An Improved Version of the Classical Banister Model to Predict Changes in Physical Condition

Area of Science:

• Sports Science
• Mathematical Modeling
• Physiology

Background:

• The classical Banister model predicts physical condition based on training load.
• Its main limitation is not accounting for the influence of previous training loads.

Purpose of the Study:

• To develop and solve two novel mathematical models for predicting physical condition.
• To extend the capabilities of the Banister model by incorporating historical training data.

Main Methods:

• Formulation of two new models: one based on functional differential equations, the other on integral differential equations.
• These models extend the Banister model to include the effects of cumulative training load over time.
• Application of the first model to a real-world cyclist training scenario.

Main Results:

• The proposed models provide solutions for predicting physical condition changes.
• They successfully address the limitation of the Banister model by considering training loads from previous days.
• Demonstration of the first model's practical utility with a cyclist's training data.

Conclusions:

• The new models offer a more comprehensive approach to understanding training load's impact on physical condition.
• These models can enhance the accuracy of athlete performance prediction and training program optimization.
• The functional differential equation model shows practical applicability in real training contexts.