# The Interaction of Fitness and Fatigue on Performance in Football
## 1 Introduction  
In recent years, elite football players have experienced a notable increase in the number of annual matches, resulting in congested weekly fixtures and heightened game demands. These demands include intensified pressing and counterattacking phases, frequent short accelerations and decelerations, and high-speed running actions interspersed throughout matches [1]. Consequently, the need for continuous \"appropriate prescription, monitoring,and adjustment of external and internal loads\" has become essential [2]. This ensures the ability to modify training loads for subsequent sessions, plan recovery phases, and protect players from injuries and illnesses [3]. Monitoring players' daily fluctuations in load and associated responses has emerged as one of the most effective strategies in this context [4]. Based on [PERSON]'s proposed model [5], a multidimensional monitoring system that calculates short- and long-term rolling averages can help identify both fitness and fatigue [6]. However, regular testing faces practical challenges, including its invasiveness, time constraints, and players' reluctance to undergo frequent assessments [7]. As a solution, \"invisible monitoring\"--a collection of techniques and data analysis methods designed to measure one or multiple training effects using a single or combination of tools with minimal burden on athletes and staff--offers a less invasive and more efficient approach to optimizing performance, minimizing injury risk, and enhancing players' physical and psychological well-being [7; 8; 9]. To address these challenges, recent studies have introduced invisible monitoring approaches to evaluate players' fitness [10] and fatigue [11] on a weekly basis. The first study developed an in situ fitness index using machine learning, calculated as the difference between the observed HRdrill (heart rate during specific drills) and the predicted HRdrill, derived from game situations and possession-based drills [10]. According to the authors, a good fitness status was indicated by observed HRdrill values lower than predicted (Fitness Index < 0), while a poor fitness status was associated with higher observed values (higher heart rate responses than the expected values). This study demonstrated that machine learning techniques provided better predictive accuracy compared to traditional linear metrics. Moreover, the use of heart rate as a daily monitoring metric offered a less invasive alternative to additional testing [10]. The second study also employed machine learning to create a locomotor efficiency index, predicting Player Load (PL) to assess players' neuromuscular status throughout the season [11]. Also in this work, a positive locomotor efficiency index, where the observed PL was lower than predicted, indicated neuromuscular readiness and ability to minimize the body load, while a negative index suggested fatigue. Additionally, the findings of this study showed clear fluctuations in the locomotor efficiency index according to the period of the season, the day within the weekly microcycle, and variations in training load [11]. Given the promising findings of these studies, combining the fitness and fatigue indices to develop a new performance score could offer significant insights. According to [PERSON]'s model, performance results from the difference between fitness and fatigue. A weekly performance score derived from these indices could help investigate if its fluctuations correlate with changes in match performance. However, defining match performance is complex, as it encompasses not only physical elements (e.g., total distance, sprints, accelerations, decelerations) but also technical/tactical parameters. Regarding players' tactical behavior efficiency, decision-making ability is critical for managing fatigue during high-intensity periods or the latter stages of a match [12]. Indeed, muscular and/or central fatigue can alter how players perform physically and tactically [13].