New perspectives for the fitness fatigue model: how to revisit questions about the science of sports training from the perspective of systems control theory

Abstract

The Fitness-Fatigue model (FFM) was initially designed to gain a better physiological understanding of the impact of training loads on sports performance. For almost 50 years, simulations have been compared with the observed response of sports performance to training loads. Understanding the relationship between training load and performance should have answered some fundamental questions for the physical trainer or sports coach: 1/ how to define the best training to achieve a performance without exhausting an athlete or how to achieve a performance in a limited time; 2/ how to assess the athlete's fatigue and fitness reliably to better understand his performance; 3/ how to prevent the risk of injury. But this was not the case. Studies dedicated to the FFM have been limited to improving somewhat on Banister's initial model without really taking the necessary step back to take advantage of the mathematical framework offered by the state representation, the implicit formalism underlying the FFM. The idea behind this research strategy is that having a valid and accurate model makes it easy to address previous questions through simulation: multiple training scenarios can be simulated until the ideal scenario for a given training question is identified. The main drawback to this approach is the combinatorial nature of the exercise. This paper is not discussing the relevance of the model, but how to use it. The state representation makes it possible to study the controllability, observability and diagnosability of a system (i.e, the athlete) and thus to formally answer the three previous practical questions. It can be considered that sports science studies have missed the richness of the FFM model. Artificial learning approaches are increasingly preferred to the FFM model because they are supposed to better capture observation. However, in the light of the state representation, the FFM model could still be extended naturally while remaining mathematically interpretable, offering mathematical tools to estimate the state of the athlete, and to define the most adequate training and prevent the risk of injury. This article does not aim to solve the question of optimal training in practice, for that it would need to be validated by specialists in physiology and sports science, it just proposes to take a fresh look at training issues and to demystify the mathematical formalism adopted by Banister.