The effect of three days accumulated workload on football players’ perceived fatigue during Pre-Season

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The effect of three days accumulated

workload on football players’ perceived

fatigue during Pre-Season

Pálmar Hreinsson

THE SWEDISH SCHOOL OF SPORT

AND HEALTH SCIENCES

Master Degree Project 26:2021

Supervisor: Helena Andersson

Examiner Magnus Lindwall

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Abstract

Aim: The aim of the study was to improve the understanding on the relationship between different training- and match load variables and subsequent perceived rating of fatigue. This was done by investigating whether traditionally used workload variables (e.g GPS, HR data) functions as a good indicator of the players' perceived ratings of fatigue. A secondary aim was to quantify the size and distribution of the accumulated workload variables effects, in a three-days sequence, on perceived rating of fatigue by using a distributed lag model. That is the workload measured the day before, two days before and three days before the perceived rating of fatigue.

Method: The current study is a retrospective observational study. Heart Rate data, data from a 10Hz GPS tracking system and data from Wellness Questionnaire were collected from a convenience sample of 13 professional male football players (average age ± SD: 24.62 ± 3.01 years, height 180.23 ± 5.04 cm, weight 74.77 ± 5.89 kg) from Swedish Allsvenskan team during a pre-season. A correlation analysis and distributed lag regression were used to detect the association between training- and match load variables and perceived rating of fatigue.

Results: Moderate correlations were found between fatigue and several internal- and external- training load variables from the previous day session. A model with Fatigue explained by Training load Score (TLS) showed a significant positive (higher TLS = more fatigue) effect from all of the three previous days training sessions or matches with the largest effect from the session closest in time, i.e the day before (size of coefficient = 0.0100)

followed by decreasing effect for the session two days ago (size of coefficient = 0.0074) and three days ago (size of coefficient = 0.0036).

Conclusions: The results showed in this study provides practitioners with a helpful tool to plan training and to estimate the dose-response relationship based on the group and

training methods used. Diverse internal- and external training load variables can be used effectively to quantify the training load. The size of the coefficients can be used as an index or multiplier when estimating the effect from the last three days training load on fatigue.

Nevertheless, a large variation in the group response depends on individuals responding differently which gives extra weight on monitoring the load on individual level and not only team-level. A larger sample, with fixed characteristics like age, playing position and gender, could provide more general conclusions.

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Sammanfattning

Syfte och frågeställningar : Syftet med studien är att bedöma sambandet mellan olika traditionellt använda tränings- och match load variabler och efterföljande uppskattning av trötthet. Detta gjordes genom att undersöka om traditionellt använda arbetsbelastnings variabler (t.ex. GPS, HR-data) fungerar som en bra indikator på spelarnas självuppskattning av trötthet. Ett sekundärt mål var att kvantifiera storleken och fördelningen av de

ackumulerade workload variablernas effekt, i en tre-dagars sekvens, på upplevd trötthet genom att använda Distributed lag modell. Det är den arbetsbelastning som mättes dagen före, två dagar före och tre dagar före den upplevda bedömningen av trötthet.

Metod : Den aktuella studien är en retrospektiv observationsstudie. Hjärtfrekvens data, data från 10 Hz GPS-system och data från Wellness frågeformulär samlades in under en försäsong. Urvalet var ett bekvämlighetsurval av 13 professionella manliga fotbollsspelare (ålder ± SD: 24.62 ± 3.01 år, längd 180.23 ± 5.04 cm, vikt 74.77 ± 5.89 kg) från en Allsvensk klubb. En korrelationsanalys och Distributed lag Regressionsanalys användes för att upptäcka sambandet mellan tränings- och match variabler samt upplevd trötthet.

Resultat : Måttlig korrelation hittades mellan trötthet och olika interna och externa träningsvariabler från föregående dags träning. En modell med trötthet förklarad av Training load Score (TLS) visade en signifikant positiv (högre TLS = mer trötthet) effekt från alla de tre föregående dagars träningspass eller matcher med störst effekt från träningen närmast i tid, dvs. dagen innan (koefficient storlek = 0.0100) följt av minskande effekt för träningen för två dagar sedan (koefficient storlek = 0.0074) och för tre dagar sedan (koefficient storlek = 0.0036).

Slutsats : Resultaten i denna studie ger utövare ett användbart verktyg vid

träningsplanering och för att uppskatta förhållandet mellan träningsdos och respons baserat på gruppen och de träningsmetoderna som används. Olika interna och externa

träningsbelastning variabler kan användas effektivt för att kvantifiera träningsbelastningen. Storleken på koefficienterna kan användas som en index eller multiplikator när man

uppskattar den totala effekten av träningsbelastningen, de senaste tre dagarna, på trötthet. En stor variation i gruppens träningsrespons beror på den individuella variationen i respons vid träning vilket ger extra vikt vid att belastningen ska planeras och övervakas på individnivå och inte bara på lagnivå. Ett större urval kontrollerat för egenskaper som ålder, position och kön skulle dock kunna ge mer generella slutsatser.

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1 Introduction

Load management and monitoring of physical load, both in training and competition, has become a popular topic in sports research (Thorpe et al., 2016) . Improved technology measuring distances, speed, accelerations, decelerations as well as heart rate are used to quantify the training load, demand of the game and players' performance. Furthermore, a majority of professional football clubs collect self-reported perceptual measures to monitor psychometric and wellbeing states (Akenhead & Nassis, 2016) .

The strain that football players are exposed to in training and competition can cause metabolic, neuromuscular and mental exhaustion which has a negative impact on

performance (Fessi et al., 2016) and increases the risk of injury (Ehrmann et al., 2016) . At the same time, appropriate exercise stimulation can improve performance and reduce the risk of injury (Gabbett, 2016) . Studies have shown that poor control of training load is one of the biggest risk factors for so-called non-contact injuries, i.e. injuries that are not a result of direct contact to another player or object, among football players (Soligard et al., 2016) . It is

therefore important for coaches to plan for the optimal training dose, in order to continue to maintain or improve the players' physical capacity without risking their freshness with associated performance decay and increased risk of injury (Ehrmann et al., 2016) .

Football is a game where high demands are placed on physical qualities such as fitness, speed, accelerations, decelerations, changes of direction, jumps and tackles. In elite football, one to three matches can be played over a seven-day period. Therefore, accuracy in optimal training dose planning is vital to prepare the players for the physical demands of a match, and at the same time to minimize the risk of injury. When it comes to planning training dose one has to consider players' different conditions, such as age, position, physical and mental conditions, the individual, cumulative load (i.e. did the player start all matches, substitutes, have they been suspended, etc.). External factors also affect planning; such as weather, matchsurface (natural or artificial grass), home or away match, long trips and so on (Dragoo & Braun, 2010) .

Training plans are important part in the process of preparing a team of football players for a competition. For a successful outcome, monitoring of the training load and its response is another important part. As the sport is complex with large variation in load and many unforeseen elements a good monitoring system is of great importance. A system where the player’s physical load is quantified can thus provide the coaches with information for

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adjustment in training planning, with the aim of avoiding overtraining and injuries and optimizing performance.

As football players are competing at least on a weekly basis the planned training load should ensure maintaining fitness and at the same time reduced fatigue on a game-day

(Thorpe et al., 2016) . Different tapering strategies have been identified among different teams (Clemente et al., 2019) . Understanding how the training load, during three consecutive days, affects players' fatigue is therefore important to find the best workload strategy.

2 Knowledge overview

2.1 Internal and external load

Estimation of training load is often done by using external and internal measurements (Halson, 2014) . External training load is defined as the work an athlete performs, and is measured in absolute terms, such as distance, speed, actions or power output during a given time. External load is important to measure the physical characteristics required of the sport and the physical capacity of an athlete. In team sports like football Global Positioning Systems (GPS) and digital video analysis systems are popular technology for measuring the external load in training and game (Halson, 2014)

Internal load, on the other hand, measures the physiological and psychological stress to which the individual is exposed during training or a match. The internal load and the internal effect of training can be measured objectively, e.g. by measuring heart rate during exercise and at rest, heart rate variation, oxygen uptake and blood and urine markers (Halson, 2014) . Internal load can also be measured subjectively, for example by rating perceived effort (RPE = rating of perceived exertion). This type of measurement can be used to estimate where a player is currently on the "tired-fresh" scale or to measure retrospectively perceived training intensity (Foster et al., 2001; Gaudino et al., 2015) .

2.2 Measuring workload - different approaches

In this chapter some questions about appropriate variables and different approaches among different tech-companies will be discussed.

Generally, football actions are classified and analysed based on the speed of the action. Even though a large part of the football game consists of movement in low speed, activities performed with high speed reflect the physical demands of the game and gets attention

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among professional coaches and in the literature (Nosek et al., 2021) . Studies have shown an increase in high intensity and sprint running distance by 30 respectively 35% in the English Premier League across 7 years period (2006/7-2012/13) while the total running distance remains unchanged (Barnes et al., 2014) . Furthermore, Mohr et al. (2003) found differences in high intensity movements between level of participation as top-class players performed 28 and 58% more high-intensity running and sprinting, respectively, Similar findings have been shown in women's football where top-class players covered 28% longer distance at high intensities and sprinted 24% longer than high-level players (Mohr et al., 2008) .

However, attention should not only be on distance covered at different running speed when assessing players' workload as such analysis does not take into account football specific movements such as accelerations, decelerations, backward and sideways running, jumping, tackling, passing and shooting. Activities that together appear several hundred times in a match and puts some physical stress on the player has to be taken into account when quantifying the workload (Bangsbo, 1994; Dalen et al., 2016) . With the development of triaxial accelerometers that record body movement acceleration in three dimensions (3D) (Dalen et al., 2016) some different accelerometry-based parameters have been created by sport technology companies to assess load in sports (Gómez-Carmona et al., 2019) . This technology has been found useful for quantifying physical demands and the “true workload” during a football game (Dalen et al., 2016) and shown to have higher correlation with internal training load compared to high-speed and very high-speed runs during football training (Scott et al., 2013) .

Advanced wearable technology such as a GPS with integrated inertial sensors and heart rate monitoring are commonly used in team sports to monitor the physiological and physical demands of the sport. However, different measures have been used in Sport Science to quantify training load and no gold standard exists. A consensus statement of the International Olympic Committee recommends using relevant internal and external load variables that are specific to the nature of each sport (Soligard et al., 2016) .

Polar Team 2 (Polar Electro Oy, Kempele, Finland) is, for example, a GPS and heart rate system used to collect objective, external and internal data. The system gives what Polar calls Training Load Score, a specific function, based on heart rate, calorie consumption, mechanical impact and the duration of training (Polar Research and Technology, 2017) , a function to quantify training intensity in the form of a numerical value that describes the use of critical energy reserves and should be able to be used when estimating the time needed to recover after a workout (Support Polar, 2016) . A similar system, Catapult Optimeye S5

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(Catapult Sport, Australian), has a variable called Player load as its variable to quantify training intensity. Player load is a function of the player's movement, i.e. the number of accelerations forwards, backwards and sideways as well as vertical movements measured with an accelerometer. Player load is calculated according to the following formula:

where a_y1 and a_{y 1}₋ stand for accelerations forward and backward, a_x1 and a_{x 1}₋ = lateral movements and a_z1 and a_{z 1}₋ = vertical movements (Hollville et al., 2015) .

GPEXE (Exelio srl, Italy) is the third system to mention with a different variable to measure the load as they use Metabolic Power (MP). MP is a product of energy cost of the activity (EC) and speed (V), derived from inclination and acceleration where accelerated running is considered to be equivalent to incline running at a constant speed where the angle between the runner and the surface is the same in both cases (Osgnach et al., 2010) .

This means that Catapult's Player Load and GPEXEs Metabolic Power are based on the external load on muscles and joints when estimating the training intensity, while Polar Team 2's focus is on internal load or energy consumption at high intensity.

Both internal and external load are important for understanding the players' training load. An integrated assessment of the load can thereof be important, where a combination of internal (subjective and objective) and external indicators are used to provide greater insight into the training load. For example, a player who repeats the same workout on different days can maintain the same external load even though the internal load (e.g. heart rate and

perceived rate of exertion) differs depending on that player's freshness, training history, illness or emotional state. It is this type of discrepancy between the external and internal load that can help differentiate between a fresh and a tired or exhausted player (Pyne & Martin, 2011) .

2.3 Training theories. Dose-response

The aim of the following section is to give an insight into relevant theories on fatigue, recovery and performance responses of athletes both to a single and repetitive training sessions.

There are several theories and models that are intended to show how training affects sports performance and these have long played an important role in training planning and

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especially in preparation for a competition. The models have in common that they assume that a given training impulse or training stress, which is the result of a training session, both have a positive and a negative effect. The positive effect is often called fitness, and the negative effect fatigue, and together these effects add value to the athlete's performance.

2.3.1 General Adaptation Syndrome - GAS

The first model to reach the world of sports is General Adaptation Syndrome (GAS), which was first introduced in the 1950s by researcher and endocrinologist Hans Seyle. The model is not specifically developed for training, but it is about how people adapt to stress of various kinds. The principle is that the body's response to stress is to become stronger and better prepared for the next opportunity, that is training or competition (Selye, 1951) .

Figure 1 illustrates three different examples on how the performance affects by repeated training impulse according to GAS. During a training session, performance deteriorates as you get more tired. After the training session, the performance curve begins to point upwards and after a certain time it exceeds the initial position (Figure 1, the blue and the green line) and you start to perform better than from the beginning. This is called supercompensation and is the positive effect of the training. The blue curve in Figure 1 shows where the timing of the next training session is at the top of the supercompensation curve with gradual improvement in performance as a result. The green line shows how the supercompensation effect decreases after a while if it takes too long before the next training stimulus occurs and the performance curve will re-adjust to the former baseline. Finally, the red line in Figure 1 illustrates where the rest is insufficient and the point of supercompensation will not be reached, with

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Figure 1. The GAS model. Examples of responses to repeated training impulse when sufficient (blue line), to long (green line) or insufficient (red line) recovery between sessions is provided (adapted from Cunaman et al., (2018) ).

2.3.2 Banister Fitness-Fatigue

The Banister fitness-fatigue model presented in the mid-70s, divides performance in two parts; a positive effect or athlete's real physical ability, called fitness and a negative effect, which is the athlete's fatigue. The performance is explained as the sum of these two parts (Banister et al., 1975) . After a hard workout the negative fatigue effect will be greater than the positive fitness effect, which means that performance deteriorates. With lighter training or rest, the level of fatigue will drop more than the level of fitness does with the associated improvement in performance. The following formula is used to calculate performance according to the Banister model;

w w p_t = p₀ + kat 1

∑

− x=0e (t s) r − − /a s− kf

∑

t 1− x=0e (t s) r − − /f _s

where stands for performance at time t, the initial performance, and are p_t p₀ ka kf constants for the size of the training effect on fitness and fatigue, respectively, and and ra rf are time constants that describe the time it takes for the effect of fitness and fatigue to

decrease. stands for the training load. Since fitness lasts longer than fatigue then is ws ra always greater than . In the original study, the values of = 1.0, = 1.8-2.0, = r_f ka kf ra

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49-50, = 11 were used. In most of the Fitness-Fatigue studies Banister's Heart Rate based r_f training impulse (TRIMP) has been used to quantify the training load. Other variables, more suitable for non-endurance and intermittent sports have also been used with good results (Coggan, 2008) .

Figure 2 shows how the Banister model can look like with simulated training data over a period of 120 days (Clarke & Skiba, 2013). In the bottom graph, the daily training load is drawn as a function of time. The athlete performs training sessions of 100 units (TRIMP) per day for 120 days. Thereafter, there were 7 days that included a gradual reduction in training load where daily TRIMP decreased by 10 units per day, i.e. down to 30. Training ceased thereafter. Fitness (PTE = positive training effect), fatigue (NTE = negative training effect) and performance were calculated from the simulated training load (TRIMPs) with the following parameter values: = 500, = 1, = 2, = 27 and = 10. p₀ ka kf ra rf

Figure 2. Performance as a function of fitness (PTE) and fatigue (NTE) according to the Banister model (Clarke & Skiba, 2013).

To adjust the model parameters to the athlete the Banister model requires large amounts of data and relevant performance tests and since the model parameters can change over time, these measurements must be obtained within short periods and repeated frequently (Banister 1975).

The Bannister Fitness Fatigue has been shown to account for >70%, and often >90%, of the day-to-day variation in athletes performance in a number of different sports, e.g., weight lifting, hammer throwing, running, swimming, cycling, triathlon (Busso et al., 1994;

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Coggan, 2008; Morton et al., 1990) . What these athletes have in common is that they are all doing individual sports, with longer build-up periods and shorter competition periods. During the build-up period the focus is on building fitness with acceptance of temporarily poorer performance. However, in football the competition season is long and occasions where the performance should be on top are more frequent, with a game day every 4 th _{to 7}th _{day during}

the entire competition season of about 8- 11 months.

2.3.3 Acute:Chronic Workload Ratio

Acute:Chronic Workload Ratio (ACWR), a simplified variant of the Banister model has been used to study the optimal relationship between fitness (Chronic Workload) and fatigue (Acute Workload) in team sports with shorter training cycles and more frequent competition, in among others football and rugby (Hulin et al., 2016; Malone et al., 2017) . Acute workload or fatigue is then often measured as the total training load during the last seven days, while Chronic Workload, which represents the players' fitness, is the average training load per week most often during the last four weeks. Different time windows and ratios for acute (2-9 days) and chronic (14-35 days) have been used as the best predictor of non-contact injury risk suggesting that the number of days for acute respective chronic time windows may need to be identified case by case and may depend on the structure of the competition and training schedule (Carey et al., 2017) . In accordance with the Banister model, ACWR gives an idea of how ready the player is to perform. If the long-term training load (Chronic Workload) is high (the player has built up good fitness) and the short-term training load (Acute Workload) is low (the player experiences minimal fatigue), then the player will be well prepared

(Gabbett, 2016) .

A number of studies have examined the optimal relationship between acute and chronic exercise load where it has been possible to identify how ACWR relates to the risk of injury. Figure 3 shows that in order to minimize the risk of injury, the ratio between acute and chronic training load should be between 0.8-1.3. This means an increased risk of injury if the load is too high or too low (Carey et al., 2017) .

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Figure 3. The relationship between ACWR and risk of injury (Carey et al., 2017) .

The ACWR can be calculated using two different models, the original rolling average model ( ACW R_RA) where the load from each session is weighted the same in the calculation and the exponentially weighted moving average model ( ACW R_{EW MA}) where the weight of the load gets less for each older session, giving the greatest weight to sessions performed most recent in time. Both of the models show significant relationships with the injury rate, but some research have reported ACW R_{EW MA} as the more sensitive one (Arazi et al., 2020; Griffin et al., 2020; Murray et al., 2017; Williams et al., 2017) .

2.4 Weekly periodisation in football

Football players are participating in a high number of matches. Due to the frequency of the matches, sometimes separated by as little as 48-72 hours, a large load is put on

physiological systems (Stølen et al., 2005) . Muscle soreness (Mohr et al., 2016) , reduction in strength (Oliver et al., 2008) and increased general fatigue (Ascensão et al., 2008) have been shown following football matches. Different oxidative stress and muscle damage markers are, moreover, shown to be negatively affected up to 72 hours following a match (Ascensão et al., 2008) . For these reasons, football coaching requires appropriate load control on a daily basis for performance improvement.

Guerrero-Calderón et al. (2021) found that physical output of players in match correlated with the training-load performed during the previous training week, as the training-total distance affected the match physical output negatively while training-high intensity distance (14-24 km/h) showed a positive effect on match physical output.

In several studies, authors have found that the highest training load in a one week microcycle is concentrated in the middle of the week, 4 and 3 days before the match and

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progressively decreases until the day before the match. (Clemente et al., 2019; Martín-García et al., 2018) .

Different workload strategies have been identified between two teams from different countries, where one of the team trained with higher intensity (measured in sprinting distance) and higher volume (total distance) all days during the week except the day before match where the other team were training with both higher intensity and more volume (Clemente et al., 2019) . Understanding how the weekly distribution of training loads affects players' performance and fatigue is therefore important to find the best training and tapering strategy.

A common experience among football players is that their body does not feel most sore or tired the day immediately after the match but even more so two days after the match. However, it may vary between players according to physiologist Paul Balsom (Sport, 2012) .

2.5 Perceived Rating of Fatigue

In the current study the relationship between training load and players' rating of fatigue, i.e. the negative effect of training, will be studied.

Quantifying an estimated level of physical or psychological status is not without its problems.

For instance Fatigue, measured in that way, is not a definite, objective unit but a personal and uncertain experience of physical status. Still, there is a need to determine our experiences, what they are about and how strong they are. Being able to make a

psychological estimate of physical properties on a ratio scale that contains properties such as order and distance as well as absolute zero point is an important subject in psychophysics (Borg, 1982) . A good example of that sort of scale is the RPE scale, also called the Borg scale, which was constructed in the 1960s by Professor Gunnar Borg who was a pioneer in this field. It is a rating scale of physical exertion that has been shown to give a linear growth with the load on work tests (Borg, 2003, 2013) . Since then different formats of RPE scales (Borg 6-20, CR10, CR100 and five-point scale) have been used to estimate symptoms such as exertion, nausea and discomfort (Borg, 2013; Lacome et al., 2018; Thorpe et al., 2016)

Rating-of-fatigue (ROF) is the dependent variable used in this study, an equivalent to the RPE scale for measuring fatigue on a ratio level. ROF is a relatively new scale designed by Micklewright et al., (2017) with the purpose to track the intensity of perceived fatigue in a variety of contexts. Previous studies on football players (Thorpe et al., 2016) and Australian

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rules football players (Gastin et al., 2013) have shown that a similar type of subjective appreciation is valid for detecting fluctuations in training load.

To my knowledge no research to date has used daily collected workload and wellness data to evaluate how accumulated workload, for three days in a row, affects perceived rating of fatigue among professional football players. By quantifying the weight of the effect day by day on players' wellness, a potential objective tool is developed. This may be used not only to predict players' fatigue, but above all, for coaches in mastering their training load plans and periodisation with regard to having players optimally trained and fresh at crucial moments.

3 Aim and research questions

3.1 Aim

The aim of the study is to improve the understanding of the relationship between different training- and match load variables and subsequent perceived rating of fatigue. This will be done by empirically investigating whether traditionally used external and internal training load variables function as good indicators of players' perceived rating of fatigue.

Furthermore, another aim is also to quantify the size and distribution of the accumulated workload variables effects, in a three-days sequence, on perceived rating of fatigue. That is the workload measured the day before, two days before and three days before the perceived rating of fatigue.

3.2 Research Questions

1) How effectively does traditional objective training load variables predict perceived rating of fatigue for football players?

By using a Distributed lag model based on daily observed data from a football team the following question will be answered:

2) How is the player’s perceived fatigue affected by the training load from three previous days?

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4 Method

4.1 Design and selection

This is a retrospective observational study in which thirteen male professional football players from an Allsvenskan football team participated (average age ± SD: 24.62 ± 3.01 years, height 180.23 ± 5.04 cm, weight 74.77 ± 5.89 kg). The players were distributed in the following way based on position; three midfielders, four central midfielders, three

fullbacks/midfielders and three forwards.

The sample is a convenience sample (Denscombe, 2000) as the researcher had access to earlier data collection from these football players. To be included in the study, players had been healthy and injury-free and participated in at least 90% of all training sessions and matches during the observation period, as well as four weeks before the start of data collection.

4.2 Ethical considerations

The participants were informed about the purpose of the study, that their participation was voluntary and about their right to withdraw from the study at any time. They were also informed that all data would be treated confidentially. The study processes were carried out in accordance with the Declaration of Helsinki and all the participants provided a written

informed consent. The length and weight of the participants were collected, analysed and presented as all other data as mean value (+/- SD) on a group-level. Personal data was treated with caution and not available for others. The data are generated from a daily monitoring routine among professional football players where players activities are measured and collected during the season.

4.3 Data collection

Data were collected during the period of 4 th _{February to 5}th _{March 2018. During the}

four weeks data collection took place, 21 training sessions and 4 training matches were carried out. Of these 25 occasions, two matches and 14 training sessions were held on artificial grass in Sweden and two matches and seven training sessions on natural grass in Portugal.

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During the training sessions the players worn a vest with a GPS unit that also collects heart rate. The data was collected continuously and were analysed afterwards. A total of 268 observations were made during training (19.54 ± 1.39 per player) and 43 observations during matches (3.31 ± 0.85 per player).

The ROF scale data was collected, every morning, from the Morning Wellness

questionnaire. The players received careful instructions on how to fill out the ROF scale. The ROF scale is described in chapter 4.3.2.

4.3.1 Independent variables

Internal load - Heart Rate

For each observation of training and match, players used Polar Team 2, short range telemetry system (Polar Team2 Pro System, Polar Electro Oy, Kempele, Finland). The

reliability of the system has been reported in previous studies (Macleod & Sunderland, 2012) . The system produces following internal load variables: time in different heart rate zones, calorie consumption, Adjusted TRIMP as well as Training Load Score (TLS), a function that combines several sources such as heart rate, calorie consumption and the duration of training (Polar Research and Technology, 2017).

External load - GPS and IMU

To measure the external load, each player was equipped with Polar GPS (Polar Team2 Pro System, Polar Electro Oy, Kempele, Finland). The device is attached to the Polar heart rate monitor and placed in the center of the player’s chest.

The measuring equipment uses data from GPS, the inertial measurement unit (IMU) and filtering algorithms to measure acceleration, speed and distance (Polar Research and Technology, 2017). Polar Team Pro uses 10 Hz GPS that has shown validated accuracy when measuring instantaneous speed (Varley et al., 2012) . Acceptable inter-unit reliability has been measured between two Polar units and low typical error of measurement (TEM) of the GPS units for total distance (TD, ICC 0.63) and distance in different speed zones (ICC 0.99). When compared to reference standard high ICCs were measured for TD (ICC 0.63) and Very high speed running (VHSR, ICC 0.65) and extremely high for Low speed running (LSR, ICC 0.99) and High speed running (HSR, ICC 0.92). Additionally, TEM was very low for TD (0.6%) and LSR (1.6%) but very high for HSR (13.8%) and VHSR (13.1%). Acceptable

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inter-unit reliability indicates that the Polar Team Pro GPS is suitable for tracking relevant team-sport variables. (Akyildiz et al., 2020) .

4.3.2 Dependent variable

Rating-of-fatigue (ROF)

Every morning at breakfast, players answered a Morning Wellness questionnaire via their mobile where they, among others, estimated their level of fatigue by using the ROF scale. It is an 11-point equidistant scale from 0-10, where the number 0 represents “Not fatigued at all” and the number 10 “Total fatigue and exhaustion - Nothing left” (Figure 4). A total of 370 questionnaires were analyzed during the observation period (26 ± 1.78 per player).

The ROF scale which includes numerical, descriptive and diagrammatic components has been found to have good face validity, implying that the scale could measure fatigue, high levels of convergent validity both during ramped cycling to exhaustion, 30 minutes resting recovery as well as

during daily living activities. As one might expect, ROF correlates strongly with RPE as well as various physiological markers during exercises. But a strong correlation is even found between ROF and physiological markers during recovery making ROF as an practical, inexpensive and useful method to track how players recover after activity (Micklewright et al., 2017) .

4.4 Data processing and analysis

Heart rate and GPS data were transferred to Polar Team Pro web service and on to Microsoft Excel where following standardised metrics were assessed for the analysis:

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External load: Total distance (m), High intensity distance (m), Accelerations(ms -2 _),

Decelerations (ms -2 _{), Number of sprints (n).}

In accordance with Polar default settings, sprint was considered as an action when a player exceeded an acceleration value over 2.8 ms -2 _{, High intensity distance as total distance}

in speed >14 km h -1 _{. Accelerations and decelerations were categorised as a change in speed}

>3ms -2 _{(Polar, 2018; Polar Research and Technology, 2017) . During the same period, the}

players' perceived ratings of fatigue were obtained every morning by using google sheet Wellness questionnaire.

Correlations, tables, diagrams and estimation of models were made using Microsoft Excel (Microsoft Corporation, USA) and SAS (SAS Institute Inc, USA).

4.5 Statistics

4.5.1 Descriptive statistics

Table 1 describes the variables used in the study, to create an understanding of how large the effects in the results are. The variables minimum and maximum value are presented as well as mean value and standard deviation. A minimum value of zero for the training load variables is explained as the model takes into account days when there were no training sessions.

Table 1. Descriptive statistics

Variable N Mean Std Dev Minimum Maximum

Fatigue - ROF (au) 370 3.26 1.49 1 8 Total distance - TD (m) 312 5 048 3 948 0 16 169 High intensity distance - HID (m) 312 1 572 1 545 0 7 280

Accelerations (n) 312 9.7 13.1 0 59

Decelerations (n) 312 13.7 15.2 0 56

Number of Sprints (n) 312 13.9 17.2 0 83 Training load score - TLS (au) 312 102 94.5 0 379 Heart rate average (%) 312 47.2 27.4 0 79 Adjusted TRIMP 312 160.8 137.0 0 535.7

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4.5.2 Correlation analysis

Correlation analyses were performed to detect the strength of the linear relationship between the objective internal and external load variables and perceived ratings of fatigue. This was done to evaluate how effectively those variables works as an estimator for players' fatigue.

To classify magnitudes of correlations between individual workload metrics and measures of fatigue following criteria were adopted: 0.1, trivial; >0.1-0.3, small; >0.3-0.5, moderate; >0.5-0.7, large; >0.7-0.9, very large; and >0.9-1.0, almost perfect (Hopkins, 2000) . Confidence intervals (95%) were also calculated.

Furthermore, a simple linear regression model was performed to describe this

relationship visually using fatigue as the dependent variable ( Y ), objective internal or external load variable as the explanatory variable ( X _i) and the error term : μ_i

Eq. 1 Y_i = β₀+ β_{1 i 1}X₋ + μ_i

For the Pearson r correlation and the linear regression, both variables should be normally distributed, have a linear relationship and be homoscedastic ( Pearson Correlation Assumptions , 2013) .

4.5.3 Distributed lag Regression model

The simple linear regression model in equation 1 combines all observations from the dataset and estimates a total model. This type of model overlooks the time series nature of the data material used and assumes that the fatigue is based only on yesterday's training session. To answer the question on how training variables during a series of three days are affecting players' fatigue, time delayed, or so-called lagged variables like the following equation for Distributed lag model explains are needed:

Eq. 2 Y_t= β₀ + β_{1 t 1}X₋ + β X_{2 t 2}₋ + β_{3 t 3}X₋ + μ_t

were , and are coefficients explaining to which extend the objective training β₁ β₂ β₃ variables from one, two respective three days before are affecting the fatigue. The intercept,

, is equal to the level of fatigue ( ) given no training exposure for the three previous

β₀ Y_t

days ( X_{t 1}₋ = X_{t 2}₋ = X_{t 3}₋ = 0) (Schliep et al., 2021) .

By using time series data and estimating the lag distribution one can consider not only how much effect workload variables have on players' level of fatigue but also when it has the

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effect. Does it come immediately? Decrease rapidly or slowly? Or is it maybe worst on the second day?

One key assumption when it comes to ordinary regression analysis is that the errors should be independent of each other. However, when using time series data the error term often becomes serially correlated or autocorrelated, which makes the ordinary least-squares (OLS) parameter estimates not desirable to use. Durbin Watson test was used to detect autocorrelation and regression estimates correction was done by using the Yule-Walker estimation method in AUTOREG procedure in SAS (SAS Institute Inc, 2015) .

5 Results

5.1 Efficiency of training load variables

As Table 2 shows, is fatigue correlated with all of the selected training- or match load variables measured the day before. The correlation was rated small (Heart rate average) or moderate (other variables). No significant difference was found between the strength of the correlation coefficient except between Training load score and Heart rate average.

In Figure 5a, 5b and 5c perceived rating of fatigue is explained as a linear function of different training load variables.

Table 2. Correlations between Perceived ratings of fatigue and internal and external training load measured the day before.

Pearson Correlation Statistics

Variable With Variable N Sample Correlation 95% Confidence Limits Fatigue Total distance (m) 269 0.451 0.350 0.541 Fatigue High intensity distance (m) 269 0.434 0.331 0.526 Fatigue Accelerations (n) 269 0.395 0.289 0.491 Fatigue Decelerations (n) 269 0.321 0.217 0.431 Fatigue Number of Sprints (n) 269 0.410 0.305 0.505 Fatigue Training load score (au) 269 0.473 0.375 0.561 Fatigue Heart rate average (%) 269 0.267 0.152 0.374 Fatigue Adjusted TRIMP (au) 269 0.471 0.372 0.559

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Figure 5a. Relationship between total distance (m) and perceived rating of fatigue (au).

Figure 5b. Relationship between training load score (au) and perceived rating of fatigue (au).

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As Figures 5 a-c shows, there is a positive relationship between these three training load variables selected and fatigue measured the following day. The slope of the regression line indicates that today’s fatigue increases by 1-unit for every 5000m TD ( β₁ = 0.0002), or

133 units of Training Load Score ( or 27 sprints ( from

~ β₁ = 0.0075) ~ β₁ = 0.0373)

yesterday's session. The intercept is between 2.5 and 3 indicating the mean of today's fatigue given that yesterday’s training load is equal to zero. The training variables in this model are explaining 16.8 to 22.4% of the variance in fatigue.

5.2 Distribution of training load affect from three previous days

Everyone who has trained a hard workout has experienced that the fatigue not only exists during the day after the workout, but will last for more days.

A Distributed lag regression model is used to investigate whether and how players' perceived rating of fatigue is still affected one, two and three days after a training session or game. In this model Polar Training Load Score is used as an explanatory variable.

The result in Table 3 shows that the estimated coefficients for the three lagged variables for Training load score are significantly different from zero. Estimated slope coefficient for TLS from the day before (one time lag) is 0.0100, for TLS with two time lags 0.0074 and TLS with three time lags 0.0036. The distribution and weight of the effect is graphically expressed in Figure 6. TLS with one time lag are significantly different from TLS with three

Table 3. Distributed lag model. Estimated coefficients for time lagged TLS variables

Distributed lag regressions. Fatigue vs TLS (lag1, lag2, lag3) The AUTOREG Procedure

Yule-Walker Estimates

Variable Estimate StdErr t Value Pr > |t| 95% Confidence Limits

Intercept 1.397 0.3329 4.20 <.0001 0.7191 2.0754 Tls_lag1 0.0100 0.0009 10.73 <.0001 0.0081 0.0119 Tls_lag2 0.0074 0.0012 5.88 <.0001 0.0048 0.0099 Tls_lag3 0.0036 0.0010 3.50 0.0006 0.0015 0.0057

Total R-Square Durbin-Watson Root MSE fatigue Mean

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lags, note however, that the slope coefficients are not significantly different between TLS lag 1 and TLS lag 2 or TLS lag 2 and TLS lag 3. The distributed regression with three lags is explaining 59.7% of the variance in fatigue.

Figure 6. Distribution of the effect of workload (TLS) with three time lags on fatigue

6 Discussion

The aim of the current study was to improve the understanding on the relationship between different training- and match load variables and subsequent perceived rating of fatigue. This was done by quantifying how effective traditional internal and external training load variables are to predict perceived rating of fatigue in a sample of professional football players' during preseason. Another aim was to study how the training load from previous three days training sessions are affecting players' perceived fatigue day by day.

A moderate linear correlation was found between Fatigue and the following internal- and external variables: Total Distance, High intensity distance, Acceleration, Deceleration, Number of Sprints, Training load score and Adjusted TRIMP. The correlation coefficients ranged from 0.328 to 0.473, meaning that these variables from yesterday's training are explaining between 10.8-22.4% of the variance in today's fatigue. The findings support the usability of different internal- and external load metrics to quantify the workload (Dalen et al., 2016; Hader et al., 2019) and are in line with the International Olympic Committee

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recommendations of using relevant internal and external variables to monitor physiological and physical demands of the sport (Soligard et al., 2016) .

The fact that no more than 22.4% of the variance in fatigue is explained by the training load from the day before supports the theory that today's fatigue is not only dependent on yesterday's training, but also on the training the day or days before. To quantify the day by day effect of training load on fatigue, a Distributed lag model was used. The model, applied in this study, includes a series of explanatory variables, lagged or delayed in time, accounting for the temporal variability in the response variable, fatigue. Training load score (TLS) was used as the explanatory variable (Figure 6) as one of the variables showing moderate correlation with day to day fluctuation in fatigue (Table 2). The coefficients of these lagged variables can be used as an index to quantify the short- (one day) and long-term (two and three days) effects of Training load score on fatigue. Similar models can be made with other of the associating variables. The results showed that players' freshness, for this sample of players, were in general negatively affected (i.e. fatigue was positively affected) by the workload, measured in Training load score, from the previous three days workout. The previous day workout (lag 1) showed to have the most significant impact followed by decreased effect for lag 2 and lag 3. The coefficients can be used as an index to estimate the effect of training load from three consecutive days on fatigue as following: The coefficient for lag 1 (0.0100) means that a Training load score of 100 units from yesterday's session will affect today's fatigue by one unit (0.0100 100). the coefficient for lag 2 (0.0074) means that · a Training load score of 100 units from the training session two days ago will affect today's fatigue by 0.74 units (0.0074 100) and the coefficient for lag 3 (0.0036) means that a · Training load score of 100 units from a session three days ago will affect today's fatigue by 0.36 units (0.00036 100). The fact that there was a decreasing size of the estimated ·

coefficients supports the theory that yesterday's workout (lag 1) has the biggest significant impact on fatigue, the day before yesterday's workout the second biggest impact and the workout three days back in time the least impact. This supports the use of exponential

weighted average calculation above rolling average when choosing the best ACWR predictor (Arazi et al., 2020; Griffin et al., 2020; Murray et al., 2017; Williams et al., 2017). This is moreover, in line with the Banister equation where both fitness and fatigue decay

exponentially with time (Morton et al., 1990) .

In theory, these results can be interpreted as follows: We have a case where there are three days to an upcoming game. We are planning for two training sessions and one day off.

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One of the training sessions with 200 TLS-units and one with 100 TLS-units. There are two scenarios to choose between, the first one is to take a day off the day called M-3 (three days before the match), then train the harder session at M-2 (two days before the match) and the lighter session at M-1 (the day before match). The second scenario is to train the harder session at M-3, day off at M-2 and lighter session at M-1. In terms of fatigue-units brought from these three days to the game it means following:

Scenario 1: M-3 = 0 units. M-2 = 1.58 units (0.0074 200). M-3 = 1.00 unit (0.0100 · · 100). Total fatigue units = 2.58

Scenario 2: M-3 = 0.72 units (0.0036 200). M-2 = 0 units. M-3 = 1.00 unit (0.0100 · · 100). Total fatigue units = 1.72.

In other words, according to Banister and earlier mentioned training theory models (Banister 1975, Carey et al., 2017), and thus given that the positive effect of training

decreases at a slower rate than the negative effect, then choosing the second scenario seems more logic when it comes to the best physical preparation for the game. Despite this, a periodization like in scenario 1 is quite common in football (Sports, 2020; Verheijen, 2014) .

As mentioned, Training load score (TLS) was in this study used as the only training variable explaining players' fatigue by the load from three previous days. Additional

associating variables should be tested when the model is used in “real life” and might show a different distribution of the day by day effect.

It is a simplification of a complex reality of training response but at the same time this is a fact for the means for the group studied during that period of time. It is important to keep in mind that the data shows the general response by a team of players during a certain period of time and that there are individual differences in players' response.

Method discussion and limitations

With the Banister model as a starting point, the effect of training load on fatigue was specifically investigated, i.e. not the effect directly on players' physical performance ability. As mentioned before, the optimal outcome measure might be the one that represent the players' performance, but at the same time it is difficult to test for physical performance in a complex sport such as football, partly because football performance is difficult to define, and in this case because of the retrospective form of this study where the researcher did not have the opportunity to influence with some interventions in the form of physical testing.

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A challenging task for a researcher is to make causal inferences from non-experimental data, where the most difficult problem is to control for variables that have not been measured or observed. With a Random experimental trial the problem is solved as the random samples make those groups approximately equal in characteristics.

The idea to use historical daily collected data from GPS and Heart rate monitoring combined with rating of wellness and no extra intervention to evaluate the effect of training has its advantages. To improve the setup, the data could be combined with objective

performance data, or biochemical markers to provide greater insight into training response. At the same time these tests are time consuming, functionally limited for football and require high levels of personal and technical support (Rebelo et al., 2014) . Guerrero-Calderón et al. (2021) found that the accumulated TD from previous week training sessions negatively affected physical output in matches, while high intensity running distance during the training week affected the match physical output positively. In that case it is certainly an accumulated six days training load to discuss compared to three days accumulated load in the current study, but adding a response variable measuring performance and not only fatigue would clearly enrich the model.

During the period the data was collected the team in the current study were playing on two different surfaces, in two different countries. These are external factors that varies between teams and should be taken into account when planning the training load.

Furthermore, it is important to keep in mind that the variation in the response depends as well on individuals responding differently on given physical stimulus, these differences may depend on individual biological differences or individual factors not directly depending on the sport activity like physical symptoms/illness, general health/well-being, motivation, quality of sleep etc. (Soligard et al., 2016). This gives extra weight to practitioners to monitor the load and the response on individual level and not only on team average.

In order to be able to use linear regression, it is required that the dependent variable, in this case fatigue, is on a continuous interval or ratio scale. This means that what you measure can be assigned a numerical value where it makes sense to enter distance between two measured values. Since the fatigue variable is a self-estimation of physical fatigue related to exercise, one might think it is most natural to classify it as an ordinal scale variable and more appropriate statistical methods would be to use logistic regression. However, the ROF scale is designed as an ratio scale with numbers were differences are equidistant (Micklewright et al., 2017) and when it comes to the criterion that the dependent variable needs to be continuous to be able to use linear regression, it is theoretically possible that the player's level of fatigue,

The effect of three days accumulated workload on football players’ perceived fatigue during Pre-Season