Fitness-Fatigue Model
Also known as: Banister Model, Two-Component Model, Performance = Fitness − Fatigue
A two-component mathematical model of how training affects performance over time. Every training session simultaneously produces two responses: a slow-building, slow-decaying 'fitness' trace, and a fast-rising, fast-decaying 'fatigue' trace. Performance at any moment is the difference between them. The model is the conceptual backbone behind modern load-monitoring metrics — TSS, CTL/ATL/TSB, ACWR, and Afitpilot's own EWMA load trend all descend from this framework.
Formula
Performance(t) = k1 × Fitness(t) − k2 × Fatigue(t)
where:
Fitness(t) = Σ TrainingLoad(i) × e^(−(t − i) / τ1) [τ1 ≈ 35-50 days]
Fatigue(t) = Σ TrainingLoad(i) × e^(−(t − i) / τ2) [τ2 ≈ 7-15 days]
k1, k2 = athlete-specific weighting constants (k2 typically 2-3× k1)
In practice this collapses into three observable proxies:
CTL (Chronic Training Load) = the fitness trace, EWMA-smoothed over ~42 days
ATL (Acute Training Load) = the fatigue trace, EWMA-smoothed over ~7 days
TSB (Training Stress Balance) = CTL − ATL = predicted form at this momentExample
Cyclist completes a 4-week build mesocycle averaging 600 TSS/week, then deloads at 250 TSS in week 5. End of week 4: CTL has climbed to ~75 (fitness up), ATL has climbed to ~85 (fatigue higher still), TSB is −10 (negative form — fatigued, can't express the fitness gain yet). Week 5 deload: ATL falls fast (-30, halving in a week) while CTL barely budges (-2, half-life 42 days). End of deload: CTL ~73, ATL ~55, TSB +18 — the supercompensation window. This is why a 4-week mesocycle + 1-week deload is a productive cadence: it engineers a TSB swing from negative to strongly positive without throwing away the fitness gain.
How Afitpilot Uses This
Afitpilot's load-trend chart implements the fitness-fatigue model directly: the chronic (28-day) and acute (7-day) EWMA curves on the chart are the fitness and fatigue traces by another name, and ACWR (acute:chronic ratio) is one common readout of where on the curve an athlete sits. We deliberately do not compute or display a TSB number, because the canonical form (CTL − ATL with athlete-specific k1, k2 constants) requires inputs we don't have for self-coached strength athletes — a calibrated FTP for TSS, or a tuned per-athlete fitness-to-fatigue weighting. AU-based load gives us the same chronic/acute shape without the false precision of a single 'form' number. Practical translation that the model gives athletes: a rising chronic trace alongside a moderate acute trace means progress is banking; a stalled chronic alongside a rising acute means fatigue is winning; deloads exist to drain the acute trace faster than the chronic decays.
Time constants and what they mean
| Who / Context | Value | Note |
|---|---|---|
| Fitness time constant (τ1) | 35-50 days half-life | Why detraining gains take weeks to fully fade — and gains take weeks to fully bank |
| Fatigue time constant (τ2) | 7-15 days half-life | Why a 1-2 week deload clears most of the fatigue while preserving fitness |
| Fatigue:fitness weighting (k2:k1) | Typically 2-3:1 | Each unit of training adds 2-3x more fatigue than fitness, short-term |
| Optimal TSB at competition | +15 to +25 in cycling/triathlon literature | Empirically derived; precision drops off in strength sports |
| How long to peak fitness from a deload | 5-10 days for the TSB to swing positive | The mesocycle close-out + 1-week deload cadence engineers exactly this |
| Model age | 1975 (Banister) | The longest-surviving training-science model in continuous use |
Known Limitations
- •The two-component model is a simplification. Real training adaptations involve at least four time scales (neural ~hours-days, metabolic ~days-weeks, structural ~weeks-months, connective tissue ~months) that the two exponentials compress into one fitness-vs-fatigue picture. The model gets the macroscopic shape right; it does not predict the discipline-specific micro-adaptations.
- •The athlete-specific weighting constants (k1, k2, τ1, τ2) are typically fitted by retrospective regression on months of performance data. Without that calibration, the model is qualitative rather than predictive — useful for explaining why your last block worked, less useful for predicting your next single race result.
- •Garbage in, garbage out on the load input. The fitness-fatigue framework assumes a load metric that scales linearly with stimulus, which is approximately true for steady aerobic work (TSS, TRIMP) and only roughly true for strength training (AU, tonnage). Heavy resistance days produce neural and structural fatigue that the model under-weights, and the curves look smoother than reality.
- •The model treats fitness and fatigue as scalar single-quantity traces. In sports with multiple distinct adaptations (a runner's VO2max vs. running economy vs. lactate threshold), one chronic-load number masks divergent traces — your CTL can rise while your VO2max-specific adaptation is regressing because the block was too easy at intensity.
- •TSB (form) prediction from CTL − ATL has empirical support in cycling and triathlon but is weak in strength sports — peaking a powerlifter from a TSB calculation alone routinely misses the timing window. The model's value for strength athletes is conceptual, not predictive.
Science Context
The fitness-fatigue model originates with Banister, Calvert and colleagues at Simon Fraser University in 1975, originally fitted to swimming performance data. The two-component differential-equation form has been re-derived and re-validated dozens of times across endurance and team sports (Busso 2003 — the comprehensive review; Clarke & Skiba 2013 in cycling). Its modern incarnation as the TSS / CTL / ATL / TSB family at TrainingPeaks (Coggan, early 2000s) is the most-used coaching application of the framework today. Strength-sport validity is weaker — Williams et al. 2017 and Vermeire et al. 2021 note that the model captures the chronic/acute shape but does not produce useful single-event peaking predictions for resistance training. The honest summary: the fitness-fatigue model is one of the few training-science frameworks where the qualitative picture (build-deload cadence, supercompensation timing, why fatigue masks fitness) is robust enough to programme around, while the quantitative single-number predictions (this exact TSB on this exact day will produce this peak) are reliable only inside calibrated steady-aerobic sport. Afitpilot uses the qualitative skeleton — chronic vs. acute load — and stops short of the quantitative readout for that reason.