The Banister Model: Mathematical Quantification of Training Load

Introduction

If Yakovlev described supercompensation in words, then Eric Banister was the one who turned this concept into a mathematical formula in 1975. His Fitness-Fatigue Model is the foundation of quantifying training load in modern sports science, and the core logic behind tools such as TrainingPeaks and Intervals.icu.

The Core Equation of the Banister Model

Performance (P) is determined by two exponential decay terms:

P = k1 × Fitness − k2 × Fatigue

• Fitness (CTL): Long-term accumulated load, decays slowly (time constant ~42–45 days)
• Fatigue (ATL): Short-term acute load, decays quickly (time constant ~7 days)
• Form (TSB) = Fitness − Fatigue

The Three Key Metrics of the TrainingPeaks PMC

How TSS Is Calculated

The load of each training session is quantified as TSS (Training Stress Score):

TSS = (seconds × NP × IF) / (FTP × 3600) × 100

• IF (Intensity Factor) = NP / FTP
• NP (Normalized Power) = weighted average power, reflecting variable intensity
• 1 hour @ FTP = 100 TSS

Planning Training with the PMC

• Base phase: CTL rises 3–5 TSS/d per week, TSB can be maintained at −10 to −20
• Race phase: Taper 7–14 days before the race to raise TSB to +5 to +15
• Warning: TSB < −30 indicates a high risk of overreaching; if ATL rises for 14 consecutive days, tapering is required

Research Directions

Banister laid the foundation of the model in Theoretical Aspects of Athlete Training; Busso refined it into a nonlinear version; Coggan turned the model into the practical TSS system, which became the mathematical standard of modern power-based training.

Practical Advice

• If you don’t have a power meter, heart rate TRIMP can be used as a substitute
• Don’t obsess over the CTL number; just compare your own year-over-year trends
• Pre-race taper standard: CTL loss no more than 10%, TSB reaching +5 to +15
• The model is a tool, not the truth; it must be combined with subjective feelings and physiological monitoring

Conclusion

The Banister model turned the subjective concept of “form” into a scientific tool that can be charted and predicted. For amateur cyclists in Taiwan, using the PMC to plan a six-month to one-year training cycle is one of the most valuable investments in advanced training. The free tool Intervals.icu already includes a full PMC, and no payment is required to use it.

Related Reading

• Mathematical Modeling of Athletic Performance: From Banister to the Modern Era—Why Formulas Won’t Save You, But They’re Worth Understanding
• The CTL, ATL, and TSB Fitness Model: Tracking Training Status with Data
• Reading the PMC Fitness Management Chart: How the Three Numbers ATL, CTL, and TSB Guide Your Training Cycle
• The Relationship Between Chronic Training Load (CTL) Tracked by Power Meters and Fatigue: A Training Peaks Data Study