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Force-Velocity Proling
among Different
Maturational Stages in
Young Soccer Players: A
Cross-Sectional Study
Leon Niederdraeing1, 2 and Karen Zentgraf2
1Eintracht Frankfurt, 2Movement Science and Training in Sports, Institute for Sports Sciences, Goethe University
Frankfurt
Niederdraeing, L., & Zentgraf, K. (2025). Force-Velocity Proling among Different Maturational
Stages in Young Soccer Players: A Cross-Sectional Study.
International Journal of Strength and Conditioning
https://doi.org/10.47206/ijsc.v5i1.366
ABSTRACT
Speed is a key component of football performance.
An individualized approach may be necessary to
achieve optimal speed development. Force-velocity
proling breaks down linear sprint performance
into force, velocity, and mechanical effectiveness
on an individual basis. In young footballers, these
factors are related to maturation and have a strong
inuence on physical performance. The aim of
this study is to investigate horizontal force-velocity
proling at different stages of maturation.
As an indicator of maturity, the age of peak height
velocity (APHV) of 85 young soccer players (age:
M = 15.7, ± 1.63 years) was determined using the
Mirwald formula. According to temporal distance
from their individual estimated APHV, players were
divided into four groups (mid-peak-height-velocity
(PHV, N = 26); 1-2y-post-PHV (N = 21); 2-3y-post-
PHV (N = 21); >3y-post-PHV (N = 17)). 30-meter
sprint performance including ve split times was
measured with timing gates in all athletes. These
splits were used to calculate an individual horizontal
force-velocity prole with its components maximum
theoretical force (FH0), velocity (VH0), and power
(Pmax). These proles also included peak ratio of
force (RFmax), actual relationship of maximum force
and velocity (FV slope), as well as the theoretically
optimal relationship of maximum force/velocity
(FVopt).
APHV-based group differences were found for FH0,
VH0 and Pmax, RFmax, and the difference between
FV slope and FVopt. Values of absolute FH0, VH0,
RFmax and Pmax were increasing with maturation.
In all groups, a lack of velocity in relation to force
production of 24% (p < .001, d = 1.15) was
detected, with the largest decit at mid-PHV (M =
35.74 ± 21.73%) and the smallest decit at >3ypost-
PHV (M = 15.90 ± 20.15%).
The current nding of a velocity decit in 30m-sprint
performance of young soccer players suggests
a need for velocity-oriented training - pronounced
around APHV.
INTRODUCTION
Striving for top performance is an integral part
of competitive sport. Athletic abilities, especially
speed, play a key role in optimizing performance
in soccer (Haugen et al., 2014a). This is, in part,
due to the fact that many goals in soccer are
scored following a sprint (Faude et al., 2012).
Simultaneously, it has been shown that the overall
ball speed of passes, the amount of high-speed
running (5.5 – 7m.s-1) and sprint distance (>7m.s-
1) per match have increased over the last decades
(Wallace et al., 2014; Lago-Penas et al., 2022;
Barnes et al., 2014). Consequently, linear speed
and acceleration have been associated with youth
players progressing to the rst team and young
Copyright: © 2025 by the authors. Licensee IUSCA, London, UK. This article is an
open access article distributed under the terms and conditions of the
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International Journal of Strength and Conditioning. 2025
players being selected for youth academies (Leyhr
et al., 2018; Meylan et al., 2010).
When assessing athletic abilities in youth sports
development, it is proposed that performance
should be related to biological maturation rather
than chronological age (Malina et al., 2004; Baxter-
Jones, 2007; Lames et al., 2008). It is well known
that physical development and athletic abilities
change rapidly with maturation (Malina et al., 2004;
Meyers et al., 2016), particularly around age at peak
height velocity (APHV). This may be due to growth-
related changes in the neuromuscular system and in
muscle and tendon properties (Radnor et al., 2018;
Radnor et al., 2020). Based on this, APHV should
be determined to assess physical performance in
an age-appropriate manner (Ferrauti et al., 2020).
Force-velocity proling (FVP) is a method that
describes the relationship between force and
velocity for muscular contraction during a given
motor task and relates to the capacities of the
neuromuscular system (Cormie et al., 2011). FVP
has been used to examine athletic performance
such as jumping and sprinting (Samozino et al.,
2014; Morin et al., 2019). In general, this approach
offers, rst, an individualized diagnostic for
mechanical factors related to force production,
and second, an interventional approach to target
individual performance limits. In jumping, an
individual prole can be generated by extrapolating
a linear relationship between force and velocity
(Samozino et al., 2008) by performing a series of
vertical jumps with increasing loads. Vertical FVP
allows to determine an optimal prole for jumping,
taking individual anthropometrics into account.
The individual relationship of force and velocity (FV
relationship) is then referenced to the individual
theoretic, optimal force-velocity relationship,
graphically represented as the slope of the linear
relationship (Samozino et al., 2012). For jumping,
FVP has been used to implement specic individual
decit-oriented training methods, which might
be superior to generic training recommendations
(Jimenez-Reyes et al., 2019). In order to address a
force decit, the authors propose resistance training
with high loads. Conversely, to improve a velocity
decit, it is recommended that practice should
employ high velocities (Jimenez-Reyes et al., 2019).
The horizontal adequate, i.e., sprint performance,
can be easily measured by the spatiotemporal
variables; the time required for a given distance
(Fernandez-Galvan et al., 2022). The evaluation
of the horizontal force-velocity relationship during
sprint acceleration (horizontal FVP) enables the
determination of the mechanical effectiveness of
linear sprint performance as the displacement of
the body’s center of mass in space per time allows
the computation of the ground reactive forces that
are changing with increasing speed, the equivalent
of the increasing loads of the vertical prole (Rabita
et al., 2015; Morin et al., 2016). The individual FV
relationship can be modeled from maximum-intent
horizontal sprint including split times (Samozino et
al., 2016; Haugen et al., 2020). The prole consists
of the following variables: maximum theoretic force
(FH0), maximum theoretic velocity (VH0 (m/s)) and
maximum power (Pmax (W/kg)), the product of FH0
and VH0. FH0 can be expressed as absolute (N) or
relative to body weight (N/kg). The aforementioned
variables can be calculated by linear regression over
a 30m sprint. (Morin et al., 2019). The relationship of
FH0 and VH0 can be described as a force-velocity
(FV) slope. In addition, the FVP in sprinting includes
the percentage of force generated in the horizontal
direction (Morin et al., 2011; Samozino et al.,
2016). The maximum ratio of horizontal to resultant
force (RFmax) and the decrease in horizontal force
ratio (DRF) are commonly used as measures of
mechanical effectiveness (Morin et al., 2011).
The overall reliability and validity of the horizontal
FV relationship described by Morin and Samozino
has been demonstrated (Samozino et al., 2016;
Simperingham et al., 2019; Haugen et al., 2020). One
study created reference FVP from soccer players
of different ages and maturational levels for FH0,
VH0, Pmax, RFmax and DRF by distinguishing youth-
academy players in pre-, mid- and post-puberty
(Fernandez-Galvan et al., 2022). The relationship of
force and velocity including its theoretic optimum
(FVopt), which exists for vertical FVP, can also be
estimated for horizontal FVP (Samozino et al., 2022a)
– but has not been explored extensively yet. The
complete biomechanical derivation for horizontal
FVP can be obtained from Samozino et al. (2018,
p. 240-244), while the mathematical derivation for
the optimal relationship of FVopt can be found in
Samozino et al. (2022a, p. 561-563). In short, the
time (t) needed to move the center of mass for a
given distance (x) can be minimized for only one
and therefore optimal FV slope with an individual
Pmax (Samozino et al., 2022a). The difference (FVDiff)
between FVopt and FV slope can be expressed in
percent (Giroux et al., 2016; Samozino et al., 2022a):
Force-Velocity Proling among Different Maturational Stages in
Young Soccer Players: A Cross-Sectional Study
2
Copyright: © 2025 by the authors. Licensee IUSCA, London, UK. This article is an
open access article distributed under the terms and conditions of the
Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).
International Journal of Strength and Conditioning. 2025 Niederdraeing, L., & Zentgraf, K.
To date, there are several studies that have
analyzed the horizontal FVP of team sports athletes
(Fernandez-Galvan et al., 2022; Bustamante-
Garrido et al., 2023; Hicks et al., 2023). However,
none of these studies have included FVopt. The
aim of this study is to determine the horizontal FVP
and the APHV in young soccer players and thus
interpret a complete FVP including FVopt in relation
to maturation. This includes the parameters FH0,
VH0, Pmax, RFmax, DRF and the relationship between
FH0 and VH0, FV slope, the optimal FV slope, FVopt,
and the difference between the latter two, FVDiff. The
elevation of the full FVP in relation to growth has
the potential to modify training methodologies for
young players considering their individual levels of
performance and maturation.
METHODS
Study Design
The study used a cross-sectional design in which
sprint performance was measured using split
times for 5 m, 10 m, 15 m, 20 m, and 30 m of a
linear sprint in young soccer players of a soccer
academy. Split times were assessed to identify the
different components of horizontal FVP, FH0, VH0,
Pmax, DRF, and RFmax, according to Samozino et al.
(2016). In addition, the FV slope was determined
and FVopt was calculated (Samozino et al., 2022a)
for each individual Pmax, the product of FH0 and VH0,
after which FVDiff could be determined.
APHV was estimated using the Mirwald formula
(2002). The corresponding maturation offset (MO,
time difference between the day of measurement
and APHV) was then individually documented
(Toselli et al., 2019). A cross-sectional statistical
analysis was carried out to establish a possible
relationship between the horizontal FVP and MO
and thus connect maturation to the mechanical
characteristics of a sprint.
Participants
For the categorical comparison of horizontal FVP,
85 elite-level junior players from U14-U19 teams
in a professional youth academy were studied
(age range: 12.8 to 18.7 years). Measurements
were taken during the rst half of the 2022/2023
season. Players had a specic soccer training
experience of 10.18 ± 1.97 years. Only players who
were medically cleared to play, free of injury, and
without physical limitations were tested. Players
were informed verbally and on a written basis about
the aims and risks of the study and gave written
consent to be part of this research project, while for
minors, parents signed that they consented to the
research project and data processing.
Methodology
Following the procedure of Fernandez-Galvan et
al. (2022), prior to sprint testing, anthropometric
variables were measured. Body mass (SECA© –
769, accurate to 0.1 kg), body height, and seated
height (wall-mounted stadiometer, accurate to 0.1
cm) were recorded. Based on the date of birth,
APHV was subsequently estimated according to
Mirwald’s method (2002). The Mirwald formula has
been established as a valid and economical tool to
determine the APHV and consequently, MO (Toselli,
et al., 2019), using the following equation (Mirwald,
2002):
Maturity offset = -(9.236 + 0.0002708 * Leg Length
and Sitting Height interaction) - (0.001663 * Age
and Leg Length interaction) + (0.007216 * Age and
Sitting Height interaction) + (0.02292 * Weight by
Height ratio).
Participants were asked to follow their normal
eating, drinking, and sleeping habits on the testing
day, which was at least 72 hours after their last
match. The testing took place immediately before
an outdoor pitch training session. The test was
carried out indoors on a PVC surface, therefore,
whether conditions (wind, temperature, etc.) were
neutral and equal for all players. The experimental
setup was based on the research of Haugen et al.
(2020) and the original experiments of Samozino et
al. (2016) and Morin et al. (2019). The design of the
estimation of FVP by split times has been criticized
in the recent past (Lindberg et al., 2021), but
Samozino et al. (2022b) point out that valid results
can be ensured with a high degree of accuracy and
reliable measurement. Split times were recorded
using doubled timing gates, 10 mW (Microgate©,
Witty-Gate), a method that can be assumed to
have very high reliability (Haugen et al., 2014b).
The starting position was a staggered stance with
the forefoot 50 cm behind the rst timing-gate. As
accurate horizontal FVP requires catching the “rst
rise of the force production” (Haugen et al., 2020, p.
1771), players had their head or chest very close (5-
10 cm) to the rst timer and the starting position was
very carefully controlled. Instructed by their strength
and resistance coach, participants performed
a standardized, 15-minute warm-up, including
3
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4
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International Journal of Strength and Conditioning. 2025
Force-Velocity Proling among Different Maturational Stages in
Young Soccer Players: A Cross-Sectional Study
common running drills, dynamic stretching, and two
submaximal sprints over 30 m. Participants were
then familiarized with the starting position. Players
performed three maximal sprints over 30 m with
split times at 5 m, 10 m, 15 m, and 20 m. They had
a minimum of 3 min rest between each trial. The
horizontal FVP was extrapolated from the best time
with an offset of +0.21 s, which is recommended
when using timing gates instead of a radar camera
(van den Tillaar et al., 2022).
Data Procedure
Maturity data were processed using the BioFinal
Tool 3.4 (IAT, Leipzig, Germany). Respecting the
limitations of ±6 months for Mirwald’s equation
(Mirwald et al., 2002), players were divided into
four groups according to their maturational stage:
Within 12 months of APHV (mid-PHV), 1-2 years
after APHV (1-2y-post-PHV), 2-3 years after APHV
(2-3y-post-PHV) and more than three years after
APHV (>3y-post-PHV). Together with body mass
and stature, split times were used to extrapolate
the horizontal FVP via linear regression using a
prespecied Excel sheet (https://jbmorinnet.les.
word-press.com/2022/01/fvpsprint_2019_basic.
xlsx.) by Morin (2019). FVopt was calculated using a
recent method (Samozino et al., 2022). Briey, the
individual Pmax was given for their best 30-m time,
and the FV slope was changed in 0.002 steps until
the equation reached its minimum. Body mass
was considered by using an individual k value,
which is a function of body mass, height, drag, and
barometric pressure. As the equation describes the
forces acting on the center of mass during sprinting,
both temperature and barometric pressure must be
integrated (Samozino et al., 2022). However, even
bigger changes in air pressure have a marginal
effect on k (Samozino et al., 2018), so barometric
pressure (PB = 760hPa) and temperature (T =
20° C) were assumed to be constant, resulting
in p = 1.205. The whole procedure, including the
mathematical derivation, can be found in detail in
Samozino et al. (2022). Following the calculation of
FVopt, the difference between FVopt and the individual
FV slope was described in percentages using the
equation for FVDiff. The equation has been created
for training recommendations in vertical proling
(Jiménez-Reyes et al., 2019) and allows for an
overview of imbalances between force and velocity
output in jumping.
Statistical analyses were performed using IBM SPSS
Statistics 28 (IBM, Armonk, NY, USA) and JAMOVI
2.3 (The Jamovi project, Sydney, Australia). Prior to
all statistical analyses, data were tested for normality
of distribution and homogeneity of variances using
a Shapiro-Wilk test and a Levene test, respectively.
Kruskal-Wallis’ non-parametric one-way analysis
of variance (ANOVA) was used to detect group
differences in horizontal FVP. It expresses effect
size in epsilon-squared (ε²) and according to Cohen
(1992), it can be interpreted like eta-squared as low
(< 0.25), moderate (0.25 to 0.49), and high (> 0.5).
The ANOVA was followed by the Dunn-Bonferroni
adjusted post-hoc test. As FVDiff was determined in
a separate procedure and then statistically tested,
Fisher’s ANOVA and Bonferroni’s post-hoc tests
were used. Multiple linear regression assumptions
were tested using residual vs. adjusted, normal
QQ and Cook’s distance plots. No evidence of
heteroscedasticity or multicollinearity was found.
Descriptive data of the dependent variables (i.e.,
FH0, VH0, Pmax, FV slope, DRF and RFmax, split times up
to 30 meters) are presented as means and standard
deviations. The signicance threshold was set at p
< 0.05 for all analyses.
RESULTS
Table 1 displays the descriptive data for
anthropometric measures age, APHV, MO, height,
body mass, seated height, training age (in years),
youth academy since (in years), strength training
experience (in years), strength training per week
this season (in hours) of participants for each group.
As can be seen in Table 1, all parameters except
the APHV increase with increasing MO. Figure 1
displays descriptive data for split times up to 30
meters.
Figure 1 illustrates the sprint times of all groups.
While no signicant group differences were
observed for the 5m time in any group, the times
improved with increasing maturity offset (MO)
from the 10m distance onwards. Signicant group
differences were found for the 10m (p = 0.02)
and 15m times (p = 0.018) between mid-PHV and
2-3y-post-PHV.
Signicant group differences were observed
for 20 m times, with both the 2-3y-post-PHV (p
< 0.001) and >3y-post-PHV (p = 0.002) groups
demonstrating faster times than the mid-PHV group.
For the 30 m times, all three groups of 1-2y-post-
PHV (p = 0.018), 2-3y-post-PHV (p < 0.001) and
>3y-post-PHV (p < 0.001) exhibited signicantly
faster times than the mid-PHV group.
International Journal of Strength and Conditioning. 2025 Niederdraeing, L., & Zentgraf, K.
5
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Table 1. Descriptive data (average and standard deviation) for anthropometric and other measures of participants for
each group.
Parameter mid-PHV
(n=26)
1-2y-post-PHV
(n=21)
2-3y-post-PHV
(n=21)
>3y-post-PHV
(n=17)
Age (years) 13.9 ± 0.6 15.2 ± 1.0 16.7 ± 0.56 17.7 ± 0.89
APHV (years) 13.68 ± 0.66 13.69 ± 0.79 14.21 ± 0.49 13.89 ± 0.66
Maturity offset (years) 0.21 ± 0.57 1.54 ± 0.31 2.52 ± 0.32 3.78 ± 0.64
Body height (cm) 168.9 ± 6.6 176.4 ± 5.1 179.0 ± 7.2 181.44 ± 7.7
Body mass (kg) 56.4 ± 6.8 64.9 ± 5.3 72.0 ± 7.1 77.8 ± 9.6
Seated height (cm) 86.4 ± 3.9 91.2 ± 2.6 92.2 ± 1.9 96.8 ± 3.2
Training age (years) 8.6 ± 1.3 10.1 ± 1.3 10.8 ± 2.1 12.0 ± 1.5
Youth academy since (years) 2.25 ± 1.68 2.93 ± 1.97 2.69 ± 2.47 4.79 ± 3.58
Strength practice since (years) 0.89 ± 0.50 1.62 ± 0.71 2.57 ± 1.00 2.91 ± 1.19
Strength exercises (h / week) 0.79 ± 0.43 1.93 ± 1.10 2.81 ± 1.32 3.18 ± 1.56
Figure 1. Split times up to 30 m for each group.
International Journal of Strength and Conditioning. 2025
Force-Velocity Proling among Different Maturational Stages in
Young Soccer Players: A Cross-Sectional Study
6
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open access article distributed under the terms and conditions of the
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Figure 2. Parameters of FVP of each group.
FH0 relative (N/kg), FH0 absolute (N), VH0 (m/s), Pmax (W/kg), FV slope (a.U.), FVDiff (%), DRF (%), RFmax (%)
7
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International Journal of Strength and Conditioning. 2025 Niederdraeing, L., & Zentgraf, K.
Figure 2 displays the parameters of the FVP, FH0
(absolute and relative numbers), VH0, Pmax, FV
slope, FVDiff, DRF, and RFmax of participants for each
group. The corresponding data can be found in the
appendix.
As described in Fig 1., signicant intergroup
differences were found for the split times >=10 m,
with the largest differences for the 30m time with
the fastest times occurring with higher MO. This
resulted in signicant higher values for VH0 (m/s)
and Pmax (W/kg) with increasing MO, but not for
FH0 (N/kg). However, FH0 in absolute numbers (N)
showed signicantly higher values for higher MO.
Additionally, RFmax (%) and FVDiff showed signicant
group differences, with RFmax (%) being higher and
FVDiff being lower with increasing MO. The specic
group differences can be observed in detail in Tables
2 and 3, while the exact numbers are provided in the
appendix.
Table 2 shows the differences in sprint performance
variables and force-velocity components between
maturity groups through one-way ANOVA (Kruskal-
Wallis) and Fisher’s ANOVA for FVDiff.
As shown in table 3, there are signicant group
differences between all groups for the 30m time and
thus the parameter VH0. Faster times are produced
by players with a higher MO. At the same time, only
marginal but increasing differences can be seen in
the 10m to 20m times. This results in the exclusive
group difference between mid-PHV and 2-3y-post-
PHV for FH0, and RFmax (%). Consequently, the
product of VH0 and FH0, Pmax, represents the mean,
with group differences evident between mid-
PHV and both 1-2y-post-PHV and 2-3y-post-PHV.
Concurrently, analogous group differences are
evident for FVDiff.
DISCUSSION
The aim of this study was to determine a cross-
sectional overview of the horizontal FV prole in
the U14-U19 teams of a professional soccer youth
academy. Furthermore, it is the rst systematic study
that determines the FVDiff for junior soccer players.
The horizontal FVP was calculated from a 30m sprint
with split times at 5 m, 10 m, 15 m, and 20 m, relative
to biological age. The APHV was determined using
Mirwald’s formula and the distance to the date of
measurement was determined to derive the MO.
Based on the MO, the players were divided into
groups to make statements about FVP variations in
different age ranges and thus maturational stages.
Older players, expectedly, have a larger MO, more
years of training and more strength training and
consequently should have higher performance
capabilities. For sprint performance, signicant
differences were found between the sprint times
for 10 m, 15 m, 20 m, and 30 m, but not for the
5m times. The effect size increased progressively
with increasing distance (ε² = 0.05 - 0.33). The
observation that the acceleration over 5m is not
Table 2. X²: Ratio of the variation between groups to the variation within groups;
df: degrees of freedom; p: p-value; ε²: effect size
Parameter X² df p ε²
5m (s) 4.22 3 0.239 0.0502
10m (s) 9.77 3 0.021 0.1163
15m (s) 11.1 3 0.011 0.1563
20m (s) 20.82 3 <.001 0.2479
30m (s) 27.43 3 <.001 0.3265
FH0 relative (N/kg) 1.21 3 0.751 0.0144
FH0 absolute (N) 28.92 3 <.001 0.3443
VH0 (m/s) 30.03 3 <.001 0.3575
Pmax (W/kg) 13.12 3 0.004 0.1562
FV slope (a.U.) 2.25 3 0.522 0.0268
RFmax (%) 9.05 3 0.029 0.1078
DRF (%) 2.47 3 0.480 0.0294
Parameter F df pEta²
FVDiff (%)* 4.81 3 0.004 0.151
International Journal of Strength and Conditioning. 2025
Force-Velocity Proling among Different Maturational Stages in
Young Soccer Players: A Cross-Sectional Study
8
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open access article distributed under the terms and conditions of the
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superior in older players seems unexpected at rst
glance. However, it is consistent with the ndings of
Loturco et al. (2018) who found faster 0-5m times in
U15 players than in U20 and senior players.
ANOVA showed a constant rise in VH0 (m/s) with
increasing MO and signicant differences in VH0
between the mid-PHV group and the three post-
PHV groups (p = 0.018, p < .001, p < .001), but not
between the other groups. The mean difference was
also greatest between mid-PHV and 1-2y-post-PHV
(M Diff = 0.66 m/s). Thus, the largest increases in
VH0 occur in the period shortly after APHV. These
results are consistent with those of Meyers et al.
(2015) and Morris et al. (2018), who found the
largest increases in linear velocity in boys at ages
during and immediately after the APHV. A possible
explanation may be changes in neuromuscular
activation and morphological factors like tendon and
muscle properties that allow greater force production
during sprinting (Radnor et al., 2018; Radnor et
al., 2020). The results of this study suggest that
the greatest increases in VH0 occur immediately
after the APHV, which would allow predictions
Table 3. shows the statistical results for Dunn-Bonferroni adjusted post-hoc tests.
Parameter Group 1-2 y-post PHV 2-3 y-post PHV >3 y-post PHV
Time 10m
mid-PHV stand. t = 1.714; adj. p = 0.519 stand. t = 2.938; adj. p = 0.020 stand. t = 2.192yd; adj. p = 0.170
1-2y-post PHV -stand. t = 1.163; adj. p = 1.000 stand. t = 0.579; adj. p = 1.000
2-3y-post PHV --stand. t = -0.546; adj. p = 1.000
Time 15m
mid-PHV stand. t = 2.065; adj. p = 0.234 stand. t = 2.973; adj. p = 0.018 stand. t = 2.278; adj. p = 0.136
1-2y-post PHV -stand. t = 0.911; adj. p = 1.000 stand. t = 0.575; adj. p = 1.000
2-3y-post PHV --stand. t = -0.199; adj. p = 1.000
Time 20m
mid-PHV stand. t = 2.617; adj. p = 0.053 stand. t = 4.048; adj. p < .001 stand. t = 3.590; adj. p = 0.002
1-2y-post PHV -stand. t = 1.361; adj. p = 1.000 stand. t = 1.078; adj. p = 1.000
2-3y-post PHV --stand. t = -0.209; adj. p = 1.000
Time 30m
mid-PHV stand. t = 2.945; adj. p = 0.019 stand. t = 4.613; adj. p < .001 stand. t = 4.173; adj. p < .001
1-2y-post PHV -stand. t = 1.585; adj. p = 0.678 stand. t = 1.341; adj. p = 1.000
2-3y-post PHV --stand. t = -0.158; adj. p = 1.000
FH0 absolute (N)
mid-PHV stand. t = 1.714; adj. p = 0.519 stand. t = 2.938; adj. p = 0.020 stand. t = 2.192; adj. p = 0.170
1-2y-post PHV -stand. t = 1.163; adj. p = 1.000 stand. t = 0.554; adj. p = 1.000
2-3y-post PHV --stand. t = -0.546; adj. p = 1.000
VH0 (m/s)
mid-PHV stand. t = -2.967; adj. p = 0.018 stand. t = -4,621; adj. p < .001 stand. t = -4.611; adj. p < .001
1-2y-post PHV -stand. t = -1.572; adj. p = 0.695 stand. t = -1.740; adj. p = 0.491
2-3y-post PHV --stand. t = -0.253; adj. p = 1.000
Pmax (W/kg)
mid-PHV stand. t = -1.978; adj. p = 0.288 stand. t = -3.299; adj. p = 0.006 stand. t = -2.736; adj. p = 0.037
1-2y-post PHV -stand. t = -1.257; adj. p = 1.000 stand. t = 0.838; adj. p = 1.000
2-3y-post PHV --stand. t = 0.351; adj. p = 1.000
RF (%)
mid-PHV stand. t = -1.804; adj. p > 0.050 stand. t = -2.784; adj. p = 0.032 stand. t = -2.164; adj. p = 0.183
1-2y-post PHV -stand. t = -0.932; adj. p = 1.000 stand. t = -0.446; adj. p = 1.000
2-3y-post PHV --stand. t = 0.435; adj. p = 1.000
FVDiff* (%)
mid-PHV stand. t = 2.292; adj. p = 0.147 stand. t = 3.131; adj. p = 0.015 stand. t = 3.234; adj. p = 0.011
1-2y-post PHV -stand. t = 0.798; adj. p = 1.000 stand. t = 1.031; adj. p = 1.000
--stand. t = 0.276; adj. p = 1.000
about the future performance of maximum sprint
velocity. This is important in the context of talent
identication. However, these predictions should be
made with caution as the trainability of VH0 has been
demonstrated (Lahti, Jiménez-Reyes et al., 2020).
While VH0 (m/s) and Pmax (W/kg) increase steadily
with increasing MO, FH0 (N/kg) shows no signicant
difference between groups. Group differences in
VH0 appear to be large enough to signicantly alter
Pmax (product of VH0 and FH0) between groups,
although FH0 shows no signicant differences. An
explanation for the results found for FH0 (N/kg) could
be that FH0 is relative to body weight and players
with a greater distance to the APHV have a greater
body weight (Mmid-PHV = 56.4 ± 6.75kg, M>3 y post-PHV=
77.8 ± 9.62kg). This was conrmed with the absolute
FH0 values (N). The mid-PHV group had signicantly
lower absolute FH0 values (N) compared to the other
groups (with increasing MO: p = 0.024, p < .001,
p < .001). Furthermore, signicantly higher absolute
FH0 values were found in the >3y-post-PHV group
compared to the 1-2y-post-PHV group (p = 0.046).
FH0 increases continuously in absolute terms, but not
International Journal of Strength and Conditioning. 2025 Niederdraeing, L., & Zentgraf, K.
in relation to body weight. This suggests that players
with a larger distance to the APHV lack relative
strength in sprint, which could be optimized via
tailored interventions, e.g., strength-power training
(Loturco et al., 2018). Notably, low expressions of
FH0 (N/kg) are linked to an increased risk of injury to
the hamstrings (Mendiguchia et al., 2016; Edouard
et al., 2021; Lahti et al., 2022). Absolute FH0 (N)
increases (M Diff = 67.6 N) the most between mid-
PHV and 1-2y-post-PHV and thus immediately
after APHV. Since all groups show signicant
differences from mid-PHV, but not in successive
groups, it can be assumed that the largest increase
in absolute FH0 (N) occurs immediately after APHV.
This is expectable as strength and quickness
develop during puberty and both are sensitive to
training (Haywood & Getchell, 2021). This is also
consistent with the ndings of Huijgen et al. (2010),
suggesting growth-related constant increases in
rate of force across the APHV. The improvements
in absolute strength during maturation are linked to
morphological factors and increased muscle size
(Olivier et al., 2013). Simultaneously, the increase
in body weight might limit increases in FH0 (N/kg).
This is consistent with the ndings of Dugdale et al.
(2024), who suggested that momentum (the product
of mass and velocity) has a large effect on sprint
performance and change of direction in maturing
adolescents. However, the relative FH0 is more
important for soccer players since their own body
weight has to be accelerated for game and practice
performance.
There has been no research to date that has
classied horizontal FVDiff. Nevertheless, vertical and
horizontal FVP have a lot in common, which suggests
that the principles of classication for vertical FVP
according to Jiménez-Reyes et al. (2019) can also
be applied to the FVDiff of horizontal FVP - although
a nal conrmation is still pending. For the entire
population, an average FVDiff of M = 124.0 ± 21.0%
is calculated for the 30m sprint, which is a signicant
deviation from 100%. According to the Jiménez-
Reyes et al. (2019) classication, this can be
interpreted as a moderate speed decit of 24%. In
cross-section, junior soccer players show a speed
decit for the 30m sprint distance. Supramaximal
(-110%) assisted sprints can be used to improve the
decit (Lahti et al., 2020). From descriptive statistics,
the speed decit is greatest during the APHV and
decreases as the MO increases. This is supported by
the signicant group differences (p = 0.011) between
mid-PHV (M = 135.74 ± 21.73%) and >3y-post-PHV
(M = 115.90 ± 20.15%). The steady increase of VH0
and Pmax with increasing MO is accompanied by the
reduction of FVDiff and a convergence towards FVopt,
possibly due to the growth process and training.
Interestingly, no signicant differences between
groups can be shown for the slope of the FVP (p
= 0.522). Thus, the ratios of FH0 (N/kg) and VH0
(m/s) did not differ signicantly, but the ratio to FVopt,
which depends on the individual Pmax. Based on the
data of this study, it can be argued that FVP change
with maturation. FVDiff changes with increasing MO,
but FV slope does not. Therefore, FV slope is not
sensitive enough to detect changes. This might be
due to the ratio computation of FH0 relative to body
weight, as players become heavier with increasing
MO. This leads to the need to determine FVopt to
assess the mechanical characteristics of the FVP.
Statements made solely based on FV slope do not
have the same validity as conclusions based on
FVDiff.
The results of this study are limited in multiple ways.
Regarding methodology, the process is based on a
theoretic model that has been applied in this study
for the rst time. Furthermore, the classication of
force and velocity decits was created for the vertical
plane, not the horizontal. However, since both
concepts rely on the same principles, it is very likely
to be valid in the horizontal plane as well; yet a nal
validation remains to be done. This could be done by
assessing many athletes in different sports; similar to
what Giroux et al. (2016) suggested for the vertical
plane. Additionally, the average sprint distance in a
game is 5.9 m. For shorter sprint distances, FVopt is
inuenced stronger by FH0 (Samozino et al., 2022),
which questions the transfer of the 30m FVopt to the
game. Nonetheless, sprints in a game do not occur
from a resting position, but mostly from jogging,
which in turn reduces the signicance of FH0 (Aughey
et al., 2011). Further research needs to be done to
(1) validate the concept of FVP for the horizontal
plane and (2) analyse the sprints in a soccer match
to nd the FVopt which inuences performance most.
CONCLUSION AND FUTURE
RECOMMENDATIONS
The horizontal FVP of soccer players from a youth
academy was established using a 30m sprint
with split times at 5 m, 10 m, 15 m, and 20 m. The
APHV of the soccer players was determined using
the Mirwald formula. Group differences of sprint
performance in relation to maturation were then
examined. Signicant differences were found for the
split times >=10 m, with the largest differences for
the 30m time. This resulted in signicant differences
9
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open access article distributed under the terms and conditions of the
Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).
10
Copyright: © 2025 by the authors. Licensee IUSCA, London, UK. This article is an
open access article distributed under the terms and conditions of the
Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).
International Journal of Strength and Conditioning. 2025
Force-Velocity Proling among Different Maturational Stages in
Young Soccer Players: A Cross-Sectional Study
for maximum theoretic velocity (m/s), but not for
maximum theoretic force in relation to body weight.
The greatest differences in maximum theoretic force
and velocity occurred immediately after growth spurt,
which supports the hypothesis of an inuence of the
biological development process on the horizontal
FVP. In the whole sample, FVDiff showed an average
speed decit of 24%, with the largest decit around
APHV and a convergence to FVopt with increasing
MO. FVDiff showed signicant group differences with
highest values at APHV, while the relationship of
force and velocity did not change signicantly. This
stresses the need to determine FVDiff since analyses
solely relying on force-velocity relationships are
not sensitive enough. FVDiff was determined for the
30m distance. While respecting individual training
adaptation, it is therefore recommended that young
soccer players train to improve maximum theoretic
velocity and thus their performance, especially
around APHV. Supramaximal (-110%) assisted
sprints have been shown to be effective in the past
Further research should explore the relationship
between biological maturity and horizontal FVP
in more detail and determine FVDiff for other sprint
distances and different populations.
CONFLICTS OF INTEREST
The authors declare no conict of interest.
FUNDING DETAILS
This study received no specic funding in order to
be completed.
ETHICAL APPROVAL
The study was approved by the Universities Ethics
Committee. All subjects were informed verbally and
on a written basis about the aims and risks of the
study and gave written consent to be part of this
research project, while for minors, parents signed
that they consented to the research project and
data processing.
DATES OF REFERENCE
Submission - 30/11/2023
Acceptance - 21/11/2024
Publication - 28/03/2025
CORRESPONDING AUTHOR
Leon Niederdraeing - leon.nieder@web.de
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13
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Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).
APPENDIX
Appendix 1
Table 4. Descriptive data for split times and adjusted split times up to 30 meters, and the parameters of the FVP, FH0
(absolute and relative numbers), VH0, Pmax, FV slope, FVDiff, DRF, and RFmax of participants for each group.
Parameter Ca.-PHV
(n=26)
1-2-y-post-PHV
(n=21)
2-3-y-post-PHV
(n=21)
>3y-post-PHV
(n=17)
5m (s) 1.22 ± 0.10 1.19 ± 0.09 1.18 ± 0.13 1.20 ± 0.11
10m (s) 2.00 ± 0.11 1.95 ± 0.11 1.92 ± 0.14 1.92 ± 0.12
15m (s) 2.71 ± 0.14 2.63 ± 0.12 2.60 ± 0.16 2.58 ± 0.17
20m (s) 3.37 ± 0.16 3.24 ± 0.15 3.18 ± 0.16 3.18 ± 0.15
30m (s) 4.66 ± 0.23 4.46 ± 0.20 4.36 ± 0.19 4.35 ± 0.19
Adj. 5m (s) 1.43 ± 0.10 1.40 ± 0.09 1.39 ± 0.13 1.41 ± 0.11
Adj. 10m (s) 2.21 ± 0.11 2.16 ± 0.11 2.13 ± 0.14 2.13 ± 0.12
Adj. 15m (s) 2.92 ± 0.14 2.84 ± 0.12 2.81 ± 0.16 2.79 ± 0.17
Adj. 20m (s) 3.58 ± 0.16 3.45 ± 0.15 3.39 ± 0.16 3.39 ± 0.15
Adj. 30m (s) 4.87 ± 0.23 4.67 ± 0.20 4.57 ± 0.19 4.56 ± 0.19
FH0 (N/kg) 7.20 ± 1.02 7.25 ± 0.91 7.37 ± 1.21 7.28 ± 1.22
FH0 absolute (N) 404.07 ± 63.56 471.67 ± 78.14 529.07 ± 97.46 564.83 ± 107.53
VH0 (m/s) 8.40 ± 0.65 9.06 ± 0.58 9.43 ± 0.56 9.52 ± 0.65
Pmax (W/kg) 15.08 ± 2.02 16.38 ± 2.05 17.26 ± 2.35 17.23 ± 2.54
FV slope (a.U.) -0.863 ± 0.16 -0.804 ± 0.12 -0.789 ± 0.16 -0.775 ± 0.16
FVDiff (%) 135.74 ± 21.73 122.52 ± 16.46 117.68 ± 19.50 115.90 ± 20.15
RFmax (%) 42.32 ± 2.55 43.67 ± 2.74 44.41 ± 3.69 44.22 ± 3.44
DRF (%) -7.82 ± 2.15 - 7.46 ± 1.13 -7.29 ± 1.42 -7.15 ± 1.44
