Behind the App.

We stand on decades of sports-science research. This page names the methods we use, cites the primary sources, and is honest about what they do and don't capture.

None of this is novel research on our part. Our job is to compose well-established methods into something useful, calibrate them sensibly, and be transparent about the limits. If you spot a citation gap or a place where we've oversimplified — please tell us. We'd rather grow with our users than pretend we have all the answers.

The methods we use

Race-time projection — Riegel formula (1977)

What it captures: how endurance fades over distance for trained runners. What it doesn't: race-day pacing, fueling, weather, course profile. Projections from training pace tend to be optimistic — your real race time is usually a touch slower. Source: Riegel, P.S. (1977). "Time predicting in distance running." Runner's World.

Race-fitness measurement — VDOT (Daniels, 2014)

What it captures: your current race fitness in a unit that maps to prescribed paces. What it doesn't: sport-specific neuromuscular adaptation, hill-running ability, heat tolerance. Source: Daniels, J. (2014). Daniels' Running Formula, 3rd ed. Human Kinetics.

Training load — ACWR EWMA (Banister; Gabbett 2016)

What it captures: whether your recent training is heavier or lighter than your typical baseline. What it doesn't: sleep debt, mental stress, prior injury history. The "above 1.5 = injury risk" finding is correlational and has been challenged in subsequent literature. Sources: Banister (1991); Gabbett, T.J. (2016). British Journal of Sports Medicine, 50(5), 273–280.

Heart-rate zones — Karvonen %HRR (1957)

What it captures: relative effort intensity, normalized to your fitness rather than a population average. What it doesn't: short-term variation from heat, illness, stress. Age-based HRmax estimates can be off by 10–15 bpm for individuals. Source: Karvonen, M.J. et al. (1957). Annales Medicinae Experimentalis et Biologiae Fenniae, 35(3), 307–315.

Effort rating — Borg RPE (1962)

What it captures: your subjective experience of effort — integrates physiological and psychological state in a way HR alone cannot. What it doesn't: RPE calibration varies between athletes and drifts over time as fitness changes. Source: Borg, G. (1998). Borg's Perceived Exertion and Pain Scales. Human Kinetics.

Strength load — Volume × effort (Foster, 1998)

What it captures: a relative-effort signal for strength sessions, combining sets × reps × weight × RPE so we can track week-over-week stimulus. What it doesn't: time-under-tension, exercise selection nuance, bar-velocity differences. Source: Foster, C. (1998). "Monitoring training in athletes with reference to overtraining syndrome." Medicine & Science in Sports & Exercise, 30(7), 1164–1168.

Where the science ends and our judgment begins

Some decisions are Crusd-specific calibrations, not derived from literature. We name them here so the boundary between "established science" and "our judgment" stays clear:

  • 14-day + 3-workout dual gate for the Training Load card. ACWR with sparser history produces wildly volatile values that mislead more than they help.
  • EWMA constants (λ_acute = 0.25, λ_chronic ≈ 0.069) — equivalent to ~7-day and ~28-day half-lives. Standard but the exact numbers come from us.
  • 60-day sample window for fitness inference. Longer risks stale data; shorter risks insufficient samples.
  • Confidence demotion rules (e.g., extrapolating Riegel beyond 2× the reference distance lowers confidence). Heuristics, not from a paper.
  • Cold-start defaults (e.g., new users start at "beginner" until we know more). Conservative by design — easier to speed you up than to walk back zones that crushed you on day one.

Spot a gap or have a better source? Email info@crusd.io — we'd rather grow with our users than pretend we have all the answers.