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Biomechanical determinants of the reactive strength index during drop jumps

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International Journal of Sports Physiology and Performance, 2018, 13, 44-49
https://doi.org/10.1123/ijspp.2017-0021
© 2018 Human Kinetics, Inc. ORIGINAL INVESTIGATION

Biomechanical Determinants of the Reactive Strength Index

During Drop Jumps
Kristof Kipp, Michael T. Kiely, Matthew D. Giordanelli, Philip J. Malloy, and Christopher F. Geiser

The Reactive Strength Index (RSI) is often used to quantify drop-jump (DJ) performance; however, not much is known about
its biomechanical determinants. The purpose of this study was to investigate the correlations between the RSI and several
biomechanical variables calculated from DJ performed with different initial drop heights. Twelve male NCAA Division I
basketball players performed DJs from drop heights of 30, 45, and 60 cm. Force plates were used to calculate DJ performance
parameters (ie, DJ height, contact time, and RSI) and DJ biomechanical variables (ie, vertical stiffness and eccentric/concentric
energetics). Regression analyses were used to assess the correlations between variables at each drop height, and ANOVAs
were used to assess the differences of all variables across drop heights. Follow-up analyses used 2 neural networks to
determine if DJ performance and biomechanical data could accurately classify DJ trials by drop-height condition. Vertical-
stiffness values were significantly correlated with RSI at each height but did not change across drop heights. Surprisingly,
the RSI and other DJ parameters also did not vary across drop height, which resulted in the inability of these variables to
accurately classify DJ trials. Given that vertical stiffness did not change across drop height and was highly correlated with
RSI at each height, the RSI appears to reflect biomechanical behavior related to vertical stiffness during DJ. However, the
inability of the RSI to accurately classify drop-height condition questions the use of RSI profiles established from DJs from
different heights.

Keywords: biomechanics, neuromuscular, neural network, training, monitoring

The Reactive Strength Index (RSI) is a measure often used to a trade-off because such systems do not provide the in-depth
quantify dynamic lower-extremity performance during a drop jump information of force-plate analyses. It would therefore be of
(DJ).1–3 The RSI represents a highly reliable (ie, intraclass corre- significant practical interest to determine the correlations between
lation coefficient > .90) and simple index of performance that is RSI- and force-plate-derived data to provide practitioners with
also easy to measure and interpret.4–6 The RSI is calculated as the better information about the biomechanical determinants of
quotient of DJ jump height and ground-contact time and reflects the RSI.
the ratio of how high an athlete jumps to how much time he or The instructions that are provided to athletes during DJs and
she spends on the ground.1 It is common for DJ testing and RSI RSI testing are typically to “jump as high and as fast as you can.”1
calculation to include conditions where the height of the drop is These instructions are provided to encourage athletes to maximize
manipulated in order to establish an RSI profile, which can jump height and minimize ground-contact time, which in combi-
purportedly be used to investigate the effects of training and nation optimize RSI. Given that such instructions likely lead to
differences in skill or strength levels.1,3 Based on its inherent large ground-reaction forces over small periods of time, it could
reliability, simplicity, and utility it has been suggested that the be hypothesized that the RSI is associated with vertical stiff-
RSI is ideal for assessing cross-sectional differences and monitor- ness.7,8 In addition, given that maximal DJ performance depends
ing longitudinal changes in maximal dynamic lower-extremity on optimal stretch-shortening-cycle function, it could also be
performance. hypothesized that the RSI is associated with the center-of-mass
Although the RSI provides simple insight into dynamic (COM) energetics.9 Furthermore, since drop height is often
lower-extremity performance during a DJ, not much is known manipulated during RSI testing and represents different stretch-
about its biomechanical determinants. Beyond the variables of and impact-load conditions during the DJ, one could further
jump height and ground-contact time, both of which are used to hypothesize that athletes adjust stiffness and energetic behavior
calculate RSI, no studies have investigated other biomechanical to scale with such changes in height.1,3 In light of these hypothe-
variables associated with the RSI. This lack of knowledge, ses, the purpose of this study was to investigate correlations
however, presents a gap that may inhibit the optimal use of the between RSI and biomechanical variables during a series of DJs
RSI as a monitoring tool in the applied strength and conditioning performed from different heights, with the rationale that the
setting, because practitioners cannot be confident of the char- knowledge of these correlations would provide useful informa-
acteristics that RSI actually measures. In this light, the benefit of tion about the biomechanical determinants of the RSI. In particu-
being easily calculated from simple jump systems also represents lar, our analysis of variables focused on athletes’ vertical stiffness
and COM energetics during the eccentric and concentric phases of
the DJ. A secondary purpose, which manifested as a follow-up
Kipp, Giordanelli, and Geiser are with the Dept of Physical Therapy, Marquette analysis, was to determine if DJ performance parameters (ie,
University, Milwaukee, WI. Kiely is with Laurus Athletic Rehab & Performance, DJ height, contact time, and RSI) and DJ biomechanical data
Roseville, MN. Malloy is with the Dept of Orthopedic Surgery, Rush University, (ie, vertical stiffness and eccentric/concentric and work) could
Chicago, IL. Kipp is corresponding author (kristof.kipp@marquette.edu). accurately classify DJ trials by drop height.
44
 Biomechanical Determinants of the RSI During Drop Jumps 45

Methods A 4000

Participants
3000
Twelve male NCAA Division I basketball players were recruited

GRF (N)
for this study (mean ± SD age 21.6 ± 1.8 y, height 1.93 ± 0.10 m,
body mass 80.5 ± 10.5 kg). Before testing, all players were briefed 2000
on the scope of the study and read and signed an informed-consent
document that was approved by the local university’s institutional 1000
review board for human subjects testing.
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0
Testing Protocol -0.1 0 0.1 0.2 0.3 0.4

All athletes were tested in the mornings before any skill or Time (s)
conditioning work. All were asked not to participate in heavy B 100
resistance training or intense conditioning sessions for 48 hours
prior to testing. Before testing, each athlete performed a brief 50
dynamic warm-up that included body-weight exercises (eg, squats,

Power (W·kg-1)
lunges) and a variety of submaximal- and maximal-effort counter- 0
movement jumps and squat jumps. Each participant then per-
formed several submaximal-effort DJs, after which he performed -50
3 maximal-effort DJs from box heights of 30.5, 45.7, and 61 cm. To
simplify, these heights are referred to as 30, 45, and 60 cm from
-100
here on. The explicit instructions were to “jump as high and as fast
as you can.” Approximately 30 seconds of rest were allowed
-150
between maximal-effort DJs. All athletes were familiar with the -0.1 0 0.1 0.2 0.3 0.4
DJ through their regular strength and conditioning practices and Time (s)
were therefore provided with only minimal familiarization, which
C 4000
was primarily allocated so that each participant could get used to
the layout of the force plates that were positioned approximately
15 cm in front of the box. DJ trials were excluded if the athlete 3000
either stepped down onto the force plate or jumped off of the box.
GRF (N)

All DJ trials were supervised by a certified strength and condition-

ing specialist. 2000

Data Collection and Processing 1000

For all DJs athletes landed on 2 AMTI force plates (Model OR6-6,
Advanced Mechanical Technologies Inc, Watertown, MA, USA) 0
-0.4 -0.2 0 0.2
that were mounted flush with the floor. Participants were posi-
tioned such that each foot landed fully on 1 of the 2 force plates. Position (m)
All processing occurred with custom-written MATLAB (The
Mathworks Inc, Natick, MA, USA) programs. Kinetic data from Figure 1 — Three-trial ensemble average of biomechanical data during
the force plates were recorded at 1000 Hz and filtered with a the stance phase of drop jumps from 30-cm (light gray line), 45-cm (dark
fourth-order low-pass Butterworth filter and a cutoff frequency of gray line), and 60-cm (black line) drop heights for 1 representative athlete.
15 Hz, which was determined after an analysis of the residuals (A) Vertical ground reaction forces (GRF) versus time. (B) Center-of-mass
from several cutoff frequencies. The filtered vertical-ground- system power versus time. (C) Vertical GRF) versus center-of-mass
reaction-force (VGRF) data from both force plates were then system position.
summed into a single VGRF vector. The peak VGRF (Fmax; N)
and ground-contact time (tc; s) were extracted for analysis
(Figure 1[A]). The vertical-ground-reaction force−time curves (JEcc; N · m−1 · kg−1) and concentric (JConc; N · m−1 · kg−1) work.
were used to calculate the acceleration of the COM. The velocity Vertical stiffness (kvert; kN/m) was defined as the ratio of Fmax to Δy.11
of the COM during the contact phase of the DJ was calculated
through numerical integration of the net vertical-acceleration Classification of Neural Networks
data. The initial velocity of the COM was calculated from the
flight times associated with the different drop heights.10 The Two separate feedforward neural networks were used to determine
same procedure was repeated to calculate the COM position. if DJ performance parameters (ie, DJ height, contact time, and RSI)
The COM velocity was multiplied with the VGRF data to produce and DJ biomechanical data (ie, vertical stiffness and eccentric/
COM power, which in turn was used to identify eccentric concentric work) could accurately classify DJ trials by drop height.
(negative power) and concentric (positive power) movement Input data for both networks were randomly divided into training
phases (Figure 1[B]). Motion of the COM was also use to calculate (70%), validation (15%), and testing samples (15%). The architec-
the maximum vertical displacement (Δy; m) during the DJ. The ture of both networks consisted of 3 input layers, 10 hidden layers,
power−time curves were numerically integrated to estimate eccentric and 1 output layer. In each case, the output layer reflected the drop
IJSPP Vol. 13, No. 1, 2018
 46 Kipp et al

height. The networks were trained with scaled conjugate gradient Results
back-propagation, and network performance was assessed from
the mean square error. Confusion matrices were then generated Main effects for drop height were observed for peak force, maxi-
to assess the percentage of correctly and incorrectly classified mum vertical displacement, eccentric work, and concentric work
DJ trials. (Table 2). Post hoc testing indicated that peak force during the
60-cm DJ was greater than during the 30-cm DJ (P = .024) and that
COM displacement during the 60-cm DJ was greater than during
Statistical Analysis the 30-cm DJ (P = .002). Post hoc testing further indicated that
Descriptive data are reported as mean ± SD. Preliminary analyses eccentric work during the 60-cm DJ was greater than during the
were performed for all data to ensure that requirements for 45-cm DJ (P = .001) and 30-cm DJ (P = .001). In addition, eccen-
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parametric testing were met. Simple linear-regression analyses tric work was greater during the 45-cm DJ than during the 30-cm
were used to test for correlations between RSI and biomechanical DJ (P = .001). Conversely, post hoc testing indicated that concen-
variables. Separate general linear analysis-of-variance (ANOVA) tric work during the 30-cm DJ was great than during the 45-cm DJ
models were used to test for differences in dependent variables. (P = .003) and the 60-cm DJ (P = .013).
Each ANOVA model consisted of a 3-way analysis to test for Several of the correlations between RSI and biomechanical
within-subject differences across the independent variable (ie, drop variables were significant (Table 3). The RSI was correlated with
height). Within-subject differences were treated as repeated mea- vertical stiffness during the eccentric and concentric phases at all
sures. Assumptions of the test statistic were verified with the drop heights. The RSI was also significantly correlated with the
Mauchly test of sphericity. Greenhouse-Geisser corrections were amount of negative mechanical work during the DJ from all 3 drop
made when assumptions of sphericity were violated. Partial eta- heights. Positive mechanical work, however, was correlated with
squared (η2) values were used to help interpret the magnitude of the RSI only at the 60-cm drop height.
main effects. The criterion for statistical significance was set at an The neural network with DJ performance parameters as input
alpha level of .05. The reliability of all dependent variables for each classified only 33.3% of all DJ trials correctly (Figure 2A). The
drop height was assessed with intraclass correlation coefficients respective percentage errors for training, validation, and testing were
(Table 1). All statistical analyses were performed in SPSS 24.0 63%, 75%, and 87%, respectively. In contrast, the neural network
(IBM Corp, Armonk, NY, USA). with DJ biomechanical data as input classified 96.3% of all DJ
trials correctly (Figure 2B), and the respective errors for training,
validation, and testing were 0%, 0%, and 25%, respectively.

Table 1 Intraclass Correlation Coefficients for All Discussion

Dependent Variables at Each Drop Height
The primary purpose of this study was to investigate correlations
30 cm 45 cm 60 cm between the RSI and other biomechanical variables during DJ from
Height .971 .853 .853 different drop heights. The major finding of this study was that
values for vertical stiffness during DJ were consistently correlated
Ground-contact time .940 .969 .978
with RSI across all drop heights. Furthermore, values of vertical
Reactive Strength Index .957 .986 .967 stiffness did not change across drop heights. In combination, these
Peak vertical ground-reaction force .975 .971 .974 results suggest that the RSI reflects biomechanical behavior asso-
Vertical displacement .916 .872 .936 ciated with the vertical stiffness of the body’s musculoskeletal
Eccentric work .930 .958 .984 system during DJ. The reason that vertical stiffness remained
Concentric work .945 .928 .956 constant was likely that both peak ground-reaction forces and
COM displacements increased concomitantly with drop height.
Vertical stiffness .985 .974 .987
An unexpected finding was that RSI did not change across drop

Table 2 Performance Parameters and Biomechanical Variables During Drop Jumps Performed From 30-, 45-,
and 60-cm Heights, Mean ± SD
30 cm 45 cm 60 cm P η2
Height (m) 0.489 ± 0.086 0.486 ± 0.073 0.495 ± 0.064 .499 .083
tc (s) 0.330 ± 0.079 0.315 ± 0.083 0.322 ± 0.095 .339 .127
RSI (m/s) 1.57 ± 0.43 1.63 ± 0.43 1.64 ± 0.42 .367 .118
Fmax (N) 3318 ± 678 3602 ± 821 3650 ± 842 .008 .455
Δy (m) −0.233 ± 0.073 −0.260 ± 0.070 −0.303 ± 0.082 .001 .713
JEcc (N · m−1 · kg−1) −5.27 ± 0.74 −7.02 ± 0.70 −8.93 ± 0.83 .001 .986
JConc (N · m−1 · kg−1) 7.14 ± 1.09 6.51 ± 1.32 6.05 ± 1.50 .003* .643
kvert (kN/m) 21.2 ± 12.3 19.9 ± 8.9 17.4 ± 7.2 .200 .195
Note: P values for significant main effects are presented in bold.
*Greenhouse-Geiser correction.

IJSPP Vol. 13, No. 1, 2018

 Biomechanical Determinants of the RSI During Drop Jumps 47

height, which may be partially explained by the decrease in Vertical stiffness during DJ was significantly correlated to RSI
concentric work at greater drop heights. In contrast, greater drop at each of the 3 drop heights. The direction of all correlations was
heights were associated with more eccentric work, which likely positive, which indicated that greater RSI values were associated
reflect the differences in initial conditions. Finally, follow-up data with greater stiffness regardless of DJ phase. The strength of the
analyses indicated that DJ biomechanical variables classified drop correlation between RSI and vertical stiffness was greater at 45-
height more accurately than DJ performance parameters, which and 60-cm heights than at the 30-cm height. That said, the actual
may question the practical utility of drop-height-based RSI profiles. values of vertical stiffness during the DJ did not differ across drop
heights. Given that the peak ground-reaction forces and COM
displacements during the DJ both increased concomitantly with
drop height, this finding may not be too surprising since vertical
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Table 3 Correlation Coefficients Between RSI

stiffness is calculated from both variables. Similarly, Ferris et al
and Biomechanical Variables During Drop Jumps reported that people run and hop with the same overall vertical
Performed From 30-, 45-, and 60-cm Heights stiffness, even across surfaces with different compliance levels.12,13
30 cm 45 cm 60 cm They suggested that, regardless of environmental condition, people
maintain the same vertical stiffness in order to keep movement
JEcc .514** .756*** .821***
mechanics (eg, hopping frequency) constant. The similarity in
JConc −.037 −.070 −.389* stiffness values observed across drop heights may thus point to
kvert .537** .676*** .754*** an attempt by the athletes to control and maintain constant jump
*P < .05; **P < .01; ***P < .001. mechanics in the face of greater impact forces, because DJ contact
time and height also did not differ. Since the RSI was highly
correlated with vertical stiffness at each drop height and did not
change across heights, it appears to be closely linked to the vertical
stiffness of the body’s musculoskeletal system during DJ.
In regard to COM energetics, the results indicated that only
the amount of mechanical work that was performed during the
eccentric phase correlated with the RSI. The direction of all
correlations between RSI and eccentric work was positive, and
the magnitude of the associated correlation coefficients increased
progressively from the 30-cm to the 60-cm drop height. Given that
eccentric work values are negative, the positive correlations thus
indicate that greater RSI values are associated with smaller mag-
nitudes of mechanical work performed during the eccentric phase
of the DJ. To what extent the RSI reflects eccentric-phase ener-
getics during the DJ is, however, less clear because the results
also showed that an increase in drop height led to an increase
in eccentric-phase work, which is likely due to the greater peak
ground-reaction forces and COM displacements that were
observed during the impact phase of DJ from greater drop heights.
Furthermore, the results showed that an increase in drop height was
associated with a decrease in concentric-phase work. Other authors
have suggested that the ratio between concentric and eccentric
work provides insight into the function and efficiency of the
stretch-shortening cycle during jumping exercises.14 The observed
changes in COM energetics during the DJ in the current study may
therefore indicate a decrease in muscle-tendon-unit efficiency and
suggest that DJ performance and RSI are limited by stretch-
shortening-cycle function.
The results showed that parameters of DJ performance
(ie, RSI, DJ height, and contact time) did not change across
drop heights. The lack of change in DJ performance parameters
agrees with findings from other studies, which indicate that DJ
starting height does not correlate well to DJ performance.15,16 More
specifically, Walsh et al suggested that contact time has a greater
effect on DJ performance parameters than drop height.16 This
implication may be especially important if technical instructions
are not controlled and athletes perform DJ under inconsistent
conditions.17 Given that participants in the current study were
Figure 2 — Confusion matrices for neural networks with A) DJ
performance parameters (ie, DJ height, contact time, and RSI) and B) provided with consistent instructions (ie, “Jump as high and as fast
DJ biomechanical data (ie, eccentric/concentric stiffness and work) as as you can”) it may thus not be a surprise that contact time did not
input. Class 1, 2, and 3 refer to drop heights 30 cm, 45 cm, and 60 cm, change.
respectively. NOTE: Target and output refer to input and predicted In the absence of drop-height-dependent changes in DJ per-
(ie, classified) data, respectively. formance parameters it became of interest to pursue a follow-up
IJSPP Vol. 13, No. 1, 2018
 48 Kipp et al

analysis to determine how accurately the DJ performance param- characteristics and/or injury potential. Second, the results suggest
eters and DJ biomechanical data could classify individual DJ that DJ performance parameters (ie, RSI, jump height, contact time)
trials by initial conditions. To this end, 2 neural networks were do not accurately differentiate individual DJ by drop height. This
trained to determine how accurately DJ trials could be classified by limitation brings into question whether it is necessary for practi-
drop heights with either DJ performance parameters or DJ bio- tioners to test DJ from multiple drop heights in order to establish an
mechanical data as inputs. The results of the classification analysis RSI profile. Collectively, these 2 results suggest that practitioners
indicated that with DJ height, contact time, and RSI as inputs, the could use the RSI from only 1 drop height to gain insight into the
neural network classified the drop height of only approximately stiffness behavior of the musculoskeletal system during DJ.
33% of all DJ trials correctly. Given that DJ performance param-
eters did not change across drop height, the poor performance of
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this classification network was not too surprising. In contrast, the Conclusions
neural network with the DJ biomechanical data classified approxi- The RSI is highly correlated with vertical stiffness across a range of
mately 96% of all DJ trials correctly. The reason that this discrep- drop heights. Furthermore, vertical stiffness did not differ across
ancy should be of interest to coaches and sport scientists is that drop height. The RSI therefore appears to reflect lower-extremity
DJ testing across a spectrum of drop heights is used to identify a DJ stiffness during DJ. However, the inability of RSI, DJ height, and
profile with an ostensible optimal drop height based on either contact time to accurately classify DJ trials by initial condition
DJ height, contact time, or RSI. However, the collective results brings into question the utility of these parameters to establish
from the current study suggest that the 3 DJ performance param- drop-height-based RSI profiles.
eters neither vary across nor accurately classify DJ trials by drop
heights. While general plyometric training can increase the RSI,18
no longitudinal studies have examined the effectiveness of targeted Acknowledgments
and RSI-specific training programs on DJ performance. In the
The results of this study do not constitute endorsement of the product by
absence of such training studies, the current results thus question
the authors or the journal. There are no conflicts of interest. There are no
the utility of RSI-based DJ profiles to guide the program-design
professional relationships with companies or manufacturers who will
process in the strength and conditioning setting. On the other hand,
benefit from the results of the present study for each author.
the current results suggest that the use of a single drop height could
be sufficient to calculate the RSI profile, which would simplify DJ
testing for practitioners.
The results from this study should be interpreted in light of a References
few limitations. First, the sample of athletes in this study consisted
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limit the generalizability of the results to that population and
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