Resultant equations for training load
monitoring during a standard microcycle
in sub-elite youth football: a principal
components approach
José Eduardo Teixeira1,2,3, Pedro Forte1,2,4, Ricardo Ferraz1,5,
Luís Branquinho1,4, Ryland Morgans6, António José Silva1,7,
António Miguel Monteiro1,2 and Tiago M. Barbosa1,2
1 Research Centre in Sports, Health and Human Development, Covilhã, Portugal
2 Department of Sport Sciences, Instituto Politécnico de Bragança, Bragança, Portugal
3 Department of Sport Sciences, Polytechnic Institute of Guarda, Guarda, Portugal
4 CI-ISCE Douro, Higher Institute of Educational Sciences of the Douro, Penaﬁel, Portugal
5 Department of Sport Sciences, University of Beira Interior, Covilhã, Portugal
6 Institute for Coaching and Performance, University of Central Lancashire, Preston,
United Kingdom
7 Sport Sciences, University of Trás-os-Montes and Alto Douro, Vila Real, Portugal
ABSTRACT
Applying data-reduction techniques to extract meaningful information from
electronic performance and tracking systems (EPTS) has become a hot topic in
football training load (TL) monitoring. The aim of this study was to reduce the
dimensionality of the internal and external load measures, by a principal component
approach, to describe and explain the resultant equations for TL monitoring during a
standard in-season microcycle in sub-elite youth football. Additionally, it is intended
to identify the most representative measure for each principal component. A
principal component analysis (PCA) was conducted with a Monte Carlo parallel
analysis and VariMax rotation to extract baseline characteristics, external TL, heart
rate (HR)-based measures and perceived exertion. Training data were collected from
sixty sub-elite young football players during a 6-week training period using 18 Hz
global positioning system (GPS) with inertial sensors, 1 Hz short-range telemetry
system, total quality recovery (TQR) and rating of perceived exertion (RPE). Five
principal components accounted for 68.7% of the total variance explained in the
training data. Resultant equations from PCA was subdivided into: (1) explosiveness,
accelerations and impacts (27.4%); (2) high-speed running (16.2%); (3) HR-based
measures (10.0%); (4) baseline characteristics (8.3%); and (5) average running
velocity (6.7%). Considering the highest factor in each principal component,
decelerations (PCA 1), sprint distance (PCA 2), average HR (PCA 3), chronological
age (PCA 4) and maximal speed (PCA 5) are the conditional dimension to be
considered in TL monitoring during a standard microcycle in sub-elite youth football
players. Current research provides the ﬁrst composite equations to extract the most
representative components during a standard in-season microcycle in sub-elite youth
football players. Futures research should expand the resultant equations within
training days, by considering other well-being measures, technical-tactical skills and
match-related contextual factors.
How to cite this article Teixeira JE, Forte P, Ferraz R, Branquinho L, Morgans R, Silva AJ, Monteiro AM, Barbosa TM. 2023. Resultant
equations for training load monitoring during a standard microcycle in sub-elite youth football: a principal components approach.
PeerJ 11:e15806 DOI 10.7717/peerj.15806
Submitted 26 January 2023
Accepted 7 July 2023
Published 4 August 2023
Corresponding author
Tiago M. Barbosa, barbosa@ipb.pt
Academic editor
Silvia Comani
Additional Information and
Declarations can be found on
page 15
DOI 10.7717/peerj.15806
Copyright
2023 Teixeira et al.
Distributed under
Creative Commons CC-BY 4.0
Subjects Kinesiology, Sports Injury, Sports Medicine
Keywords Youth, Workload, Soccer, Global positioning system, PCA
INTRODUCTION
Training load (TL) monitoring has become a research hot topic in youth football
(Impellizzeri et al., 2022; Staunton et al., 2021). This is largely due to the growing access to
electronic performance and tracking systems (EPTS) that provides valid TL measures (de
Dios-Álvarez et al., 2021; Oliva-Lozano & Muyor, 2022). In recent years, the weekly TL
variation has been extensively analyzed in elite and sub-elite football contexts (Teixeira
et al., 2022a). Training monitoring has been extensively performed using objective and
subjective methods to monitor internal training load (ITL) and external training load
(ETL) (Impellizzeri et al., 2022). Global positioning system (GPS) devices have become a
customary, low-cost and optimal navigation satellite system to extract valid and reliable
ETL outcomes (e.g., distances, sprints, accelerations (ACC), change of directions or body
impacts) (Beato et al., 2018; Buchheit et al., 2021). Otherwise, the ITL has been usually
monitored by heart rate (HR) and perceived exertion using non-invasive wearable sensor
systems, rating perceived exertion (RPE) and total quality recovery (TQR) scales (Haddad
et al., 2017; Brink et al., 2010). The research has shown a signiﬁcant correlation between
ETL and ITL in young athletes, however it is still difﬁcult to interpret ﬁtness-recovery
status (Impellizzeri et al., 2022). Combining ETL and ITL has been reported as a valid
strategy to analyse dose-response dissonances, however the major inﬂuencing factor
remain to be deﬁned (Bourdon et al., 2017; Teixeira et al., 2021a).
Additionally, the emergent tracking tools appears to have created confusion in
dose-response considerations given the data analysis requirement to extract relevant
information from large amounts of data (Grifﬁn et al., 2021; Scantlebury et al., 2020). This
kind of tracking device can provide big datasets express as a thousand data per second
expressed by a large number of variables depending on the time-motion technology used
(Rojas-Valverde et al., 2020; Ruan et al., 2022). Otherwise, another challenge has been to
standardize the physical and psychophysiological data in meaningful information
(Impellizzeri et al., 2022; Staunton et al., 2021; Vanrenterghem et al., 2017). As well,
capturing the training frequency, intensity, time/duration, type, volume, and progression
(FITT-VP) variables is another critical challenge created by tracking systems (Staunton
et al., 2021; Scantlebury et al., 2020). Thus, it is more critical than ever to turning datasets
into relevant information for athlete-monitoring cycle (Teixeira et al., 2021a; Weaving
et al., 2019). Afterwards, the data-reduction techniques has been applied to explain the
dimensionality of the TL variables in different football codes such as futsal (Rico-González
et al., 2022a), Australian football (Sheehan et al., 2020), rugby (Scantlebury et al., 2020;
Weaving et al., 2020) and Gaelic football (Gamble et al., 2019).
Principal component analysis (PCA) is one of the most used data-reduction techniques
to extract redundant information from TL data in football (Rico-González et al., 2022b;
Rojas-Valverde et al., 2020). Using a PCA approach, a signiﬁcant percentage of the total
variance in a dataset can be extracted (Warmenhoven et al., 2019). Thus, PCA analysis
allows to reduce the complexity in a large group of correlated variables by determining the
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principal components (O’Donoghue, 2008; Rojas-Valverde et al., 2020). Recently, a
systematic review conducted in football reported a 77.1% of explained variance in 12.8
extracted variables out of 51.4 variables distributed over 6.4 principal components (Rojas-
Valverde et al., 2020). However, the studies with PCA approaches has focused mainly on
TL monitoring in professional and elite youth football (Casamichana et al., 2019;
Scantlebury et al., 2020; Sheehan et al., 2020). Until now, PCA approaches were only
applied in elite football contexts to simplify the TL having regard to different game formats
(Casamichana et al., 2019; Zurutuza et al., 2020), contextual factors (Gonçalves et al., 2019;
Oliva-Lozano et al., 2021), competition level (Ricotti et al., 2013), positional role (Moura
et al., 2015), tactical behaviour (Ric et al., 2016; Rico-González et al., 2022b) and motor
skills (Los Arcos, Mendiguchia & Javier, 2017). Recently, some studies have described the
application of TL monitoring strategies during a weekly microcycle in sub-elite youth
football, expressing by a low seasonal variation and a high weekly variation (Teixeira et al.,
2021b, 2022b). Therefore, it is important to establish the major inﬂuencing factor for an
accurate training monitoring and manipulation during a standard microcyle. Also, an
optical TL monitoring can enhance a proper long-term athlete development, injury
prevention and training design (Pino-Ortega et al., 2021; Rico-González et al., 2022c; Rojas-
Valverde et al., 2020). More speciﬁcally, this can help research, practitioners and coaches to
prescribe adequate training intensity over a standard microcycle in youth football (Rico-
González et al., 2022a). Therefore it is critical to standardize and reduce the dimensionality
of the weekly training data in young football players from sub-elite contexts (Teixeira et al.,
2022c; Trecroci et al., 2018). Thus, the aim of this study was to reduce the dimensionality of
the internal and external load measures, by a PCA approach, in order to describe and
explain the resultant equations for TL monitoring during a standard microcycle in a
sub-elite youth football players. Additionally, it is intended to identify the most
representative measure for each principal component.
METHODS
Participants
Sixty sub-elite youth and male football players were included this study from an under (U)
15 (n = 20), U17 (n = 20) and U19 (n = 20) sub-elite youth football academy (Table 1).
All parents or legal guardians were written briefed about research aims and risks, providing
a written consent for participant’s inclusion. The research was developed in accordance
with the Declaration of Helsinki (Winter & Maughan, 2009) with an ethical approval from
the local Ethical Committee from the University of Trás-os-Montes e Alto Douro (3379-
5002PA67807).
Quasi-experimental approach
Current research has a prospective, observational and cross-sectional design, by applying
an individual TL strategy via GPS technology, HR monitoring system, RPE and TQR
scales. Resultant equations for TL monitoring in sub-elite youth football was obtained by a
PCA approach. The weekly TL was continuously monitored during 2019–2020 in-season,
representing a total of 6-week period from 18 training sessions and 324 observation cases
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(Teixeira et al., 2021b, 2022d). A minimum of 150 observation cases (i.e., 5 to 10 cases per
variable) was assured to perform PCA analysis (Jolliffe & Cadima, 2016). Figure 1
summarizes the procedures for quasi-experimental approach.
Procedures
The training data eligibility considered the following inclusion criteria: (a) youth football
players aged between 13 and 20 years old (i.e., U15, U17 and U19) (Teixeira et al., 2021a);
(b) young football players should have at least 5 years of competitive experience in football
(Ford et al., 2020); (c) training data featured at least 35 consecutive playing minutes
without any break for injury, abandonment or other arbitrary reason (de Dios-Álvarez
et al., 2021); (d) training data considered a competitive one-game week schedule and three
training sessions per week (Teixeira et al., 2021b, 2022a). The exclusion of cases occurred
when the following exclusion criteria were met: (a) event of absence, injury, illness and
abandonment during monitored training sessions; (b) players that were not integrated in
the common team session due to rehabilitation, complementary and/or individual training
sessions; (c) the match data was not included in the analysis (Teixeira et al., 2022d).
For ETL and ITL monitoring, each participant wore the micro-technology (i.e., GPS and
HR) within a little pocket on the upper back between both scapulae of a custom-made vest
Table 1 Description baseline characteristics of participants.
Variables
U15 (n = 20)
U17 (n = 20)
U19 (n = 20)
Overall (n = 60)
Age (y)
13.28 ± 0.49
15.39 ± 0.51
17.29 ± 0.55
15.19 ± 1.75
RA (a.u.)
0.25 ± 0.17
0.25 ± 0.17
0.24 ± 0.20
0.25 ± 0.18
MO (a.u.)
−0.42 ± 0.76
2.02 ± 1.09
2.23 ± 1.49
1.33 ± 1.67
Height (m)
1.69 ± 0.78
1.76 ± 0.48
1.76 ± 0.70
1.74 ± 0.08
Weight (kg)
55.67 ± 9.41
64.28 ± 6.61
68.90 ± 8.39
62.48 ± 10.03
BMI (kg/m2)
19.29 ± 1.99
20.68 ± 1.79
22.11 ± 1.50
20.61 ± 2.14
Sitting height (cm)
81.96 ± 5.78
92.02 ± 7.61
90.73 ± 8.06
88.36 ± 8.51
PHV (cm)
14.18 ± 0.80
13.90 ± 1.09
14.46 ± 1.87
14.20 ± 1.39
Experience (y)
4.82 ± 0.90
6.64 ± 1.65
8.81 ± 1.70
6.76 ± 1.42
Note:
Abbreviations: a.u., arbitrary unit; BMI, body mass index; MO, maturity offset; PHV, peak high velocity; RA, relative age;
y, years.
Figure 1 Training load monitoring using a prospective, observational and cross-sectional design.
Full-size
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DOI: 10.7717/peerj.15806/ﬁg-1
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(Beato et al., 2018). All methodological procedures for ETL and ITL were previously
applied for 2 weeks to familiarize players with data collection (de Dios-Álvarez et al., 2021).
Using a “match day minus format” (MD), the weekly microcycle included the training
sessions MD-3 (Tuesday), MD-2 (Wednesday), and MD-1 (Friday). The number of
observation for each training day was: MD-3 (n = 41), MD-2 (n = 38), and MD-1 (n = 44)
(Teixeira et al., 2022d, 2021b). The training days for the three age groups were the same
following this order: U15—6 to 7:30 PM; U17—7:30 to 9:00 PM; U19—9:00 PM to 10:30
PM. The average duration of training sessions had the following lengths for each age
group: U15 = 148.99 min; U17 = 132.46 min; U19 = 195.95 min. Medical and logistical
staff members ensured that all training classes had standardized clothes, nutrition and
medical care during training sessions (Teixeira et al., 2022d). All training sessions were
performed on a synthetic turf outdoor pitch with ofﬁcial dimensions (FIFA standard;
100 m × 70 m) and similar environment conditions (i.e., 14–20 C; relative humidity
52–66%) (Coutinho et al., 2015).
Weekly standard microcycle
Table 2 showed the weekly training overview in the studied sub-elite youth football
academy. The standard microcycle was planned in accordance with the following key
points: (i) training aims, time duration and pitch dimensions; (ii) physiological target and
speed, agility and quickness (SAQ) emphasis; (iv) training tasks and exercises. Weekly
training overview was designed according to ﬁeld notes and academy training model. Also,
current typical microcycle was designed during an in-season standard microcycle with
aforementioned training days (i.e., MD-3, MD-2 and MD-1) (Branquinho, Ferraz &
Marques, 2021; Rago et al., 2020). Small, medium, large-sided, and simulated games (i.e.,
Table 2 Weekly standard microcycle in the sampled sub-elite youth football academy.
Construct
MD-3 (Tuesday)
MD-2 (Wednesday)
MD-1 (Friday)
Aim (tactical) Recovery/technical skills
Acquisitive training focused on game
principles (collective behaviour and
organization)
Finishing situations and tactical schemes
Duration
90 min
90 min
90 min
Dimensions
50 m × 60 m (half ﬁeld)
100 m × 60 m (entire ﬁeld)
50 m × 60 m (half ﬁeld)
Physiological
set
75–80% HRmax
90–95% HRmax
>85% MRS
SAQ
Strength (Quickness, COD
and agility)
Endurance/Aerobic
Speed
Warm up
Technical and coordination
skills
Dynamic stretching
Plyometric exercises and SSC
Training
tasks
(1) SSG, MSG, and ball
possession (small areas);
(1) Ball possession, LSG and simulated games; (1) Finishing exercises (i.e., individual, sectional and
intersecional situations: 1 × 0 + GK to 11 × 0 + GK);
(2) Individual enrichment
training (i.e., 1v1 to 3v3).
(2) Game strategy.
(2) Tactical schemes (i.e., outsides and corners).
Note:
Abbreviations: COD, change of direction speed; GK, goalkeeper; HRmax, maximal heart rate; LSG, large-side games; MD, “match day minus” format; MSG, medium-sided
games; MRS, maximum running speed; PHV, peak high velocity; SAQ, speed, agility and quickness; SSC, stretch-shortening cycle; SSG, small-sided games.
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SSG, MSG, LSG) was categorized in accordance with Zurutuza et al. (2020). The SAQ
training was classiﬁed by Trecroci et al. (2016) for sub-elite football players.
Training load measures
Table 3 described the construct, measurement unit, and formula for each ETL and ITL
measure. All constructs were considered according to previous TL-based reports,
speciﬁcally: (i) total distance (TD); (ii) average running velocity; (iii) high-speed running
(HSR); (iv) explosiveness, ACC and body impacts; (v) HR-based measures; and (vi)
perceived exertion and recovery (Rico-González et al., 2022a; Sheehan et al., 2020; Teixeira
et al., 2021a).
External load measures
The ETL was tracked using a 18 Hz global positioning system (GPS) coupled with
accelerometer (100 Hz), magnetometer (10 Hz) and gyroscope (100 Hz) (STATSports
Apex, Northern Ireland) (Buchheit et al., 2021). With a reliable satellite signal, all devices
were turned on 30 min before the training data collection (Beato et al., 2018; Buchheit et al.,
Table 3 Construct, description and formulas from external and internal training load.
TL
Constructs
Variable
Description and formula
ETL Total distance
TD (m)
Total distance covered (in meters)
Average running velocity
AvS
(m·min−1)
Game pace or average speed distance in meter per minutes.
MRS (m·s−1) Maximal speed in meter per seconds
High intensity running
rHSR (m)
Relative high-speed running (rHSR) distance (m) covered at 19.8–25.1 km·h−1.
SPR (n | m)
The sprints were measured by number and average sprint distance (m) in a velocity >25.1 km·h−1.
Explosiveness,
accelerations and
impacts
HMLD (m)
High metabolic load distance (HMLD) is a metabolic variable deﬁned as the distance, expressed in
meters, covered by player when the metabolic power exceeds 25.5 W·kg−1.
DSL (au)
The DSL was computed by measuring the sum of the accelerations in the three orthogonal axes of
movement (expressed as a G force > 2G).
ACC | DEC
(m·s−2)
Number of accelerations (>3 m·s−2) and decelerations.
ITL
HR
HRmax
(bpm)
Maximum heart rate (HRmax)
AvHR
(bpm)
Average heart rate (AvHR).
%HRmax
Percentage of HRmax (%HRmax)
TRIMP (au)
Akubat TRIMP (iTRIMP) = Training duration × 0.2053e3.5179x. Among which e = Napierian
logarithms, 3.5179 is the exponent, and x = HRratio.
Perceived exertion
and recovery
RPE (au)
Perceived exertion was measured by 15-point Portuguese Borg Rating of Perceived Exertion 6–20
Scale (Borg RPE 6–20).
sRPE
The sRPE was obtained by multiplying total duration of training sessions for each individual RPE
score.
TQR (au)
To monitor recovery, each player was asked to report the TQR score on a scale from 6 to 20.
Note:
Abbreviations: ACC, acceleration; AvHR, average heart rate; AvS, average speed; DEC, deceleration; HMLD, high metabolic load distance; HRmax, maximal heart rate;
MRS, maximum running speed; SPR, average sprint distance; SPR_N, number of sprints; sRPE, session ratings of perceived exertion; TD, total distance; TL, Training load;
TQR, total quality recovery; TRIMP, training impulse.
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2021). The accuracy of GPS Apex devices was good (bias 5%) (Beato et al., 2018).
The ETL measures were as follows: TD covered (m), average speed (AvS (m·min−1)),
maximal running speed (MRS (m·s−1)), relative high-speed running (rHSR (m):
19.8–25.1 km·h−1) distance (m), high metabolic load distance (HMLD (m) > 25.5 W·kg−1),
number sprints (n) and average sprint distance (SPR (m) (>25.1 km·h−1)) (m), dynamic
stress load (DSL (a.u.)), number of ACC (>3 m·s−2) and number of decelerations
(DEC < 3 m·s−2) (Teixeira et al., 2021b, 2022a) (Table 3).
Internal training load measures
The ITL were obtained by RPE, TQR, and the HR monitors. A Garmin TM HR band
(Garmin Ltd, International Ltd., Olathe, KS, USA) was used to capture HR-based
measurements utilizing a 1 Hz short-range telemetry system (Gómez-Carmona et al.,
2020). Maximum heart rate (HRmax), average heart rate (HRmean), percentage of HRmax (%
HRmax) and individual players’ training impulse (TRIMP) were monitored (Akubat et al.,
2012; Branquinho, Ferraz & Marques, 2021). The Yo-Yo intermittent recovery test level 1
(YYIR1) was used to determine HRmax (Bangsbo, Iaia & Krustrup, 2008). The 15-point
Portuguese Borg’s RPE 6-20 scale (Cabral et al., 2020) and TQR 6-20 score (Brink et al.,
2010; Kenttä & Hassmén, 1998) were used to evaluate perceived effort. The entire time of
training sessions for each participant was multiplied to get the session RPE (sRPE = RPE ×
session duration). Individual RPE’s and TQR’s were taken 30 min after and before each
training session, respectively. Players were already familiarized with the RPE procedures by
reporting in a Microsoft Excel spreadsheet (Microsoft Corporation, Redmond, WA,
USA) (Teixeira et al., 2021b, 2022a) (Table 3).
Baseline characteristics
Players’ individual characteristics were collected by height (m), weight (kg), chronological
age (years), sitting height (cm) and experience level (years). Anthropometric measures
were measured using standard the International Society for the Advancement of
Kinanthropometry (ISAK) guidelines (Marfell-Jones et al., 2006). Body mass (kg) was
evaluated by an electronic scale Tanita MC 780-P MA (Tanita Corporation, Tokyo,
Japan) with minimum clothing. Height (cm) was collected using an electronic stadiometer
(Seca, Hamburg, Germany). Players’ height (m), weight (kg) and sitting height (cm) were
recorded by the average of three measurements to the nearest 0.1 using international units
(IU). Body mass index (BMI) was calculated by dividing weight by the square of height
(kg/m2). BMI’s cut-offs used were: underweight < 18.5 kg/m2, normal 18.50–24.99 kg/m2,
overweight ≥ 25 kg/m2, obese ≥ 30 kg/m2 (Suarez-Arrones et al., 2018). Relative age (a.u.)
was calculated as the difference between the player’s birthdate and the cut-off date (31st
August) was divided by the number of 365 days a year (Hill et al., 2020). Based on a
predictive set of Mirwald’s equations, maturity offset and peak high velocity (PHV) were
calculated (Mirwald et al., 2002; Teixeira et al., 2022a). Sub-elite young football was
divided into pre-PHV (n = 52), mid-PHV (n = 65) and post-PHV (n = 207).
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Resultant equations for training load monitoring
The individual-based principal component in the resultant equations for TL monitoring
were: low-moderate volume, high intensity, explosiveness, change of direction, collisions
and body impacts (Rico-González et al., 2022a; Sheehan et al., 2020; Teixeira et al., 2021a).
Also, the resultant equations added the baseline characteristics (i.e., anthropometric and
maturational status) and the ITL measures (de Dios-Álvarez et al., 2021; Suarez-Arrones
et al., 2018). Thus, the resultant equations was computed by a PCA approach can be
expressed by the following algorithm (Jolliffe & Cadima, 2016):
PCAn ¼
X
Φi1  xi þ Φi2  x2 . . .
ð
ÞΦin  xn
where the PCAn is the n principal component, Φ is the loading vector comprising loadings
(i1, i1…) of the ﬁrst principal component. The loadings must have a sum of squares of
exactly one. This is due to the possibility of a considerable variation when loadings are of a
great magnitude.
It also speciﬁes how the major component will move (PCAn), along which data varies
the most (Jokiniemi, Pietilä & Mikkonen, 2021). The outcome is a line that is closest to the
n observations in p-dimensional space. Euclidean distance squared is used to gauge
proximity; xn are normalized predictors. Normalized predictors (xn) have mean values
equal to zero and standard deviations equal to one (Jokiniemi, Pietilä & Mikkonen, 2021;
Jolliffe & Cadima, 2016). Resultant equation to quantify the weighted TL was expressed by:
TLweekly ¼
X
PCA1 þ PCA2 . . .
ð
ÞPCAn
where the TLWeekly is the sum of each PCA (p) and its weighted load vector (Jolliffe &
Cadima, 2016).
Statistical analysis
A data reduction technique was conducted using a principal component analysis (PCA)
with 95% conﬁdence intervals (95% CI) (Pino-Ortega et al., 2021; Rojas-Valverde et al.,
2020). Monte Carlo parallel analysis were conducted to determine the number of extracted
factors (Jokiniemi, Pietilä & Mikkonen, 2021). Z score were computed to scaled and
centered ﬁnal selection variables for PCA using Kaiser–Meyer–Olkin (KMO) values for
measure of sampling adequacy and the Bartlett Sphericity test to ensure the sampled
training data was suitable for data reduction. Factor analysis was acceptable when KMO
values are greater than 0.6 and Bartlett Sphericity less than 0.05 (Pino-Ortega et al., 2021).
The number of PCA to be retained was determined using the scree plot for the derived
factor eigenvalues, considering eigenvalues greater than 1 (Rojas-Valverde et al., 2020).
Factor’s components loading was computed using an orthogonal rotation with a VariMax
method due to perpendicularity in the correlation matrix of the interest variables
(Warmenhoven et al., 2019). Selection criteria for extraction of non-correlated variables
was performed in r < 0.4 (Rojas-Valverde et al., 2020). Weightings (eigenvectors) are
represented by a 2D plot and the results of the PCA are presented in a path analysis.
The sample size was calculated by GPower, Version 3.1.5.1 (Institut für Experimentelle
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Psychologie, Düsseldorf, Germany) with an effect size ß of 0.4, an a of 0.05, and a power of
0.8 (1−ß) (Teixeira et al., 2022a). Kolmogorov–Smirnov and Levene’s test were used to
assess the normality and homogeneity. Statistical signiﬁcance was set at p < 0.05. Data are
presented as the mean ± SD using JASP software (JASP Team, 2022; jasp-stats.org).
RESULTS
Data-reduction procedure, eigenvalue and component number
Figure 2 presents the eigenvalue ranged between 1.44% and 5.21%. Overall, ﬁve PCA
accounted for 68.6% of the total explained variance. The ﬁve extracted PCA explained
27.4%, 16.2%, 10.0%, 8.3% and 6.7% of the variance in TL dataset, respectively. Thus, the
ﬁrst PC explained 27.4% of the TL by TD, HMLD, DSL, ACC and DEC. The second PCA
explained 16.2% of the TL thought HSRr and SPR. The thirty PCA explained 10.0% of the
TL via HRmax, AvHR, %HR and TRIMP. The fourth PCA explained 8.3% of the baseline
outset (i.e., sRPE, TQR, maturation offset and chronological age). The ﬁfth PCA explained
6.7% of the accumulated TL (i.e., AvS and MRS). Constantly, PHV, relative age, experience
level and BMI were excluded from the PCA (r < 0.4).
Table 4 also shows the data-reduction procedure resulting from rotated component
matrix for accumulated TL variables with factor component loadings (eigenvectors). Four
variables were excluded from the PCA due to the communalities below 0.4 (i.e., PHV,
relative age, experience level and BMI). Also, KMO’s criteria reported a sampling adequacy
of sampled data, reporting a considerable proportion of the variance as result of the
underlying factors (KMO = 0.73). Furthermore, signiﬁcant Barlett Sphericity test was
signiﬁcant (p < 0.001).
Resultant equations and paths from principal components analysis
The weightings (eigenvectors) of the PCA analysis are represented by a path graph in
Fig. 3. Overall, the weightings ranged between −0.52 to 0.97. The highest weightings were
observed in AvHR (bpm) (PCA 3) and the lowest weightings in sRPE (au) (PCA 4).
0
1
2
3
4
5
6
0
5
10
15
20
Component
Eigenvalue
Data
Simulated (95th quantile)
Figure 2 Scree plot for principal component analysis representing the component, explained
variance and eigenvalues.
Full-size
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Considering the highest factor in each principal component, the variables considered were
TD (0.698), SPR (0.940), AvHR (0.967), Age (0.836) and MRS (0.790) for PCA 1 to PCA 5.
The resultant equations from extracted principal component are presented in Table 5.
On this basis, the resultant equations for TL monitoring during a weekly microcycle can be
expressed into ﬁve principal components determine the equations for the baseline
variables: (1) explosiveness and impacts; (2) HSR; (3) HR measures; (4) baseline
characteristics; (5) average running velocity.
DISCUSSION
The aim of this study was to reduce the dimensionality of the internal and external load
measures, by a PCA approach, in order to describe and explain the resultant equations for
TL monitoring during a standard microcycle in a sub-elite youth football players.
Additionally, it is intended to identify the most representative measure for each principal
component. After data reduction, ﬁve principal components were extracted from TL
dataset explaining 68.7% of the total variance. The TL measures with the highest weight in
each PCA were DEC, SPR distance, average HR, chronological age and MRS.
Resultant equations for TL monitoring during a standard microcycle in sub-elite youth
football was split into: (1) explosiveness, ACC and impacts (27.4%); (2) HSR (16.2%); (3)
heart bate-based measures (10.0%); (4) baseline characteristics (8.3%); (5) average running
Table 4 Principal component analysis: data reduction procedure using varimax for rotated
component matrix with factor loadings (eigenvectors) >0.4.
Variables
PC1
PC2
PC3
PC4
PC5
Uniqueness
TD (m)
0.698
0.365
AvS (m·min−1)
0.680
0.321
MRS (m·s−1)
0.790
0.259
HSRr (m)
0.928
0.041
HMLD (m)
0.788
0.501
0.123
SPR (n)
0.895
0.088
SPR (m)
0.940
0.066
DSL (au)
0.705
0.465
ACC (m·s−2)
0.844
0.233
DEC (m·s−2)
0.877
0.184
HRmax (bpm)
0.763
0.366
HRAv (bpm)
0.967
0.055
%HRmax
0.953
0.081
TRIMP (au)
0.692
0.501
sRPE (au)
−0.516
0.629
TQR (au)
−0.553
0.676
OFFSET (y)
0.669
0.343
Age (y)
0.836
0.261
Note:
Abbreviations: ACC, acceleration; AvHR, average heart rate; AvS, average speed; DEC, deceleration; HMLD, high
metabolic load distance; HRmax, maximal heart rate; MRS, maximum running speed; SPR, average sprint distance;
SPR_N, number of sprints; sRPE, session ratings of perceived exertion; TD, total distance; TQR, total quality recovery;
TRIMP, training impulse.
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Table 5 Resultant equations from extracted principal component analysis.
PCA Construct
Variables
Calculation
1
Explosiveness,
accelerations and
impacts
TD (m), HMLD (m), DSL (au), ACC
(>3 m·s−2), DEC (<3 m·s−2)
0.698 × TD (m) + 0.788 × HMLD (m) + 0.705 × DSL (au) + 0.844 ×
ACC (m·s−2) + 0.877 × DEC (m·s−2)
2
High intensity running
rHSR (19.8–25.1 km · h−1), SPR (n), SPR
(m)
0.928 × rHSR (km · h−1) + 0.895 × SPR (n) + 0.940 × SPR (m)
3
Heart rate
HRmax (bpm), AvHR (bpm), %HRmax,
TRIMP (au)
0.763 × HRmax (bpm) + 0.967 × AvHR (bpm) + 0.953 × %HRmax +
0.692 × AkubatTRIMP (au)
4
Baseline characteristics
TQR (au), sRPE (au), Offset (y), Age (y)
−0.553 × TQR (au) + −0.516 × sRPE (au) + 0.669 × Offset (y) + 0.836
× Age (y)
5
Average running velocity
AvS (m·min−1), MRS (m·s−1)
0.680 × AvS (m · min−1) + 0.790 × MRS (m·s−1)
Note:
Abbreviations: ACC, acceleration; AvHR, average heart rate; AvS, average speed; DEC, deceleration; HMLD, high metabolic load distance; HRmax, maximal heart rate;
MRS, maximum running speed; SPR, average sprint distance; SPR_N, number of sprints; sRPE, session ratings of perceived exertion; TD, total distance; TQR, total quality
recovery; TRIMP, training impulse.
Figure 3 Principal component analysis and weightings (eigenvectors) were presented with a path.
Full-size
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DOI: 10.7717/peerj.15806/ﬁg-3
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velocity (6.7%). Considering the highest representative factor in each principal component,
the variables considered were DEC (PCA 1), SPR distance (PCA 2), average HR (PCA 3),
chronological age (PCA 4) and MRS (PCA 5). In football, Pino-Ortega et al. (2021) also
determined conditional dimensions such as angular velocity, speed displacements, HMLD,
HSR, SPR, TD covered, metabolic power, DSL, jumps, impacts, ACC and DEC. The ﬁrst
PCA complies TD, HMLD, DSL, ACC and DEC, being grouped as explosiveness, ACC and
impacts. Although there is a deﬁnite correlation between body impacts, ACC, and DEC.
Otherwise, the TD may be due to an inverse relationship between training volume and
intensity (Castillo et al., 2020). Also, the metabolic power was rather than speed-based
zones to express running intensity (Osgnach et al., 2010). Nevertheless, the TD could fall
outside this construct at ﬁrst sight. An interaction effect between TD and DEC had already
been documented for sub-elite football players (Teixeira et al., 2021b). The second PCA
extracted HSRr and SPR, wherefore the HSR is an excellent variable to give meaning about
training intensity (Harper et al., 2020). Zurutuza et al. (2020) combined peak velocity and
distance covered at different velocities in the same principal component, conﬁrming our
results on high intensity demands. The third PCA complied the HR-based measures (i.e.,
HRmax, AvHR, %HRmax and TRIMP), conﬁrming the correlation between HR-based
measures and ETL outcomes (de Dios-Álvarez et al., 2021; Ellis et al., 2021). The fourth
PCA was explained by TQR, sRPE, maturation offset and chronological age. Although the
fourth PCA has a lower variance explained it is fundamental to consider the inﬂuence of
chronological age, biological age and perceived exertion (Teixeira et al., 2022a). In line
with this component, the perceived exertion seems to be better explained with trainability,
maturation and stage of development (Malina et al., 2019). Also, the TL could be
inﬂuenced by acute: chronic workload ratio, training monotony and well-being variations
(Clemente et al., 2021a, 2021b; Rico-González et al., 2022c). Indeed, the literature reported
that greater acute: chronic workload ratio and training monotony levels are normally
associated with an increased risk of injury or health issues. These measurements might be
utilized to comprehend how the data changes throughout in-season phases (Rico-González
et al., 2022a). Effectively, perceived exertion in young football players may be also
inﬂuenced psychophysiological determinants as self-perception of competence and
practice experience (Branquinho et al., 2021; Ferraz et al., 2017, 2018). Leading biological
maturation in youth sports has become a research-practice gap still lacking knowledge
about sub-elite environments using data reduction approaches (Cumming, 2018; Teixeira
et al., 2021b, 2022c). Finally, the ﬁfth PCA explained 6.7% of the accumulated TL thought
AvS and MRS. Pacing behavior was also reported as a key point to football performance
(Ferraz et al., 2018, 2020).
Research ﬁndings was slightly small than previous research in futsal (Rico-González
et al., 2022a), Australian football (Sheehan et al., 2020), rugby (Scantlebury et al., 2020;
Weaving et al., 2020) and Gaelic football (Gamble et al., 2019). Wherefore, the
comparisons with current research would consider the differences between football codes.
Scantlebury et al. (2020) reported a cumulative explained variance of 91%, 96% and 91%
variance in TL in rugby union, ﬁeld hockey and soccer. Casamichana et al. (2019) reported
an explained variance of the external training intensity between 39% and 44%. Also, the
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eigenvalue of this study ranged between 1.44% to 5.21% by setting up values of
accumulated TL substantially lower compared to other studies (i.e., eigenvalues between
1.0% and 68.0%) (Pino-Ortega et al., 2021; Scantlebury et al., 2020). Albeit, current research
represents the ﬁrst time that this statistical approach has been used in a sub-elite youth
football, speciﬁcally using training data (Rico-González et al., 2022b; Rojas-Valverde et al.,
2020).
Current applied PCA determine the resultant equations from individual-based principal
components, expressing by major component weightings (Rico-González et al., 2022a;
Sheehan et al., 2020; Teixeira et al., 2021a). Indeed, this is the traditional PCA algorithm
that computes the principal components based on the covariance matrix or the singular
value decomposition the data. It is widely used methods in team sports for dimensionality
reduction, data visualization, and feature extraction (Pino-Ortega et al., 2021; Rico-
González et al., 2022b; Rojas-Valverde et al., 2020). Other ratios, scores and equivalent
equations have already been proposed to measure the TL, by emphasizing training
intensity, volume or locomotion proﬁle (Clemente et al., 2019; Owen et al., 2017; Rago
et al., 2019). However, the PCA algorithms are diverse and some have not yet been
implemented in football (Rico-González et al., 2022b; Rojas-Valverde et al., 2020). Hence,
future perspective can explore other PCA algorithms such as incremental, Kernel, sparse
and robust PCA approaches (Rojas-Valverde et al., 2020). Incremental PCA allows for
incremental updates to the principal components as new data points are added in large
datasets or when new data is continuously acquired, such as in real-time monitoring of
football players’ performance or training data (Jokiniemi, Pietilä & Mikkonen, 2021).
Kernel, sparse and robust PCA has been mainly applied for nonlinear dimensionality
reduction, sparsity constraints and noisy or incomplete data (Teixeira et al., 2022c).
Futures research should expand the resultant equations by considering other well-being,
technical-tactical and match-related contextual factors. Also, PCA approach must also
consider the principal component in TL monitoring when considering training mode (i.e.,
small-sided and conditioned games), training day (i.e., MD-3, MD-2, and MD-1), age
group (i.e., U15, U17, and U19) and maturational bands (i.e., pre-, mid- and post-PHV)
(Teixeira et al., 2021a). Additionally, the training data represents only a speciﬁc sub-elite
football academy and must be considered carefully when applied to another to other teams
and contexts. As study limitations, the sample size and number of factors was rather small
than previous studies with longer monitoring period (Rojas-Valverde et al., 2020). Also, the
total variance was also relatively smaller for this PCA paths than other reports in football
codes (Pino-Ortega et al., 2021; Rojas-Valverde et al., 2020). However, it must be ensured
that football had the lowest percentage of the variance comparing with other football codes
(Rojas-Valverde et al., 2020). Furthermore, choosing a higher threshold for total variance
(%) may result in fewer retained principal components and a higher degree of data
reduction with a consequent loss, noise or redundant information (Jokiniemi, Pietilä &
Mikkonen, 2021; Jolliffe & Cadima, 2016). In general, there is no strict rule for the
minimum value for percentage of total variance in PCA, as it depends on the speciﬁc
application and the trade-off between data reduction and information retention (Rojas-
Valverde et al., 2020). Furthermore, a commonly used threshold for retaining a principal
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component is to choose those components that explain at least 60–80% of the total
variance, depending on the speciﬁc data analysis requirements (Jokiniemi, Pietilä &
Mikkonen, 2021; Jolliffe & Cadima, 2016). Finally, the TL strategies applied in this
quasi-experimental approach for only compiles GPS, HR and perceived exertion, however
more objective measure of fatigue and recovery should be considered in futures reports,
such as HR variability, electromyography signal intensity, biochemical markers and other
well-being measures (Clemente et al., 2021a, 2021b). Also, further PCA approaches are
needed to consider the principal components when integrating physical, physiological and
tactical factors in football under an integrative perspective (Teixeira et al., 2022c).
PRACTICAL APPLICATIONS
 Current resultant composite equations can be applied to relative contribution of the ITL
and ETL measures for monitoring and management load in sub-elite youth football.
 Data reduction techniques decrease the redundant information and dimensionality of
the training data, expressing in the following principal components: explosiveness and
impacts, high-speed running, heart bate-based measures, baseline characteristics and
average running velocity.
 Considering the highest factor in each principal component, DEC (PCA 1), sprint
distance (PCA 2), average HR (PCA 3), chronological age (PCA 4) and maximal speed
(PCA 5) are the conditional dimension to be considered in TL monitoring during a
standard microcycle in sub-elite youth football players.
 Maturational status should be carefully considered in the TL monitoring together with
relative age effect, chronological and baseline characteristics.
 Self-perception and practice experience may affect the variance explained by perceived
exertion and pacing behavior.
 Training intensity and volume can be more accurately measured by current resultant
composite equations and/or most representative factor for a standard microcycle in
sub-elite youth football players.
 Futures research should expand the resultant equations for TL monitoring in sub-elite
youth football with well-being, technical-tactical and match-related contextual factors.
CONCLUSION
Using a PCA approach, ﬁve principal components could be applied to extract to describe
and explain resultant equations for TL monitoring during an in-season standard
microcycle in sub-elite youth football. Current research provides the ﬁrst composite
equations to extract the TL in this speciﬁc population expressed as explosiveness and
impacts, high-speed running, HR-based measures, baseline characteristics and average
running velocity. Considering the highest factor in each principal component, DEC (PCA
1), SPR distance (PCA 2), average HR (PCA 3), chronological age (PCA 4) and maximal
SPR (PCA 5) are the conditional dimension to be considered in TL monitoring during a
standard microcycle in sub-elite youth football players.
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Future research should expand the resultant equations within the microcycle, by
considering other well-being measures, technical-tactical factors and match-related
contextual factors.
ADDITIONAL INFORMATION AND DECLARATIONS
Funding
This project was supported by the National Funds through FCT—Portuguese Foundation
for Science and Technology (UIDB/DTP/04045/2020). The funders had no role in study
design, data collection and analysis, decision to publish, or preparation of the manuscript.
Grant Disclosures
The following grant information was disclosed by the authors:
National Funds through FCT—Portuguese Foundation for Science and Technology:
UIDB/DTP/04045/2020.
Competing Interests
Tiago M. Barbosa is an Academic Editor for PeerJ.
Author Contributions
 José Eduardo Teixeira conceived and designed the experiments, performed the
experiments, analyzed the data, prepared ﬁgures and/or tables, authored or reviewed
drafts of the article, and approved the ﬁnal draft.
 Pedro Forte conceived and designed the experiments, prepared ﬁgures and/or tables,
authored or reviewed drafts of the article, and approved the ﬁnal draft.
 Ricardo Ferraz performed the experiments, analyzed the data, authored or reviewed
drafts of the article, and approved the ﬁnal draft.
 Luís Branquinho performed the experiments, analyzed the data, authored or reviewed
drafts of the article, and approved the ﬁnal draft.
 Ryland Morgans analyzed the data, authored or reviewed drafts of the article, and
approved the ﬁnal draft.
 António José Silva conceived and designed the experiments, authored or reviewed drafts
of the article, and approved the ﬁnal draft.
 António Miguel Monteiro conceived and designed the experiments, authored or
reviewed drafts of the article, and approved the ﬁnal draft.
 Tiago M. Barbosa conceived and designed the experiments, authored or reviewed drafts
of the article, and approved the ﬁnal draft.
Human Ethics
The following information was supplied relating to ethical approvals (i.e., approving body
and any reference numbers):
Informed consent was obtained from all subjects involved in the study.
The experimental approach was approved and followed by the local Ethical Committee
from University of Trás-os-Montes & Alto Douro (3379-5002PA67807).
Teixeira et al. (2023), PeerJ, DOI 10.7717/peerj.15806
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Data Availability
The following information was supplied regarding data availability:
The raw measurements are available in the Supplemental File.
Supplemental Information
Supplemental information for this article can be found online at http://dx.doi.org/10.7717/
peerj.15806#supplemental-information.
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Resultant equations for training load monitoring during a standard microcycle in sub-elite youth football: a principal components approach.
Teixeira, José Eduardo,Forte, Pedro,Ferraz, Ricardo,Branquinho, Luís,Morgans, Ryland,Silva, António José,Monteiro, António Miguel,Barbosa, Tiago M