International Journal of Sports Physiology and Performance, 2016, 11, 267 -272
© 2016 Human Kinetics, Inc.
One of the main physical performance determinants in sports
such as athletics, rugby, soccer, football, volleyball, and basketball
is the ability to produce high mechanical power output during jumps
and sprint accelerations.
This power output depends on the ability
of athletes’ neuromuscular and osteoarticular systems to generate
high levels of force, apply it with effectiveness onto the environ-
ment (ie, supporting ground, ball, projectile), and produce this
force at high contraction velocity. Force and velocity are therefore
considered the underpinning features of mechanical power output
in sport movements.
Although the assessment and long-term
monitoring of these capabilities is paramount for both performance
and rehabilitation processes, such an accurate evaluation has long
been associated with expensive and often laboratory-based tech-
nologies. Recently, our research group has presented simple eld
methods to compute force, velocity, and power output in jumping
calculated via measurements from widely accessible
and practical devices. Thanks to these methods, all the important
mechanical outputs of jumping and sprinting can be derived from
basic measures of body mass, lower-limb length, jump height, and
distance–time or speed–time measurements only.
Recently, we had the opportunity to discuss the implementa-
tion of these “simple methods” with many sport practitioners, and
we realized that beyond the description presented in the published
papers, it was necessary to detail how to interpret the measurements
for an efcient use in everyday practice. Our aim here is to provide
a practical vade mecum to readers wishing to use power-force-
velocity proling for more individualized diagnostic and efcient
training. The key points of this commentary will be supported by
illustrations of typical data collected in our research, training, or
consultancy practice over the past decade.
The power-force-velocity–proling approach is based on force–
velocity (F–V) and power–velocity relationships characterizing the
maximal mechanical capabilities of the lower limbs’ neuromuscular
system. The denition and the practical interpretation of the main
mechanical variables of interest are presented in Table 1.
Vertical Profiling for Ballistic Push-Off
The input measurements necessary to correctly determine vertical
are the athlete’s body mass, lower-limb length in fully
extended position, starting height, and jump height (measured under
a spectrum of loading parameters). The latter can now be easily and
accurately measured using simple and accessible devices.
height should be measured across repeated measurements with at
least 5 additional loads (evenly ranging between 0 kg and the addi-
tional load with which the athlete is able to jump about 10 cm), after
which the F–V prole and all other computations can be completed.
Research conclusions show that jumping performance is deter-
mined by maximal mechanical power output (VTC-Pmax) and the
magnitude of the relative difference between the slope of the linear
F–V relationship (Sfv) and Sfv
for a given individual (FVimb).
Thus, in practical terms, should a training program be designed to
improve athletes’ ballistic push-off performance (eg, jumps, single
maximal push-offs, change of direction), the focus should be placed
on increasing VTC-Pmax and/or decreasing FVimb. With regard to
athletes displaying signicant imbalance in mechanical capacities,
Interpreting Power-Force-Velocity Profiles
for Individualized and Specific Training
Jean-Benoît Morin and Pierre Samozino
Recent studies have brought new insights into the evaluation of power-force-velocity proles in both ballistic push-offs (eg,
jumps) and sprint movements. These are major physical components of performance in many sports, and the methods the authors
developed and validated are based on data that are now rather simple to obtain in eld conditions (eg, body mass, jump height,
sprint times, or velocity). The promising aspect of these approaches is that they allow for more individualized and accurate
evaluation, monitoring, and training practices, the success of which is highly dependent on the correct collection, generation,
and interpretation of athletes’ mechanical outputs. The authors therefore wanted to provide a practical vade mecum to sports
practitioners interested in implementing these power-force-velocity–proling approaches. After providing a summary of theo-
retical and practical denitions for the main variables, the authors rst detail how vertical proling can be used to manage bal-
listic push-off performance, with emphasis on the concept of optimal force–velocity prole and the associated force–velocity
imbalance. Furthermore, they discuss these same concepts with regard to horizontal proling in the management of sprinting
performance. These sections are illustrated by typical examples from the authors’ practice. Finally, they provide a practical and
operational synthesis and outline future challenges that will help further develop these approaches.
Keywords: explosive performance, jump, sprint, team sports, athletics, strength training
Morin is with the Laboratory of Human Motricity, Education Sport and
Health, University of Nice Sophia Antipolis, Nice, France. Samozino is
with the Inter-Universitary Laboratory of Human Movement Biology,
University Savoie Mont Blanc, Le Bourget-du-Lac, France. Address author
correspondence to Jean-Benoît Morin at email@example.com.
268 IJSPP Vol. 11, No. 2, 2016
Table 1 Definition and Practical Interpretation of the Main Variables of Interest When Using Power-Force-Velocity
Profiling in Ballistic Push-Offs (Vertical Profiling) and Sprinting (Horizontal Profiling)
Profiling variable Definition and computation Practical interpretation
VTC-F0 (N/kg) Theoretical maximal force production of
the lower limbs as extrapolated from the
linear loaded jump squats’ force–veloc-
ity (F–V) relationship; y-intercept of the
linear F–V relationship.
Maximal concentric force output (per unit body mass) that the athlete’s lower
limbs can theoretically produce during ballistic push-off. Determined from
the entire F–V spectrum, it gives more integrative information on force capa-
bility than, eg, concentric squat 1-repetition-maximum load.
VTC-V0 (m/s) Theoretical maximal extension velocity
of the lower limbs as extrapolated from
the linear loaded jump squats’ F–V rela-
tionship; x-intercept of the linear F–V
Maximal extension velocity of the athlete’s lower limbs during ballistic
push-off. Determined from the entire F–V spectrum and very difcult, if not
impossible, to reach and measure experimentally. It also represents the capa-
bility to produce force at very high extension velocities.
VTC-Pmax (W/kg) Maximal mechanical power output,
computed as Pmax = F0 × V0/4 or as the
apex of the P–V 2nd-degree polynomial
Maximal power output capability of the athlete’s lower-limb neuromuscular
system (per unit body mass) in the concentric and ballistic extension motion.
Sfv Slope of the linear F–V relationship,
computed as Sfv = –F0/V0.
Index of the athlete’s individual balance between force and velocity capa-
bilities. The steeper the slope, the more negative its value, the more “force-
oriented” the F–V prole, and vice versa.
For a given push-off distance, body
mass, and Pmax, the unique value of Sfv
that maximizes jump height. For detailed
computation, see Appendix in Samozino
The optimal F–V prole that represents the optimal balance, for a given indi-
vidual, between force and velocity capabilities. For a given maximal power
Pmax, this prole will be associated, ceteris paribus, with the highest ballistic
push-off performance possible for this individual. Training programs should
be designed to both increase Pmax and orient Sfv toward Sfv
FVimb (%) Magnitude of the relative difference
between Sfv and Sfv
for a given indi-
vidual. Computed as (Sfv/Sfv
) × 100
and expressed in percentage.
Magnitude of the difference between actual and optimal F–V proles. A value
of 100% means Sfv = Sfv
, ie, optimized F–V prole. Values above 100%
mean an imbalance with a decit in velocity, and vice versa. The larger the
difference with the optimal 100% value, the larger the imbalance.
HZT-F0 (N/kg) Theoretical maximal horizontal force
production as extrapolated from the
linear sprint F–V relationship; y-inter-
cept of the linear F–V relationship.
Maximal force output (per unit body mass) in the horizontal direction. Cor-
responds to the initial push of the athlete onto the ground during sprint accel-
eration. The higher the value, the higher the sprint-specic horizontal force
HZT-V0 (m/s) Theoretical maximal running velocity as
extrapolated from the linear sprint F–V
relationship; x-intercept of the linear
Sprint-running maximal velocity capability of the athlete. Slightly higher than
the actual maximal velocity. The theoretical maximal running velocity the
athlete would be able to reach should mechanical resistances (ie, internal and
external) against movement be null. It also represents the capability to pro-
duce horizontal force at very high running velocities.
HZT-Pmax (W/kg) Maximal mechanical power output in the
horizontal direction, computed as Pmax
= F0 × V0/4, or as the apex of the P–V
2nd-degree polynomial relationship.
Maximal power-output capability of the athlete in the horizontal direction
(per unit body mass) during sprint acceleration.
RF (%) Ratio of force, computed as the ratio of
the step-averaged horizontal component
of the ground-reaction force to the cor-
responding resultant force.
Direct measurement of the proportion of the total force production that is
directed in the forward direction of motion, ie, the mechanical effectiveness
of force application of the athlete. The higher the value, the more important
the part of the total force output directed forward.
RFmax (%) Maximal value of RF, computed as max-
imal value of RF for sprint times >0.3 s.
Theoretically maximal effectiveness of force application. Direct measurement
of the proportion of the total force production that is directed in the forward
direction of motion at sprint start.
Rate of decrease in RF with increasing
speed during sprint acceleration, com-
puted as the slope of the linear RF–V
Describes the athlete’s capability to limit the inevitable decrease in mechani-
cal effectiveness with increasing speed, ie, an index of the ability to maintain
a net horizontal force production despite increasing running velocity. The
more negative the slope, the faster the loss of effectiveness of force applica-
tion during acceleration, and vice versa.
IJSPP Vol. 11, No. 2, 2016
Power-Force-Velocity Profiles and Training 269
training programs should prioritize training the lacking mechanical
capability to shift Sfv toward Sfv
. The main interest of the current
approach is that the diagnostics, and resultant training periodization,
are individualized and easily monitored. Consequently, the ability
to frequently monitor these outputs permits the analysis of changes
in VTC-Pmax and FVimb over time (eg, once every month) and
can assist in the targeted implementation and reimplementation of
efcient and dynamic programming practices. The rst case report
(Figure 1) illustrates this with data from 2 athletes with a similar
push-off distance. Although athlete A has a higher VTC-Pmax, his
squat-jump performance is lower because he has an F–V imbalance.
Athlete B has a lower VTC-Pmax, but his prole is almost exactly
equal to his individual optimal prole (only 1% imbalance). The
current approach would suggest, therefore, that athlete A’s training
should prioritize the development of maximal force capabilities to
correct his imbalance and increase VTC-Pmax. Once this goal is
achieved, he may transition into training similar to that of athlete
B, to improve his VTC-Pmax while maintaining his corrected (ie,
The second example shows 2 young players from the same
soccer team (French rst-league professional club academy U19).
As shown in Figure 2, these players have quite similar VTC-Pmax
values but display opposing FVimb characteristics: Player
A shows a force decit, whereas player B shows a velocity decit.
Furthermore, the absolute difference with their respective Sfv
lower in player B than in player A (28% vs 37%). This relatively
smaller FVimb and slightly higher VTC-Pmax in player B explain
his higher squat-jump performance.
With this result in mind, this approach suggests that the most
efcient way to train and improve ballistic push-off performance
in both these players would be an individualized program (indexed
on each player’s FVimb) that targets the development of different
Figure 1 —
Vertical force–velocity proles of 2 track and eld athletes (body mass for A, 67.2 kg, and B, 82.8 kg; push-off distance for A, 0.34 m, and
B, 0.35 m) obtained from maximal squat jumps (SJ) against additional loads of 0, 10, 20, 30, and 40 kg. Despite a higher VTC-Pmax (maximal mechanical
power output) value, athlete A’s squat-jump performance is lower because his FV
(magnitude of the relative difference between the slope of the linear
force–velocity relationship [Sfv] and Sfv
) is greater than for athlete B. For athlete A, the black line indicates the actual prole, and the dashed line, the
optimal prole. Note that athlete B’s prole if almost optimal, and therefore the actual and optimal relationships are confounded in the right panel (gray
line and black dashed line). Abbreviations: VTC-F0, maximal force production of the lower limbs; VTC-V0, maximal extension velocity of the lower limbs.
Figure 2 — Vertical force–velocity proles of 2 elite young (under-19) soccer players (body mass for A, 78 kg, and B, 75.5 kg; push-off distance for
A, 0.26 m, and B, 0.28 m) obtained from maximal squat jumps (SJ) against additional loads of 0, 10, 20, 40, and 50 kg. One player has a force decit
(magnitude of the relative difference between the slope of the linear force–velocity relationship [Sfv] and Sfv
] of 72%), whereas the other has a
velocity decit (FV
of 137%). Player A is a central defender and player B is a goalkeeper. Abbreviation: VTC-Pmax, maximal mechanical power output.
IJSPP Vol. 11, No. 2, 2016
270 Morin and Samozino
capabilities. Our yet-unpublished observations have shown that
such an individually optimized approach is more efcient that a
one-size-ts-all program, identical for those 2 players.
The latter example raises an important question, however, with
regard to the application of improving ballistic push-off performance
in cyclic movements such as sprint running. This particular question
is the main interest when developing forward (sprint) acceleration
and performance characteristics, for instance, in soccer or rugby
players (except for some players like goalkeepers or some specic
sport actions involving jumps), and will be discussed in the follow-
ing section detailing horizontal proling for sprint performance.
Horizontal Profiling for Sprint Performance
The inputs that must be measured to determine the horizontal
are the athlete’s body mass and height and either distance–
time or speed–time running data. The latter can be measured using
a series of timing gates (at least 5 split times, eg, 5, 10, 20, 30,
and 40 m) or a laser or radar device (eg, ~50-Hz Stalker ATSII
radar, Applied Concepts Inc, Plano, TX). Wind speed, ambient
temperature, and pressure must also be known to accurately esti-
mate air-friction force. The entire power-force-velocity prole can
then be computed from the simple modeling of the derivation of
the speed–time curve that leads to horizontal acceleration data.
Likewise, the mechanical effectiveness of force application can be
determined via the linear relationship between ratio of force (RF)
and running velocity
(Figure 3). Our research has shown that, in
addition to maximal mechanical power output in the horizontal
direction (HZT-Pmax), 100-m performance was related to the ability
to apply high amounts of force in the horizontal direction (RF and
rate of decrease in RF [D
With regard to shorter
sprints (ie, acceleration-only phases, eg, up to 10–20 m in rugby
or soccer specialists), recent results have shown that the shorter
the distance considered, the higher the relationship between sprint
performance and maximal horizontal force production (HZT-F0)
(unpublished observations). Thus, in practical terms, if a training
program is designed to improve sprint-acceleration performance,
the focus should be placed on increasing HZT-Pmax by improving
its components (HZT-F0 and maximal running velocity [HZT-V0]).
This could be done by rst comparing the relative strengths and
weaknesses in each player’s prole with the rest of the team, and
then programming the training content depending on the distance
over which sprint acceleration should be optimized. As for vertical
proling, the main value of this approach is that the diagnostic and
subsequent targeted training interventions are individualized, and
frequent monitoring of program-induced changes in HZT-Pmax and
its mechanical determinants can make this program more efcient
and dynamic in terms of adaptation to individual changes over
time. In particular, since HZT-F0 and RF are paramount for short
sprint-acceleration performances, coupling the vertical proling to
the horizontal proling can help identify the determinants of HZT-
F0. Using this approach, we consider HZT-F0 to result from the
interaction of the overall strength capability of the athlete at each
lower-limb extension (as assessed by the vertical prole) and his
or her ability to transfer this overall strength level to the specic,
forward sprint motion at the rst steps (as evidenced by RFmax) or
at steps at high velocities (as evidenced by D
) (Table 1, Figure 4).
In short, a high HZT-F0 can result from high VTC-Pmax and a high
quality of vertical-to-horizontal transfer (ie, good RFmax and D
values), whereas a low HZT-F0 can result from a high VTC-Pmax
with a low-quality transfer (poor RFmax and D
values); vice versa,
a low VTC-Pmax with a high-quality transfer (good RFmax and D
values); or any possible intermediate combination.
The case report used to illustrate these points shows data from
2 players of an elite rugby union team. Figure 3 shows that the 2
players have similar 20-m times (maximal acceleration from a stand-
ing start) and HZT-Pmax values, yet with opposite F–V proles and
RF-velocity proles. Indeed, player C has higher horizontal force-
production capabilities (in the specic context of sprint push-off),
especially at the beginning of the sprint and notably due to a higher
effectiveness of ground-force application (indicated in a higher
RFmax). However, his D
is more negative, meaning his higher
initial effectiveness decreases at a greater rate as speed increases
than for player D. This has likely contributed to higher velocity
Figure 3 — Horizontal force–velocity proles of 2 elite rugby union players (body mass for C, 108.8 kg, and D, 86.1 kg) obtained from maximal
30-m sprints. Both players reached their maximal running speed before the 30-m mark. Abbreviations: HZT-Pmax, maximal mechanical power output
in the horizontal direction; D
, rate of decrease in ratio of force with increasing speed during sprint acceleration; HZT-F0, maximal horizontal force
production; HZT-V0, maximal running velocity.
IJSPP Vol. 11, No. 2, 2016
Power-Force-Velocity Profiles and Training 271
capabilities, which explains the higher HZT-V0 of player D. As for
ballistic push-off, we suggest that the training program designed to
improve sprint performance (eg, here 20-m time) in each of these
2 players should target different capabilities. A similar program
given to these players (which is current practice in the majority of
teams, based on our perception) will very likely result in subopti-
mal adaptations for both of them. In particular, player D’s training
should target as a priority his HZT-F0 capabilities. Here, in terms of
injury prevention, this suggests that this player could be given more
strength and horizontal strength work than others and probably less
maximal sprint velocity work. This could directly reduce the risk for
sprinting-related injuries for this player by reducing the total time
he would be exposed to high-speed running.
For this player,
compared with player C (and potentially compared with the average
value of the group/team), HZT-F0 should be developed, especially
through increasing RFmax. Adding the previously described verti-
cal proling to this horizontal proling could help better determine
whether a lower HZT-F0 is due to an overall decit of lower-limb
strength (as indicated by a low VTC-Pmax) and/or a decit in the
transfer of this strength in the specic horizontal push-off motion
(technical capability). Differences in horizontal proles have been
reported in elite rugby players according to individual player posi-
and in young soccer players.
Figure 4 shows a decision tree, with a specic focus on ballistic
push-off and sprint-acceleration performance, which are 2 major
physical determinants in many sports. This gure is designed to help
practitioners use the vertical and horizontal proling approach to
better detect the strengths and weaknesses in their athletes and design
more-effective training interventions. Vertical proling will provide
information as to what physical capabilities should be developed
to improve ballistic push-off performance and as to the maximal
levels of force and velocity of the athlete’s neuromuscular system.
Horizontal proling will provide information as to the specic sprint-
acceleration motion and as to what underlying physical or technical
feature(s) mainly limit each individual’s sprint performance.
Conclusion and Perspectives
These novel approaches of vertical and horizontal force-velocity-power
proling have the potential to provide sport practitioners simple, cheap,
yet accurate methods for more individualized monitoring and training
of physical and technical capabilities. These methods can be easily
implemented on a regular basis, since they are based on common and
sport-specic movements (ballistic push-offs and sprint accelerations),
and can therefore be used for long-term monitoring and training pro-
cesses. Furthermore, they may also be implemented in injury-prevention
and -rehabilitation processes since diagnostic information will assist in
better-designed sprint-related training programs, and clear differences
have been observed between injured and noninjured players.
The limitations of these approaches have been extensively
and the main perspective stems from the fact that
these proling methods give information as to what specic muscle
outputs should be developed, not how this should be done. This
will be the next challenge that we are pleased to undertake: testing
and investigating the most-efcient practical (training) methods to
improve each mechanical determinant of performance and further
extending the current knowledge on this topic
using the novel
approaches presented here.
We are forever grateful for the help (and trust) of all the sports practitioners
(coaches, physiotherapists, managers, doctors, researchers, students) who have
helped us develop these approaches over the last 10 years. We also thank all
the athletes, of all levels of performance, who did, do, or will give voluntarily
and enthusiastically their best effort during testing. A special thanks goes to
our friend and colleague Pedro Jimenez-Reyes, for his dedicated work and
help in developing this approach. We gratefully thank Matt Cross and Matt
Brughelli for their careful reading and comments on the revised manuscript.
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Figure 4 — Decision tree to interpret the force-velocity-power proles in relationship with ballistic push-off (eg, jumping) and sprinting performances.
These mechanistic relationships are based on both the theoretical features of our models
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data). In sprinting, the shorter the acceleration distance, the higher the importance of HZT-F0 capabilities compared with HZT-V0, and vice versa. Abbre-
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