PLoS ONE plos plosone PLOS ONE 1932-6203 Public Library of Science San Francisco, CA USA 10.1371/journal.pone.0245791 PONE-D-20-29309 Research Article Biology and life sciencesPhysiologyBiological locomotionJumping Biology and life sciencesAnatomyBody limbsLegs Medicine and health sciencesAnatomyBody limbsLegs Engineering and technologyMeasurement Biology and life sciencesPsychologyBehaviorRecreationSports Social sciencesPsychologyBehaviorRecreationSports Biology and life sciencesSports scienceSports Physical sciencesMathematicsNumerical analysisExtrapolation Physical sciencesPhysicsClassical mechanicsMotionVelocity Computer and information sciencesSoftware engineeringComputer software Engineering and technologySoftware engineeringComputer software Research and analysis methodsMathematical and statistical techniquesStatistical methodsRegression analysisLinear regression analysis Physical sciencesMathematicsStatisticsStatistical methodsRegression analysisLinear regression analysis Force-velocity profiling in athletes: Reliability and agreement across methods Force-velocity profiling in athletes: Reliability and agreement across methods https://orcid.org/0000-0001-5860-6273 Lindberg Kolbjørn Investigation Visualization Writing – original draft Writing – review & editing 1 2 * Solberg Paul Methodology Supervision Writing – review & editing 2 https://orcid.org/0000-0002-4010-8038 Bjørnsen Thomas Data curation Formal analysis Project administration Resources Supervision Writing – review & editing 1 2 Helland Christian Data curation Formal analysis Investigation Methodology Writing – review & editing 2 Rønnestad Bent Conceptualization Formal analysis Funding acquisition Investigation Methodology Project administration Resources Supervision Writing – review & editing 2 3 Thorsen Frank Martin Investigation Methodology Writing – original draft Writing – review & editing 1 Haugen Thomas Data curation Investigation Project administration Writing – review & editing 2 4 Østerås Sindre Investigation Writing – review & editing 2 5 Kristoffersen Morten Investigation Writing – review & editing 2 6 Midttun Magnus Investigation Writing – review & editing 2 Sæland Fredrik Investigation Writing – review & editing 2 Paulsen Gøran Conceptualization Formal analysis Funding acquisition Investigation Project administration Resources Supervision Validation Writing – review & editing 2 7 Department of Sports Science and Physical Education, Faculty of Health and Sport Sciences, University of Agder, Kristiansand, Norway Norwegian Olympic and Paralympic Committee and Confederation of Sports, Oslo, Norway Department of Health and Exercise Physiology, Faculty of Social Sciences, Inland Norway University of Applied Sciences, Lillehammer, Norway School of Health Sciences, Kristiania University College, Oslo, Norway Department of Neuromedicine and Movement Science, Faculty of Medicine and Health Sciences, Centre for Elite Sports Research, Norwegian University of Science and Technology, Trondheim, Norway Department of Sport and Education, Bergen University College, Bergen, Norway Department of Physical Performance, Norwegian School of Sport Sciences, Oslo, Norway Boullosa Daniel Editor Universidade Federal de Mato Grosso do Sul, BRAZIL

The authors have declared that no competing interests exist.

 * E-mail: kolbjorn.a.lindberg@uia.no 1 2 2021 2021 16 2 e0245791 17 9 2020 7 1 2021 2021 Lindberg et al This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

The aim of the study was to examine the test-retest reliability and agreement across methods for assessing individual force-velocity (FV) profiles of the lower limbs in athletes. Using a multicenter approach, 27 male athletes completed all measurements for the main analysis, with up to 82 male and female athletes on some measurements. The athletes were tested twice before and twice after a 2- to 6-month period of regular training and sport participation. The double testing sessions were separated by ~1 week. Individual FV-profiles were acquired from incremental loading protocols in squat jump (SJ), countermovement jump (CMJ) and leg press. A force plate, linear encoder and a flight time calculation method were used for measuring force and velocity during SJ and CMJ. A linear regression was fitted to the average force and velocity values for each individual test to extrapolate the FV-variables: theoretical maximal force (F0), velocity (V0), power (Pmax), and the slope of the FV-profile (SFV). Despite strong linearity (R2>0.95) for individual FV-profiles, the SFV was unreliable for all measurement methods assessed during vertical jumping (coefficient of variation (CV): 14–30%, interclass correlation coefficient (ICC): 0.36–0.79). Only the leg press exercise, of the four FV-variables, showed acceptable reliability (CV:3.7–8.3%, ICC:0.82–0.98). The agreement across methods for F0 and Pmax ranged from (Pearson r): 0.56–0.95, standard error of estimate (SEE%): 5.8–18.8, and for V0 and SFV r: -0.39–0.78, SEE%: 12.2–37.2. With a typical error of 1.5 cm (5–10% CV) in jump height, SFV and V0 cannot be accurately obtained, regardless of the measurement method, using a loading range corresponding to 40–70% of F0. Efforts should be made to either reduce the variation in jumping performance or to assess loads closer to the FV-intercepts. Coaches and researchers should be aware of the poor reliability of the FV-variables obtained from vertical jumping, and of the differences across measurement methods.

 The author(s) received no specific funding for this work. Data Availability All relevant data are within the manuscript and its Supporting Information files. Introduction

Within strength and power training, force-velocity (FV) profiling has received increasing attention as a means to monitor training adaptations [1–3] and to serve as a basis for individual training prescriptions for athletes [3–6]. The concept of FV-profiling is based on the fundamental properties of skeletal muscles, where there is an inverse relationship between force and velocity [7].

In multi-joint movements, the FV-relationship is commonly described as linear [8], in contrast to the hyperbolic relationship observed in isolated muscles or single-joint movements [7]. In practice, athletes can perform maximal efforts against different loads while force and velocity are measured during vertical jumping or similar multi-joint movements. Based on such data, one can draw a linear regression line and extrapolate the theoretical maximal force (F0) (i.e., force at zero velocity) and velocity (V0) (i.e., velocity at zero force). Following that, the theoretical maximal power (Pmax) can be calculated as (F0·V0)/4 and the slope of the FV-profile (SFV) as F0/V0 [9]. However, controversy exists about the linearity of FV-relationships obtained from multi-joint movements [8].

The value of a test is highly dependent on its reliability, especially when evaluating individual data from high-performing athletes [10]. However, although several studies have evaluated the within-session reliability of FV-variables [11–18], limited attention has been directed towards the between-session reliability of these FV-variables in athletes. Additionally, only encoders and the flight time calculation method have been used for measurements of between-session reliability of the FV-variables [12, 13, 19]. Hence, the reliability of other commonly used methods such as force plates and leg press devices is unknown [11–18]. Furthermore, different devices and methods (e.g., force plates, linear position transducers, pneumatic resistance apparatus and the flight time calculation method) are used to assess the lower limb FV-variables, but the agreement among these has received limited attention [17, 20–22].

Giroux et al. [20] previously investigated the reliability and agreement among three measurement methods (accelerometry, linear position transducer and flight time calculation method) during vertical jumps. However, they reported only average values of force, velocity and power for each jump, and not the extrapolated FV-parameters (F0, V0, Pmax and SFV) that are increasingly used for individual training prescriptions [3–5, 23]. García-Ramos et al. [22] investigated the agreement across methods for CMJ (force platform, linear position transducer and flight time calculation method), but not SJ. As the test-retest reliability of the different methods for assessing individual FV-profiles is of crucial importance, it is of great interest to investigate the mentioned shortcomings in the literature.

A novel aspect of FV-profiling during vertical jumping is the possibility of obtaining the extrapolated variable V0 and the calculated SFV, as there are numerous methods for assessing maximal force and maximal power [24]. Interestingly, SFV and V0 have previously shown poorer reliability than F0 and Pmax in vertical jumping [11]. Cuk et al. [25] hypothesized that this lower reliability might be due to the distance of extrapolation, as all measurements are performed closer to F0 compared to V0, in addition to the small range in loads assessed during incremental loading protocols in vertical jumping. These speculations were partly confirmed by García-Ramos et al. [26], who reported that the load range used to acquire the FV-profile significantly affects the reliability of V0. Assessing loads close to F0 is limited by the technical demand of jumping with heavy loads, while attempts closer to V0 are limited by the subject’s own bodyweight during vertical jumping. However, the bodyweight issue is not present during the leg press exercise, making it possible to assess loads closer to both F0 and V0, potentially improving the reliability for the FV-variables. It is therefore of great interest to investigate the reliability of the extrapolated FV-variables from commonly used vertical jumping exercises as well as from the leg press exercise.

The aim of the present study was to examine the i) test-retest reliability and ii) agreement across methods for assessing individual FV-profiles of the lower limbs in well-trained athletes.

 Methods Experimental approach and design

The participants in the present study underwent physical testing four times. The first two testing timepoints were separated by ~1 week, before a training period of 2~6 months. The two last timepoints were also separated by ~1 week (Figs 1 and 2).

10.1371/journal.pone.0245791.g001 Flow chart representing study design. 10.1371/journal.pone.0245791.g002 Flow chart representing study design and sample size for main analysis.

The data were collected from multiple regional Olympic training and testing centers. Because not all facilities had the same testing capacities, the sample size differed across the measurement methods. Therefore, the main analysis in this study was performed on the participants tested under all methods (reliability and agreement), with an additional aggregated analysis including all participants, with varying sample sizes across methods (only reliability analysis). For the main analysis, the test leaders were constant, and for the aggregated analysis the test leaders and equipment differed across centers but were kept constant for each participant (sample sizes for all tests are presented in the results section). Written informed consent was obtained from all participants prior to commencing their involvement in the study.

The study was reviewed by the ethical committee of Inland Norway University of Applied Sciences, approved by the Norwegian Centre for Research Data and performed in agreement with the Declaration of Helsinki. The athletes in the main sample were familiar with the testing procedures, whereas the subjects in the mixed sample had various levels of experience prior to the study.

Participants

For the main analysis, a total of 27 well-trained male athletes from handball and ice hockey were included (age 21 ± 5 years; height 185 ± 8 cm; body mass 84 ± 13 kg; Table 1).

10.1371/journal.pone.0245791.t001 Performance characteristics of the athletes for main analysis.
Mean ± SD Max Min
CMJ (cm) 38 ± 4 43 28
SJ (cm) 36 ± 4 43 28

Values from baseline measures, sample size = 27, SJ: Squat jump, CMJ: Countermovement jump, cm: Centimeters, s: seconds, SD: Standard deviation.

For the aggregated mixed sample, both male (approximately 80% of sample) and female athletes participated (age 21 ± 4 years; height 182 ± 9 cm; body mass 78 ± 12 kg; Table 2). Most of the participants were team sport players in handball, ice hockey, soccer, and volleyball, while the remaining participants competed in Nordic combined, ski jumping, weightlifting, athletics, badminton and speed skating. The competition level ranged from world class (Olympic medalist) to club level, with the majority competing at national and international level in their respective sports.

10.1371/journal.pone.0245791.t002 Performance characteristics of the athletes for aggregated analysis.
n = Mean ± SD Max Min
CMJ (cm) 83 38 ± 5 58 25
SJ (cm) 72 35 ± 6 51 22

Values from baseline measures, sample size in table. SJ: Squat jump, CMJ: Countermovement jump, Centimeters, s: seconds, SD: Standard deviation.

 Testing procedures

All participants were instructed to prepare for the test days as they would for a regular competition in terms of nutrition, hydration, and sleep, and to refrain from strenuous exercise 48 hours prior to testing. All testing was performed indoors, and the participants were instructed to use identical footwear and clothing on each test day.

Bodyweight was measured wearing training clothes and shoes (as total bodyweight is used to calculate force in some of the methods). All participants performed a standardized ~10-min warm-up procedure prior to testing, consisting of jogging, local muscle warm-up (hamstring and hip mobility–consisting of light dynamic stretches), running drills (e.g. high knees, skipping, butt-kicks, explosive lunges) and bodyweight jumps.

The different tests were separated by 5–10 min to ensure proper recovery, and light snacks and drinks were offered to the participants during the testing sessions. The testing protocol consisted of a series of squat jumps (SJ), countermovement jumps (CMJ) and a leg press test with incremental loads.

SJ and CMJ were initially performed with bodyweight, accompanied by an incremental loading protocol consisting of 0.1 (broomstick), 20, 40, 60 and 80 kg. In the aggregated sample, for some weaker participants (i.e., those unable to jump with 80 kg), a protocol of approximately 5 loads up to 80% of bodyweight was used. The increase in loads was then individually determined. In both the SJ and CMJ, the FV-relationship was derived from a force plate (For main analysis: Musclelab; Ergotest AS, Porsgrunn, Norway and for aggregated analysis some tested at: AMTI; Advanced Mechanical Technology, Inc Waltham Street, Watertown, USA) and a linear position transducer encoder (Ergotest AS, Porsgrunn, Norway). The encoder was placed on the ground and connected to the barbell. Participants were instructed to keep their hands on their hips for the bodyweight trials, and a broomstick was used as the 0.1 kg load. Two valid trials were registered for each load. The recovery after each attempt was 2–3 min.

For the SJ, participants were asked to maintain their individual starting position (∼90° knee angle) for about 2 s and then apply force as fast as possible and jump to the maximum possible height before landing with their ankles in an extended position. Countermovement was not allowed for the SJ and was checked visually with the direct force output from the force plate. The starting position for both SJ and CMJ was standardized to the athlete’s self-selected starting position and kept constant for all jumps and testing sessions. The starting position for the SJ and the depth of the CMJ was controlled using a rubber band beneath the thighs of the athletes. If these requirements were not met, the trial was repeated. The CMJ test procedure was similar to that for SJ, except for the pause in the bottom position.

For the leg press, Keiser Air300 horizontal pneumatic leg press equipment with an A420 force and velocity measuring device (Keiser Sport, Fresno, CA) was used. The FV-variables were derived from a 10-repetition FV-test pre-programmed in the Keiser A420 software. To determine the loading range, each participant’s 1RM was obtained at the familiarisation session for the main analysis, whereas the 1RM was individually estimated for the participants in the aggregated analysis. The test started with two practice attempts at the lightest load, corresponding to ∼15% of 1RM. Thereafter, the load was gradually increased with fixed steps (∼20–30 kgf) for each attempt until reaching the ∼1RM load and a total of 10 attempts across the FV-curve (15–100% of 1RM). The rest period between attempts got longer as the load increased. The rest period between attempts was ∼10–20 seconds for the initial five loads, and 20–40 seconds for the last four loads. The seating position was adjusted for each participant, aiming at a vertical femur, equivalent to an 80-90° knee angle, and the feet were placed with the heels at the lower end of the foot pedal. Participants were asked to extend both legs using maximum effort during the entire 10-repetition FV-test. Due to the pneumatic semi-isotonic resistance, maximal effort does not cause ballistic action, and the entire push-off was performed with maximal intentional velocity. The leg press was performed as a concentric-only action without countermovement, as the pedals were resting in their predetermined position prior to each repetition. The eccentric phase was submaximal and not registered.

 Data analysis

All FV-variables were obtained from the average force and velocity during the concentric phase of the movement. For each incremental loading test, a linear regression was fitted to the average force and velocity measurements to calculate the individual FV-variables. F0 and V0 were defined as the intercepts of the linear regression for the corresponding force and velocity axis, while SFV refers to the slope of the linear regression. Pmax was then calculated as F0·V0/4. All FV-variables were obtained from FV-profiles with a coefficient of determination greater than 0.95 [9].

Force plate: FV-variables derived from the force plate were analysed using a customized Microsoft Excel spreadsheet (Microsoft Office Professional Plus 2018, version 16.23). Velocity was calculated by integrating the acceleration obtained from the ground reaction forces. The centre of mass position was the integral of velocity, while power was the product of force and velocity [27]. The start of the concentric phase for the SJ was defined as the point at which force exceeded 5 SD of the steady-stance weight prior to the jump [27–29]. For the CMJ, the integration of velocity started when the force fell below 5 SD of the steady-stance weight. The concentric phase was defined as the point at which velocity was greater than 0 m/s. The end of the concentric phase for both SJ and CMJ was defined as the instant when the participant left the force plate (i.e., take-off: when forces fell below 10N).

Encoder: By measuring the position of the cable (connected to the bar) as a function of time, the software calculates force and velocity (MuscleLab, version 10.5.69.4815). Average force was calculated as the product of mass and acceleration. Acceleration was calculated as the average velocity divided by the duration of the positive displacement, with the addition of the gravitation constant, while mass was calculated as bodyweight plus external load. In agreement with the manufacturer´s recommendation and previous studies [30], 90% of body mass and 100% of external load were used to calculate force during SJ and CMJ. Flight time method: Average force (F¯) and average velocity (v¯) were calculated using two equations, considering only simple input variables: body mass, jump height and push-off distance [15, 31]. The vertical push-off distance was determined as previously proposed [9], corresponding to the difference between the extended lower limb length with maximal foot plantar flexion and the crouch starting position of the jump.

Keiser leg press: The Keiser Air300 horizontal leg press dynamometer uses pneumatic resistance and measures compression forces at the cylinder, while velocity is measured with a position transducer. The values at the cylinder are then calculated to match the range of motion and velocity at the apparatus pedals [1]. Average force and velocity were calculated as a function of time, where the software excludes 5% of the range of motion from the start and end of the movement.

The measurement sample rate for the MuscleLab force plate and encoder was 200 Hz and for the leg press apparatus was 400 Hz. The force signal from the Musclelab force plate data was upsampled to 1000 Hz by spline integration using the integrated software. The AMTI force plate sampled at 2000 Hz.

 Statistical analysis

The coefficient of variation (CV%), interclass correlation coefficient (ICC 3,1) and mean percent change (%Δ) were used to assess reliability across the testing sessions. CV% and %Δ were calculated from the log-transformed data. The Pearson product-moment correlation coefficient (Pearson r) was used to determine the association across methods. For comparison across methods, the mean difference (systematic bias) was calculated and presented in absolute and in relative terms (% from log transformed data) with percent and standardized difference (mean difference divided by the standard deviation of the criterion measure).

The standardized difference was qualitatively interpreted using the scale (<0.2 Trivial; 0.2–0.6 Small; 0.6–1.2 Moderate; 1.2–2.0 Large; 2.0–4.0 Very large; >4.0 Extremely large) [32]. A paired sample t-test was used to test the significance level of the differences in means. Additionally, a linear regression analysis with corresponding slope and Y-intercept of the regression line was used for comparison across methods. The standard error of the estimate (SEE) was calculated from the linear regression and presented in absolute and relative terms. For comparison across methods, the averages of the two first testing timepoints were included.

The smallest worthwhile change (SWC%) was calculated as 0.2 of the between-athlete SD, presented as a percentage of the mean. Confidence limits (CL) for all analyses were set at 95%. The Pearson’s r coefficients were interpreted categorically (<0.09 trivial; 0.10–0.29 small; 0.30–0.49 moderate; 0.50–0.69 large; 0.70–0.89 very large; 0.90–0.99 nearly perfect; 1.00 perfect) as defined by Hopkins and Marshall [33].

Acceptable reliability was considered as ICC ≥ 0.80 and CV ≤ 10%, while good reliability was considered as ICC ≥ 0.90 and CV ≤ 5% [34–41]. Descriptive data are reported as mean ± SD. All statistical analyses were performed using a customized Microsoft Excel spreadsheet [32].

 Results Test-retest reliability of the FV-variables

All FV-profiles displayed linearity, with individual R2 values ranging from 0.95 to 1.00. All the following results presented in the text correspond to results from the main analysis, whereas results from the aggregated analysis are only presented in tables. Fig 3 and Table 3 show the reliability measures of the FV-variables for the main analysis. Table 4 shows the reliability measures of the FV variables for the aggregated analysis.

10.1371/journal.pone.0245791.g003 Measures of reliability for the FV variables obtained from main analysis.

Panel A- Coefficient of variation (CV%), panel B- Smallest worthwhile change (SWC%), panel C- Interclass correlation coefficient (ICC), panel D- Mean % change (%Δ). All values were obtained by combining test 1–2 (n = 27) and 3–4 (n = 19). Error bars represent 95% confidence intervals. Dotted line represents line of acceptable reliability.

 10.1371/journal.pone.0245791.t003 Measures of reliability for the FV variables obtained from the main analysis with corresponding 95% confidence intervals.
Coefficient of variation (CV%) Interclass correlation (ICC) Percent change (%Δ)
Test F0 V0 Pmax SFV F0 V0 Pmax SFV F0 V0 Pmax SFV
CMJ Force plate 1–2 8.6 ± 2.6 19.2 ± 6.2 10.8 ± 3.4 29.0 ± 9.8 0.81 ± 0.14 0.20 ± 0.37 0.74 ± 0.18 0.40 ± 0.32 -2.3 ± 4.5 6.5 ± 10.5 4.0 ± 6 -8.3 ± 13.1
3–4 5.1 ± 1.8 12.6 ± 4.6 8.8 ± 3.1 17.5 ± 6.5 0.89 ± 0.10 0.16 ± 0.43 0.77 ± 0.19 0.47 ± 0.34 -2.6 ± 3.1 7.1 ± 8.2 4.3 ± 5.7 -9.1 ± 9.5
CMJ Encoder 1–2 6.8 ± 2 9.8 ± 2.9 4.4 ± 1.3 16.9 ± 5.2 0.82 ± 0.13 0.43 ± 0.30 0.95 ± 0.04 0.47 ± 0.29 -3.1 ± 3.4 3.9 ± 5.2 0.6 ± 2.3 -6.7 ± 7.8
3–4 7.0 ± 2.5 8.4 ± 3.1 3.9 ± 1.4 15.5 ± 5.9 0.78 ± 0.19 0.44 ± 0.37 0.95 ± 0.04 0.38 ± 0.39 1.4 ± 4.5 -1.8 ± 5.3 -0.4 ± 2.5 3.2 ± 9.9
CMJ Flight time 1–2 10.1 ± 3.1 18.7 ± 6 9.6 ± 2.9 30.1 ± 10.2 0.79 ± 0.15 0.29 ± 0.35 0.74 ± 0.18 0.50 ± 0.29 -3.0 ± 5.2 4.4 ± 10 1.2 ± 5.2 -7.1 ± 13.7
3–4 5.2 ± 1.8 11.8 ± 4.3 7.8 ± 2.8 16.9 ± 6.3 0.92 ± 0.08 0.70 ± 0.23 0.82 ± 0.15 0.79 ± 0.18 -1.7 ± 3.2 7.7 ± 7.8 5.9 ± 5.1 -8.8 ± 9.2
SJ Force plate 1–2 11.2 ± 3.5 17.4 ± 5.6 9.4 ± 2.9 29.3 ± 9.9 0.69 ± 0.21 0.60 ± 0.25 0.87 ± 0.10 0.51 ± 0.29 0.5 ± 6.0 -2.7 ± 8.8 -2.2 ± 4.9 3.2 ± 14.9
3–4 6.7 ± 2.4 15.4 ± 5.7 10 ± 3.6 22.3 ± 8.5 0.84 ± 0.13 0.54 ± 0.32 0.81 ± 0.16 0.57 ± 0.30 -2.2 ± 4.1 4.1 ± 9.6 1.8 ± 6.2 -6.0 ± 12.2
SJ Encoder 1–2 12.1 ± 3.5 11.1 ± 3.2 11.5 ± 3.4 21.0 ± 6.4 0.61 ± 0.24 0.59 ± 0.24 0.81 ± 0.13 0.36 ± 0.32 2.0 ± 6.1 -1.4 ± 5.5 0.6 ± 5.8 3.4 ± 10.4
3–4 6.5 ± 2.2 10.2 ± 3.6 5.2 ± 1.8 16.9 ± 6.1 0.77 ± 0.18 0.62 ± 0.27 0.94 ± 0.05 0.42 ± 0.36 -3.0 ± 3.8 6.0 ± 6.5 2.9 ± 3.3 -8.5 ± 9.0
SJ Flight time 1–2 5.2 ± 1.6 8.6 ± 2.6 4.4 ± 1.3 13.9 ± 4.4 0.92 ± 0.06 0.79 ± 0.16 0.97 ± 0.03 0.76 ± 0.17 0.8 ± 2.9 -2.7 ± 4.5 -1.9 ± 2.4 3.7 ± 7.5
3–4 6.4 ± 2.3 11.6 ± 4.2 5.8 ± 2 18.5 ± 7.0 0.86 ± 0.13 0.63 ± 0.27 0.93 ± 0.07 0.62 ± 0.28 -1.7 ± 3.9 6.7 ± 7.6 4.9 ± 3.8 -7.9 ± 10.1
Keiser leg press 1–2 4.2 ± 1.3 5.0 ± 1.5 4.2 ± 1.3 8.3 ± 2.5 0.98 ± 0.02 0.82 ± 0.14 0.97 ± 0.02 0.95 ± 0.04 0.2 ± 2.3 2.2 ± 2.8 2.4 ± 2.4 -2.0 ± 4.4
3–4 3.7 ± 1.4 4.3 ± 1.6 4.2 ± 1.6 7.0 ± 2.6 0.98 ± 0.02 0.82 ± 0.16 0.97 ± 0.03 0.96 ± 0.04 1.3 ± 2.5 0.4 ± 2.9 1.7 ± 2.9 0.9 ± 4.6

Bold text denotes CV<10% and ICC>0.80. Sample size for test 1–2 = 27, and test 3–4 = 19. SJ: Squat jump, CMJ: Countermovement jump, F0:Theoretical maximal force, V0: Theoretical maximal velocity, Pmax: Theoretical maximal power, SFV: slope of the force-velocity profile.

 10.1371/journal.pone.0245791.t004 Measures of reliability for the FV variables obtained from aggregated analysis with corresponding 95% confidence intervals.
Coefficient of variation (CV%) Interclass correlation (ICC) Percent change (%Δ)
  Test n = F0 V0 Pmax SFV F0 V0 Pmax SFV F0 V0 Pmax SFV
CMJ Force plate 1–2 34 8.0 ± 2.1 17.5 ± 4.9 9.9 ± 2.7 26.5 ± 7.7 0.81 ± 0.12 0.22 ± 0.32 0.76 ± 0.15 0.40 ± 0.29 -3.2 ± 3.7 6.9 ± 8.5 3.4 ± 4.8 -9.4 ± 10.5
3–4 21 5.1 ± 1.8 12.6 ± 4.6 8.8 ± 3.1 17.5 ± 6.5 0.89 ± 0.10 0.19 ± 0.43 0.78 ± 0.18 0.45 ± 0.35 -2.6 ± 3.1 7.1 ± 8.2 4.3 ± 5.7 -9.1 ± 9.5
CMJ Encoder 1–2 82 6.8 ± 1.1 8.6 ± 1.4 4.0 ± 0.6 15.5 ± 2.6 0.89 ± 0.05 0.74 ± 0.10 0.96 ± 0.02 0.78 ± 0.09 -2.4 ± 2.0 2.2 ± 2.6 -0.3 ± 1.2 -4.5 ± 4.3
3–4 56 7.3 ± 1.5 9.4 ± 1.9 3.7 ± 0.7 17.0 ± 3.6 0.81 ± 0.09 0.51 ± 0.19 0.96 ± 0.02 0.48 ± 0.20 -0.7 ± 2.6 0.5 ± 3.4 -0.2 ± 1.4 -1.1 ± 5.9
CMJ Flight time 1–2 34 9.0 ± 2.4 16.8 ± 4.7 8.8 ± 2.4 26.7 ± 7.8 0.80 ± 0.13 0.31 ± 0.31 0.78 ± 0.14 0.51 ± 0.26 -2.5 ± 4.2 3.8 ± 8.0 1.2 ± 4.2 -6.1 ± 11
3–4 21 5.2 ± 1.8 11.8 ± 4.3 7.8 ± 2.8 16.9 ± 6.3 0.92 ± 0.08 0.69 ± 0.24 0.81 ± 0.16 0.78 ± 0.18 -1.7 ± 3.2 7.7 ± 7.8 5.9 ± 5.1 -8.8 ± 9.2
SJ Force plate 1–2 45 10.8 ± 2.5 15.3 ± 3.6 8 ± 1.8 26.6 ± 6.6 0.71 ± 0.15 0.64 ± 0.18 0.87 ± 0.07 0.59 ± 0.20 -1 ± 4.3 -1.6 ± 6 -2.7 ± 3.2 0.6 ± 10.1
3–4 40 11.6 ± 2.9 19.6 ± 5 11.5 ± 2.8 31.8 ± 8.6 0.61 ± 0.20 0.43 ± 0.26 0.73 ± 0.15 0.42 ± 0.26 -7.1 ± 4.6 8.4 ± 8.8 0.7 ± 4.9 -14.3 ± 10.7
SJ Encoder 1–2 34 12.1 ± 3.3 11.6 ± 3.2 10.9 ± 2.9 22.0 ± 6.3 0.58 ± 0.23 0.54 ± 0.25 0.82 ± 0.12 0.28 ± 0.31 0.3 ± 5.6 0.4 ± 5.5 0.8 ± 5.1 -0.1 ± 9.8
3–4 23 8.7 ± 3.0 13.6 ± 4.7 5.9 ± 1.9 23.2 ± 8.4 0.63 ± 0.26 0.39 ± 0.36 0.92 ± 0.07 0.14 ± 0.42 -1.3 ± 5.1 3.4 ± 8.1 2.0 ± 3.5 -4.6 ± 12.2
SJ Flight time 1–2 47 5.6 ± 1.2 8.9 ± 2.0 4.8 ± 1.0 14.5 ± 3.3 0.89 ± 0.06 0.77 ± 0.13 0.96 ± 0.02 0.70 ± 0.15 -0.8 ± 2.2 -0.8 ± 3.5 -1.6 ± 1.9 -0.1 ± 5.6
3–4 33 6.7 ± 1.8 11.5 ± 3.2 5.6 ± 1.5 18.6 ± 5.3 0.81 ± 0.12 0.68 ± 0.19 0.94 ± 0.04 0.58 ± 0.23 -1.2 ± 3.2 3.7 ± 5.6 2.4 ± 2.8 -4.7 ± 8.2
Keiser leg press 1–2 66 4.7 ± 0.9 5.1 ± 0.9 4.2 ± 0.8 9.0 ± 1.7 0.96 ± 0.02 0.83 ± 0.08 0.98 ± 0.01 0.91 ± 0.04 1.8 ± 1.6 -0.4 ± 1.7 1.2 ± 1.5 2.2 ± 3.0
3–4 45 4.1 ± 0.9 4.5 ± 1.0 4.0 ± 0.9 7.6 ± 1.7 0.97 ± 0.02 0.86 ± 0.08 0.98 ± 0.01 0.94 ± 0.04 0.3 ± 1.7 0.0 ± 1.9 -0.2 ± 1.7 0.2 ± 3.1

Bold text denotes CV<10% and ICC>0.80. sample size in table. SJ: Squat jump, CMJ: Countermovement jump, F0:Theoretical maximal force, V0: Theoretical maximal velocity, Pmax: Theoretical maximal power, SFV: slope of the force-velocity profile.

Of all the investigated measurement methods, only the leg press showed acceptable reliability for the four FV-variables (CV: 3.7–8.3%, ICC: 0.82–0.98). Several of the measures for Pmax and F0 obtained from the vertical jumps showed acceptable reliability (CV: 3.9–12.1%, ICC: 0.61–0.97) (Table 3). However, V0 and SFV showed unacceptable reliability for all the investigated SJ and CMJ measurement methods (CV: 8.4–30.1%, ICC: 0.16–0.79). The typical error for both SJ and CMJ jump height was 1.2 cm, corresponding to a coefficient of variation of 6.8%. For each loading condition (0, 20, 40, 60 and 80 kg) the typical error was: 1.7, 1.2, 0.9, 1.0 and 1.0 cm corresponding to a CV of 5.1, 4.6, 5.5, 7.6 and 10.2% respectively.

 Agreement across methods

The agreement and comparisons for the different measurement methods are shown in Table 5. Mean±SD values for all the FV-methods are shown in Table 6 and illustrated in Fig 4. The agreement across methods for F0 and Pmax ranged from (Pearson r): 0.56–0.95, SEE%: 5.8–18.8, and for V0 and SFV r: -0.39–0.78, SEE%: 12.2–37.2. The mean bias for F0 ranged from trivial to moderate (-6-14%, ES: -0.4–0.9); small to large for Pmax (-30-55%, ES: -1.8–1.7); trivial to very large for V0 (-35-70%, ES: -2.8–2.2); and small to very large for SFV (-32-165%, ES: -1.2–3.8) (Tables 5 and 6 and Fig 4).

10.1371/journal.pone.0245791.g004 Shows averaged force-velocity profiles from all methods for the main analysis (n = 27).

The shaded area represents the 95% confidence interval for the vertical jumps.

 10.1371/journal.pone.0245791.t005 Agreement and comparison for CMJ Force plate and SJ Force plate vs encoder, flight time and leg press measurements.
Mean bias (±SD) Mean bias % (±SD) Standardized SEE (±CL) SEE % (±CL) Pearson r (±CL) Slope of Y-intercept
difference (±CL) regression line of regression line
CMJ Force plate VS CMJ Encoder F0 (N) 19 ± 233 1.2 ± 8.9 0.0 ± 0.2 238 ± 71 8.6 ± 2.7 0.865 ± 0.108* 1.03 -88
V0 (m/s) -1.0 ± 0.5** -22.8 ± 15.6 -1.7 ± 0.3 0.5 ± 0.2 14.4 ± 4.6 0.508 ± 0.293* 0.89 1.3
Pmax (W) -643 ± 248** -22.2 ± 9.9 -1.3 ± 0.2 243 ± 72 9.5 ± 3.0 0.878 ± 0.098* 1.19 275
SFV (N/m/s) 256 ± 174** 44.1 ± 25.5 1.3 ± 0.3 163 ± 49 23.2 ± 7.8 0.597 ± 0.258* 0.64 110
CMJ Flight Time F0 (N) 11 ± 180 0.0 ± 6.9 0.0 ± 0.2 152 ± 45 5.8 ± 1.8 0.947 ± 0.045* 0.81 507
V0 (m/s) -0.8 ± 0.5** -19.3 ± 17.2 -1.4 ± 0.3 0.5 ± 0.1 13.9 ± 4.5 0.562 ± 0.272* 0.71 1.6
Pmax (W) 218 ± 199** 31.4 ± 24 1.1 ± 0.4 126 ± 38 18.8 ± 6.2 0.783 ± 0.161* 0.50 267
SFV (N/m/s) -550 ± 296** -19.4 ± 13.3 -1.1 ± 0.2 302 ± 90 12.2 ± 3.9 0.802 ± 0.149* 1.00 545
Leg press F0 (N) 415 ± 500** 13.6 ± 17.8 0.9 ± 0.4 246 ± 73 9.5 ± 3.0 0.855 ± 0.115* 0.48 1243
V0 (m/s) -1.6 ± 0.6** -34.8 ± 21.3 -2.8 ± 0.4 0.6 ± 0.2 16.8 ± 5.5 0.106 ± 0.376 0.27 3.2
Pmax (W) -895 ± 253** -30 ± 14.2 -1.8 ± 0.2 255 ± 76 10.7 ± 3.4 0.865 ± 0.108* 1.10 723
SFV (N/m/s) 764 ± 444** 164.6 ± 42.7 3.8 ± 0.9 177 ± 53 26.4 ± 9.0 0.490 ± 0.299* 0.19 460
SJ Force plate VS SJ Encoder F0 (N) -194 ± 294** -6.3 ± 10.9 -0.4 ± 0.2 300 ± 89 10.3 ± 3.2 0.817 ± 0.140* 0.96 310
V0 (m/s) 0.0 ± 0.5 2.6 ± 21.7 0.1 ± 0.3 0.5 ± 0.1 19.9 ± 6.6 0.548 ± 0.278* 0.93 0.2
Pmax (W) 215 ± 251** 12.1 ± 12.4 0.5 ± 0.2 203 ± 60 11.1 ± 3.5 0.892 ± 0.088* 0.72 350
SFV (N/m/s) -278 ± 327** -19.4 ± 36.3 -0.7 ± 0.3 331 ± 99 29.4 ± 10.2 0.569 ± 0.27* 0.85 421
SJ Flight Time F0 (N) -134 ± 400** -4.4 ± 15.2 -0.3 ± 0.3 389 ± 116 13.5 ± 4.3 0.662 ± 0.228* 0.74 872
V0 (m/s) 0.2 ± 0.6** 11.4 ± 28 0.4 ± 0.4 0.5 ± 0.2 22.8 ± 7.7 0.405 ± 0.325* 0.47 1.2
Pmax (W) 99 ± 236** 5.8 ± 13.2 0.2 ± 0.2 224 ± 67 12.4 ± 4.0 0.866 ± 0.106* 0.82 244
SFV (N/m/s) -186 ± 422** -12.5 ± 51.2 -0.5 ± 0.4 394 ± 117 36.1 ± 12.9 0.207 ± 0.366 0.32 899
Leg press F0 (N) 238 ± 704 6.0 ± 28.9 0.5 ± 0.5 437 ± 130 15.4 ± 5.0 0.541 ± 0.281* 0.33 1877
V0 (m/s) -0.3 ± 0.7** -11.7 ± 34.7 -0.6 ± 0.4 0.6 ± 0.2 24.0 ± 8.1 -0.177 ± 0.370 -0.45 3.5
Pmax (W) -136 ± 187** -7.2 ± 10.6 -0.3 ± 0.2 191 ± 57 10.1 ± 3.2 0.905 ± 0.078* 1.03 95
SFV (N/m/s) 276 ± 665** 23.5 ± 84.5 0.7 ± 0.7 401 ± 120 37.2 ± 13.3 -0.074 ± 0.378 -0.06 1327
CMJ Force plate F0 (N) -177 ± 424** -5.9 ± 16.5 -0.3 ± 0.3 406 ± 121 14.0 ± 4.5 0.623 ± 0.246* 0.68 1042
V0 (m/s) 1.3 ± 0.8** 70.0 ± 34.7 2.2 ± 0.6 0.6 ± 0.2 24.6 ± 8.3 -0.015 ± 0.380 -0.02 2.5
Pmax (W) 759 ± 306** 54.8 ± 15.7 1.7 ± 0.3 274 ± 82 14.9 ± 4.8 0.793 ± 0.155* 0.70 1.0
SFV (N/m/s) -488 ± 423** -32 ± 62.9 -1.2 ± 0.4 400 ± 119 37.1 ± 13.3 0.105 ± 0.376 0.21 1083

Sample size = 27

*Significant correlations p<0.05

**Significantly different from comparison measure (SJ/CMJ force plate) p<0.05. SJ: Squat jump, CMJ: Countermovement jump, SEE: Standard error of estimate. SD: Standard deviation, CL: 95% Confidence limit.

 10.1371/journal.pone.0245791.t006 FV-variables for all methods.
F0 (N) V0 (m/s) Pmax (W) SFV (N/m/s)
CMJ Force plate 2741 ± 491 3.8 ± 0.7 2537 ± 527 771 ± 260
CMJ Encoder 2760 ± 415 2.8 ± 0.4 1906 ± 360 1016 ± 225
CMJ Flight time 2759 ± 549 3.1 ± 0.6 2090 ± 380 948 ± 346
SJ Force plate 2915 ± 561 2.5 ± 0.7 1806 ± 464 1249 ± 483
SJ Encoder 2621 ± 404 2.5 ± 0.4 1652 ± 361 1065 ± 244
SJ Flight time 2794 ± 476 2.7 ± 0.5 1925 ± 498 1059 ± 270
Keiser leg press 3156 ± 831 2.1 ± 0.2 1660 ± 389 1519 ± 510

Sample size = 27. SJ: Squat jump, CMJ: Countermovement jump, F0:Theoretical maximal force in newtons, V0: Theoretical maximal velocity in meters per second, Pmax: Theoretical maximal power in watts, SFV: slope of the force-velocity profile. Values are presented as mean ± standard deviation.

 Discussion

This is the first study to investigate the between-session reliability of FV-profiles measured in SJ and CMJ with a force plate, linear encoder, and a flight time calculation method, in addition to a leg press task. The main finding of the present study was that regardless of strong linearity for individual FV-profiles, SFV and V0 were unreliable for all measurement methods assessed from vertical jumping using loads ranging from bodyweight to 80 kg (relative position on the FV-curve, force values 40–70% of F0). Only the leg press exercise showed acceptable reliability for the four FV-variables (relative position on the FV-curve, force values 20–80% of F0). There was a large to nearly perfect association across measurement methods for F0 and Pmax, while the association for V0 and SFV ranged from trivial to large.

Test-retest reliability of the FV-variables

To the authors’ knowledge, this is the first study to assess the test-retest reliability of the FV-variables in well trained and elite athletes. The present results are in accordance with previous research in other populations showing mostly acceptable reliability for F0 and Pmax (CV<10%) and poor reliability for V0 and SFV (CV >10%) during vertical jumping [12, 19, 25, 42, 43]. In contrast, FV-profiles derived from the leg press exercise displayed acceptable reliability for all variables in the present study (CV<10%, ICC>0.8). Feeney et al. [11] proposed that the low reliability for V0 (and thereby SFV) during vertical jumping could be a consequence of calculating velocity from a force signal (force plate). However, our data show low reliability for V0 from CMJ and SJ regardless of the velocity calculation method. The velocity from the leg press exercise is calculated as the derivation of position over time, identical to the encoder during SJ and CMJ, making it less likely that the variation in V0 is caused by calculation error. Further, Meylan et al. [12] speculated that the low V0 reliability is caused by greater biological variation closer to V0. However, our data show similar typical errors across loads and similar typical errors for F0 and V0 from the leg press (using loads with similar distance to both intercepts), making this questionable.

Furthermore, García-Ramos et al. [26] showed that the low V0 reliability during vertical jumping was most likely due to the distance of the extrapolation to the V0 intercept [26], as the lightest load possible to assess is the subject’s own bodyweight. The influence of the extrapolation distance has been discussed earlier [25], and the present results reinforce this assumption. F0 and V0 displayed similar reliability in the leg press exercise as the loads approached both ends of the FV-spectrum. The high reliability in the FV-variables obtained from the leg press can also partly be attributed to better standardisation in terms of fixed seat position, and thereby less technical variation in the exercise execution compared to the free weight conditions during CMJ and SJ [17, 18, 44, 45]. The influence of standardisation is also supported by the findings of Valenzuela et al. [19], which showed superior reliability of the FV variables obtained using a smith machine compared to free weights. It is therefore likely that the observed variations in the extrapolated variables V0 and SFV are caused by extrapolation error (i.e., small variations in the individual attempts are amplified because of the “extrapolation distance”) and the combination of technical/instrumental and biological variations. Consequently, in addition to superior standardisation compared to the other tests, the larger load range in the leg press exercise reduces the need for extrapolation for both force and velocity, explaining the high reliability of all the FV variables (Table 7).

10.1371/journal.pone.0245791.t007 Loading ranges used to assess the force velocity profiles.
Force in % of F0 Velocity in % of V0
Heaviest load Lightest load Heaviest load Lightest load
CMJ Force plate 75 ± 6 56 ± 6 26 ± 6 46 ± 7
CMJ Encoder 63 ± 6 39 ± 6 37 ± 6 61 ± 6
CMJ Flight time 75 ± 7 56 ± 6 25 ± 7 46 ± 9
SJ Force plate 68 ± 10 50 ± 8 33 ± 9 56 ± 14
SJ Encoder 66 ± 7 37 ± 6 35 ± 7 63 ± 5
SJ Flight time 70 ± 10 52 ± 8 32 ± 9 58 ± 15
Keiser leg press 80 ± 9 18 ± 3 22 ± 8 84 ± 4

Sample size = 27. SJ: Squat jump, CMJ: Countermovement jump, F0:Theoretical maximal force, V0: Theoretical maximal velocity. Values are presented as mean ± standard deviation.

The FV variables showed some slight differences in reliability between the CMJ and SJ conditions (Table 3). These small differences can partly be explained by slope steepness differences between SJ and CMJ, as the extrapolation distance to each intercept varies between these conditions (Table 7 and Fig 4). Additionally, SJ is prone to integration errors when calculating velocity with the force plate method [29]. This is linked to the assumption of zero start velocity, which is technically more challenging during SJ compared to CMJ. This challenge is similar for the encoder method, as the average force and velocity are calculated at the instance of the encoder’s registration of a positive displacement. These issues are reinforced by the fact that the flight time method showed the highest reliability for all FV-variables in SJ compared to the other methods (Table 3). Hence, the poor reliability of the SJ force plate and encoder method may be explained by calculation errors rather than physiological differences between the CMJ and SJ condition. Consequently, when calculating FV-profiles from encoders and force plates during SJ, careful attention should be given to the pause at the bottom (static position) of the squat to improve the detection of movement with this equipment (i.e., giving athletes extra practice attempts and/or familiarization).

Interestingly, the FV-variables measured with the encoder during CMJ exhibited the lowest CV% of all the CMJ measurement methods during the vertical jumps (Table 3). Notably, the encoder software uses the entire positive displacement curve, including the airtime. Additionally, average force is calculated as the product of mass and acceleration, where acceleration is the average velocity divided by the duration of the positive displacement. Especially in light loading conditions where the flight time is relatively long, changes and variability in force or velocity for the propulsive phase are inevitably harder to detect. Although the software manufacturer uses these calculations to improve reliability, the validity of the FV-profile will also be affected, considering the ability to detect changes. Additionally, changes in the estimated force in the light loading conditions are proportionally more affected by changes in bodyweight than changes in propulsive force (when the flight phase is greater than the push-off phase). With lower flight times, the encoder’s measures will to a greater degree reflect changes in propulsive force. This is supported by the correlation of 0.86 for F0 between the force plate method and the encoder. The greater reliability observed for the FV-variables assessed by the encoder may be misleading, as the usefulness of a test is determined not only by reliability and validity, but also by the ability to detect changes in performance [10].

The reliability results for the force plate method and flight time method were practically identical for all FV-variables during CMJ, but not SJ (Table 3). The differences between the force plate method and flight time method for SJ were probably due to the difficulty of detecting the zero starting velocity in the SJs for the force plate method, as discussed earlier [29]. This contention is supported by the fact that both methods (flight time and force plate method) showed similar reliability in the CMJ, as the zero starting velocity issue is not present in the CMJ. Furthermore, the slightly better reliability in SJ for the flight time method compared to the CMJ condition was probably due to less variation in starting position, as this is easier to control with the pause at the bottom of the squat.

Conjointly, the reliability of F0, V0 and Pmax was affected by the variation in the measurements–of each individual load–combined with the degree of extrapolation to the FV-intercepts. Hence, SFV was inevitably affected by the variation in both F0 and V0. Researchers and coaches should be aware of these limitations when assessing individual FV-profiles. Indeed, the 5–10% CV in jump height observed in this study was not acceptable for accurately assessing the accompanying FV-variables V0 and SFV, regardless of measurement method, with a loading range of bodyweight to 80 kg (forces ranging from 40–70% of F0). Typical error can only be decreased by reducing the variation in jumping performance or including loads closer to the F0 and V0 intercept. Additionally, the usefulness of a test is determined by the ability to detect changes in performance; more specifically, by comparing the typical error (CV%) with SWC [46]. Indeed, the FV-variables obtained from the leg press apparatus showed a superior signal-to-noise ratio compared to the other measurement methods in this study (Fig 3).

 Agreement among methods

Calculating the velocity of the center of mass from ground reaction forces has previously shown comparable reliability, with only small measurement errors compared to the “gold standard” 3D motion capture systems [47, 48]. It can therefore be argued that the force-plate method is the most valid method for assessing FV-profile during vertical jumping compared to all other measurement methods used in this study.

Only a few studies have examined the relationships among varying FV-profile methods for the lower limbs. García-Ramos et al. [22] also observed strong correlations for F0 and Pmax and trivial correlations for V0 and SFV across methods (force plate, linear encoder and flight time methods). Similar to the present study, the poor agreement for V0 and SFV was explained by the large extrapolation error for V0 [22].

Contrary to our findings, Jiménez-Reyes et al. [15] reported excellent agreement between the flight time and force plate method for the FV-variables (r: 0.98–0.99). This discrepancy from our findings can probably be attributed to several methodological differences. The flight time method calculates force and velocity based on jump height [15]. However, flight times are inevitably prone to small errors in technical execution [49], in addition to systematic errors compared to jump height obtained from force data [50, 51]. As Jiménez-Reyes et al. [15] point out, the FV-variables are associated with cumulative extrapolation errors, consecutively decreasing the validity of these variables. The small systematic and random differences in jump height between flight time and force data are even greater for the extrapolated FV-variables. Additionally, the assumption of constant acceleration during the push-off phase in the flight time method could also affect the agreement with the force plate method, as variations in average force and velocity during the push-off phase are not necessarily related to jump height variations [17, 18, 52, 53].

Furthermore, the flight time method assumes constant push-off distance across loads and trials [15, 31]. However, from the force plate data, we observed 5–10% (2–4 cm) variation in push-off distance across trials and loading conditions, even when controlling the depth as previously recommended [54]. This variation may be due to changes in jump mechanics across trials and loads [45], making it challenging to assume a constant push-off distance despite controlled knee angle. Jiménez-Reyes et al. [15] have previously reported a 0.4% variation (CV%) in push-off distance across trials for CMJ when using a smith machine. This apparatus probably reduces the variation in jump mechanics compared to the free weight jumps used in the present study. This implies that the poor agreement in our study can also be attributed to poor control of the center of mass for the subject, and not solely the flight time method.

Contrary to previous research showing an overestimation of V0 measured with an encoder compared to a force plate (72.3%) [22, 47], we observed an underestimation for the CMJ condition (-23%) (Table 6). The overestimations of velocity during light loading conditions in previous investigations are explained by the attachment point at the bar, as the bar velocity is higher than the centre-of-mass velocity during jumping [22, 47]. However, because the velocity from the encoder used in this study is based on the entire positive displacement curve (including the airtime), the average velocity is lower. Combined with the extrapolation error, this partly explains the higher agreement between the force plate and encoder for F0 and Pmax compared with V0 and SFV. Practitioners and researchers should be aware of the limitations of using linear encoders for measuring FV-profiles, especially to obtain V0 and SFV.

Padulo et al. [21] observed an underestimation in V0 (-46%) and overestimation in F0 (21%) in the leg press compared to the squat exercise. The underestimation in V0 can be attributed to biomechanical differences, as the squat movement involves a larger contribution from the hip joint, resulting in higher system velocity [21]. In addition, approximately 30% of the work during a vertical jump is contributed by the ankle joint [45]. This contribution is likely lower for the leg press due to the more plantarflexed orientation of the ankles in this apparatus. These biomechanical differences probably explain why the leg press has the largest bias of all the tested methods (Table 6). Another explanation is the pneumatic resistance in the present leg press apparatus, allowing higher average velocities for a given force due to the absence of inertia [55]. Additionally, the software excludes 5% of the range of motion from the start and end of the movement, inevitably affecting the average values in the lighter resistance conditions to a greater degree compared to the higher resistance conditions, resulting in higher V0. These issues may explain the high V0 in the leg press exercise and the low agreement in V0 compared to the other measurement methods. Intriguingly, V0 was negatively correlated with the three SJ measures and the leg press exercise (Fig 5). The extrapolated V0 during the leg press exercise is highly influenced by the push-off distance [56], where it has been previously argued that comparisons across individuals should only be done when participants perform the vertical jumps with their usual or optimal push-off distance Samozino et al. [57]. The initial push-off distance during vertical jumping in this study was self-determined, while the push-off distance in the leg press was standardised, possibly explaining the poor correlation in V0 between the leg press and the jump exercises. Furthermore, as shown by Bobbert [56], the linear shape of the FV-relationship during multi-joint movements is influenced by segmental dynamics, and this influence is magnified by increasing movement velocity [56]. Hence, segmental dynamics probably influence the agreement of V0 to a greater degree than F0 when comparing exercises with varying push-off distances and joint contributions [56]. Consequently, segmental dynamics partly explain the larger agreement for measures closer to F0 and poorer agreement and correlations for V0 across leg press and vertical jump tasks. As illustrated in Fig 4 and shown in Table 5, differences in V0 are larger across methods and conditions compared to F0.

10.1371/journal.pone.0245791.g005 Correlation matrix showing Pearson r coefficients for the FV-profile variables (F<sub>0</sub>, P<sub>max</sub>, V<sub>0</sub>, S<sub>FV</sub>) for cross sectional data.

Colored circles indicate P<0.05, where circle size and color represent corresponding r values (color legend is presented with the figure). SJ: Squat jump, CMJ: Countermovement jump, F0: Theoretical maximal force, V0: Theoretical maximal velocity, Pmax: Theoretical maximal power, SFV: slope of the force-velocity profile. Sample size for all correlations n = 27.

Small but important differences across methods accumulate, with larger differences for V0 and SFV compared to F0 and Pmax. The agreement across methods is highly influenced by the combination of measurement errors, as well as the distance of extrapolation to the FV-intercepts. All FV-variables depend on the measurement condition, including equipment, exercise type, resistance modality and push-off distance.

 Strengths and limitations

The present study included a large sample of male and female athletes with varying sport backgrounds, using a multicenter approach. This design allows for larger sample sizes and higher ecological validity as athletes are assessed by different test leaders and using different equipment [58]. The conclusions from the study are based on the results from the main analysis and supported by the data from the larger aggregated analysis.

There are several methodological limitations that need to be considered for the findings from this study. The difference in number of loading conditions (i.e., 5 for vertical jumping and 10 for leg press) and relative position on the FV-curve inevitably affect the agreement measures due to differences in the accuracy of obtaining the extrapolated variables. Additionally, the difference in push-off distance from the leg press (standardized to vertical femur) and vertical jumping (standardized to self-selected depth) may influence the variation across these conditions. The leg press protocol included breaks of 10–20 sec for the light loads and 20–40 for the heavy loads, which may cause some fatigue between repetitions and influence the FV-relationship. For the force plate method, the 5 SD threshold for determining the start of the movement will influence the average values of force and velocity and thereby the FV-variables. Especially in the SJ, but also in the CMJ, this threshold is sensitive to small movements and is a source of error that is not controlled for. In the leg press software, the average values have a 5% cut-off from the range of movement, which can lead to i) taller athletes having a larger cut-off in terms of absolute values compared to shorter athletes, and ii) in the lighter loads where more range of motion is achieved, the cut-off in terms of absolute values will be larger for lighter loads compared to heavier loads. The results from the encoder used in the present study cannot be generalized to other linear encoder devices with different calculation methods for acceleration and force. The jumps in this study were performed with free weights, where it was difficult to accurately standardize the center of mass of the jumps using only thigh depth or knee angle as a reference. These variations in the center of mass are likely smaller using smith machines. These limitations inevitably affect both the test-retest reliability and the agreement across methods, where it is impossible to differentiate which source of variability leads to the results observed in this study. Nevertheless, the use of free weights increases the ecological validity of the study as these are commonly used by athletes. Additionally, for the analysis for agreement the force plate was sampled at 200 Hz compared to 1000 Hz used previously [15], which may have influenced the findings. For the aggregated reliability analysis, both 200 Hz and 2000 Hz force plates were used, and we would argue that the findings of reliability seem independent of sampling frequency.

 Conclusions and practical applications

A 5–10% between-session CV in jump height is not acceptable for accurately assessing SFV and V0, regardless of measurement method, using a loading range of bodyweight up to 80 kg (forces ranging from 40–70% of F0). Caution is advised when using similar protocols for individual training recommendations or interpreting training adaptions for athletes. Efforts should be made to either reduce the variation in jumping performance or to assess loads closer to the FV-intercept. Increasing the loading range can be achieved by using alternative exercises such as a leg press exercise. Reducing the variation in jumping performance may possibly be achieved through additional practice attempts, and attention should be given to the depth of the squatting motion during the vertical jumps. F0 and Pmax showed high reliability and generally good agreement across measurement methods, indicating that these variables can be used with confidence by researchers and coaches. However, one should be aware of the poor reliability of the FV-variables V0 and SFV obtained from vertical jumping, as well as differences across measurement methods for assessing individual FV-relationships.

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Spreadsheets for analysis of validity and reliability. Sportscience. 2015;19: 36–42. Hopkins WG, Marshall SW, Batterham AM, Hanin J. Progressive statistics for studies in sports medicine and exercise science. Med Sci Sports Exerc. 2009;41: 3–13. doi: 10.1249/MSS.0b013e31818cb278 19092709 Cronin JB, Hing RD, McNair PJ. Reliability and validity of a linear position transducer for measuring jump performance. J Strength Cond Res. 2004;18(3):590–593. doi: 10.1519/1533-4287(2004)18<590:RAVOAL>2.0.CO;2 15320688 Cormack SJ, Newton RU, McGuigan MR, Doyle TL. Reliability of measures obtained during single and repeated countermovement jumps. Int J Sports Physiol Perform. 2008;3(2):131–144. doi: 10.1123/ijspp.3.2.131 19208922 Gathercole R, Sporer B, Stellingwerff T, Sleivert G. Alternative countermovement-jump analysis to quantify acute neuromuscular fatigue. 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Potential benefits of multicenter reliability studies in sports science: A practical guide for its implementation. 2020(Preprint):1–6. 10.1371/journal.pone.0245791.r001 Decision Letter 0 Boullosa Daniel Academic Editor 2021 Daniel Boullosa This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Submission Version 0

9 Nov 2020

PONE-D-20-29309

Force-velocity profiling in athletes:

Reliability and agreement across methods.

PLOS ONE

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Reviewer #1: The present study assessed the between-day reliability of the f-v parameters computed from different exercises (CMJ, SJ and leg press) and using different methods (force plate, encoder, flight time), as well as the differences in the magnitude of the f-v parameters assessed with these methods. Additionally, the authors examined the association of these parameters with some performance measures.

I think the topic is relevant, particularly given the growing popularity of these methods for guiding training prescription and for performance assessment. Moreover, the results are quite novel and could have practical implications. My main concern is that the manuscript (including the text, figures and tables) is a bit difficult to follow in some parts, and it could maybe be simplified to enhance readability. Moreover, some typos should be corrected.

Specific comments:

Abstract

- Line 24. The athletes ‘were’ tested…?

- Line 41. I suggest including in the last sentence of the abstract that coaches should also be aware of the low reliability of f-v parameters (particularly v0 and Sfv) assessed during jumping.

- There is no comment on the association between fv parameters and performance measures. In my opinion, and just as a suggestion that the authors are free to obviate, the manuscript is strong enough when presenting reliability and magnitude comparison methods, and adding the association between fv parameters and performance measures complicates the manuscript. This last section, which is presented as a secondary aim of the study, could be presented even in a separate paper, but this is just in my humble opinion.

Introduction

- It would be nice to cite this review, which gives a nice overview of the applications of VBRT (and of the assessment of the fv profile): https://journals.lww.com/nsca-scj/Abstract/9000/Velocity_Based_Training__From_Theory_to.99257.aspx

- Line 50. It would be nice to mention that there is some controversy regarding the linearity of the f-v relationship, at least at very low force values (PubMed ID: 32255757, PubMed ID: 26103786).

- Line 57. Can the authors include a reference for this equation? Maybe one of the studies/reviews of Morin and Samozino would be nice.

- Line 60. Please, specify how these f-v parameters were computed. From jump height? From force platforms? linear encoders? Has the between-day reliability of the f-v profile estimated from jump height been proven?

- Line 65. Please, specify which measurement methods.

- Line 69. Please, specify the method of measurement. Jump height? Force platform?

- Line 72. A recent study by Valenzuela et al (accepted in IJSPP, but still in press) reported a low between-day reliability for f-v parameters computed from jump height during vertical jumps. Please, see attached document. It would be nice to briefly mention this article in the introduction or discussion section.

- Line 74. Should it be "there exist numerous methods..."?

- Line 87. "...as well as from the leg press exercise".

- Line 88. Previous research "has" investigated...

Methods

- Line 134. Which was their experience with the testing procedures?

- Line 167. It would be nice to include a new paragraph with each test, as done for SJ and CMJ.

- How much time was left between tests?

- Line 202. It would be nice to start a new paragraph with each measurement method (as done for the Keiser leg press)

Results

- Line 259. coma not needed before ‘ranging’.

- Line 269. 1.2 cm for both SJ and CMJ?

- There is no mention to the SWC in the results section. Were differences between days or between methods greater than the SWC?

- Line 291. The results on the association between fv parameters and performance measures should be explained in greater detail in the text (if the authors want to keep these analyses). On which tests (CMJ, SJ, leg press) was an association found? With which measurement method? (encoder, force plate, flight time).

Discussion

In my opinion the discussion section could be shortened and simplified. The authors could try to avoid repeating concepts.

- Line 298. ‘were’ unreliable? The authors are mentioning two variables.

- Line 332 and Line 423. Small differences in starting position during jumping (impulse distance) can have meaningful effects on the fv variables (PMID: 32223526).

- Line 397. ‘has’ previously shown…

- Line 509. Values for analysis "are" used

- Line 510. the observation ... has, or the observations .... have..

- Line 511. that ‘appears’ when using…

- Line 517. less error for V0? Wouldn’t this error be larger given that the relationship losses linearity particularly at values closer to v0?

- Line 534. push-off instead of push of.

- Line 547. The jumps…’were’

- Line 549. These variations…’are’.

Conclusions

- Line 55. Specify that this CV is between-session

Tables 3-5. Just in case it is possible. Could the tables be simplified assessing between-session reliability pooling all subjects together? Without dividing tests 1-2 and 3-4.

Table 6. Please, specify what methods are being compared. What does the bias refer to in each line? CMJ vs leg press? CMJ vs SJ? Encoder vs flight time? Where is the comparison of leg press vs SJ flight time, for instance?

Table 6. Footnote. Units are already specified in the table, no need to explain them in the footnote.

Table 6. Footnote. ‘significant differences’, or ‘significantly different’? Significant different would be incorrect.

Table 7. Please specify the units for F0, v0, Pmax and Sfv

Figure 2. tested instead of tester. Also, please, include the "n" always in capital or lowercase.

Figure 3. Panel B. The Y axis can be reduced (the maximum value is lower that 10-15). Also, the SWC is not discussed in the results section, and almost not discussed in the discussion section. I suggest either discussing this result in greater detail, or removing it. Were differences between days or between methods greater than the SWC?

Figure 5. If the aim is to assess the association between f-v parameters and performance measures, could this figure be simplified by removing the analyses on the left? The authors would just need to show the association between F0, v0, Pmax and Sfv with 1RM, CMJ, SJ, 10m sprint and 30m sprint, but there is no need to show the association between f0 leg press and f0 CMJ force plate, for instance.

Reviewer #2: Manuscript ID: PONE-D-20-29309

GENERAL COMMENTS: First, I would like to congratulate the authors on their effort. The study comprises a large sample given the elite level of the participants. The fact that several training centers participated on the research adds value to it. The aim of the study was to investigate the test-retest reliability and agreement across methods for assessing individual Force Velocity-profiles of the lower limbs in well-trained athletes. The research idea is interesting, and the conclusions may have important implications in current athlete profiling procedures. The investigation has a sound scientific background given the previously questioned reliability of the FVP parameters. However, some methodological aspects must be polished before I can recommend the publication of the study. I believe that some changes are necessary to strengthen the quality of the data reported and the conclusions. I do think that the data collected may positively impact the sport science field. The authors should interpret my comments as constructive.

Abstract

Changes in the abstract will not be addressed prior to all the other issues within the manuscript are solved.

Introduction

In general, the introduction tries to explain and introduce the research problem and is fairly successful. It is clear for the reader the need to conduct the present investigation.

Specific comments:

Line 59-60. "However, although several studies have evaluated the between-session reliability of FV-parameters". In general terms, what did these studies found? It would be interesting for the reader if the authors presented a bit more detail here.

Methods

The methods are interesting but that are some details that must be addressed.

Specific comments:

Line 103-105. “The first two (...) figure 1 & 2)". This sentence is somehow confusing. Based on the information presented in Figure 1, the authors should consider rephrasing as follows:

"The first two testing timepoints were separated by ~1 week, before a period of 2~6 months. Then, the two-last testing timepoints were conducted also were separated by ~1 week (figure 1 & 2)."

Line 114. Please consider replacing "are" before "constant" with "were".

Line 116. Please consider replacing "was" before "constant" with "were kept".

Line 133. "national and elite level". What did the authors consider to be national and elite level? A better description of the criteria used to classify the athletes would be interesting for the reader.

Line 143. "hamstring and hip mobility". What do the authors mean by hamstring mobility? Please clarify.

Line 150-151. "for some weaker subjects, a protocol of approximately 5 loads up to 80% of bodyweight were used". Was there a specific criteria to determine this? Which athletes were considered as "weaker subjects"? And the 5 loads, were they standardized or individually determined? Please clarify.

Line 161. Please consider replacing "was verbally forbidden" by "was not allowed".

Line 167. Please consider starting a new paragraph with "For the leg press,...". Otherwise, the paragraph will be too long and hard to follow.

Line 168-170. “(...) the FV-parameters were derived from a dedicated software based on a 10-repetition FV-test with incremental loading based on each athlete's 1RM load". This sentence is confusing. Please consider rephrasing.

Line 171. “∼20% of 1RM”. The 1RM load was previously determined? Or was the athlete's perceived 1RM used?

Line 177. It is spelled "heels" and not "heals". Please correct.

Line 179. Please consider replacing "are" before "performed" with "is".

Line 183. Please consider starting a new paragraph with "Prior to the 30-m sprint, …".

Line 183. Did all participants perform the 30 m sprint test or just the athletes from running-based sports (e.g., soccer, handball or athletics)? I mean, did the weightlifters, ski-jumpers or badminton players also performed a 30-m sprint?

From what I understand one of the aims of the study is to "investigate the association between the FV-parameters obtained from vertical jumping and leg press with 1RM squat, jump height and 10 and 30m sprint time". I see no problem with investigating the association between the FV parameters and 1RM squat and jump height for the entire sample. However, when it comes to the sprint test, I am not sure that the analysis should include the weightlifters or sky-jumpers, for example. Do the authors consider that any meaningful practical application can be drawn from a ski-jumper's 30-m sprint performance?? If these athletes were included in the analysis for the sprint variables, I strongly recommend the authors to exclude them from this outcome. Also, I strongly suggest doing a sub-group with only the athletes from running-based sports (i.e., soccer, handball, ice-hockey, speed skating and possibly athletics - depending on the modality) and test the associations between FV parameters and 1RM, vertical jump and sprint outcomes. For the rest of the sample, I suggest testing the relationship between the FV parameters and only the 1RM and vertical jump (exclude sprint).

This will greatly strengthen the quality and, especially, the logic behind the study as it will provide meaningful data for practitioners, based on the specific physical performance variables from each sport without inducing them to perform unnecessary and “injury risk tests” (e.g., maximal sprint test for a weightlifter or a sky-jumper).

Line 188. Please consider starting a new paragraph with "The 1RM back-squat…".

Line 230. The fact that one force plate recorded at 200 Hz while other at 2000 Hz must be acknowledged as a limitation that may potentially affect data analysis and comparison between methods.

Results

The figures are well designed and facilitate the interpretation of the data.

Line 291. As stated before, I strongly recommend the authors to exclude the athletes from non-running based sports from the sprint analysis to strengthen the conclusion and ecological validity of the data reported in the study.

Discussion

Overall, the discussion is well written, and the authors do a good job comparing the results obtained with previous research. They present a sound reasoning for their findings, supporting their data adequately based on previously published literature. However, the section is too lengthy and would greatly benefit if the authors were able to be more concise with their writing and reduce the word count. Some of the paragraphs repeat information, which makes this section hard to follow at times. I strongly recommend the authors to invest time re-arranging the discussion because I do believe that the paper is interesting for the sport science community and has the potential to be published and impact current athlete profiling practices.

Specific comments:

Line 306-334. This paragraph is too long. I recommend the authors to shorten it or divide it into multiple paragraphs.

Line 334. All tables should be presented in the Results section. I recommend the authors to move Table 8 into the mentioned section.

Line 353. According to the table presented in Table 7, the Pmax obtained in the SJ was higher than the CMJ when using the encoder. However, in the other methods, the Pmax was higher in the CMJ (as it would be expected). The authors must explain these contradicting results in this paragraph.

Line 378-385. The information presented in this paragraph have been previously presented in the discussion section (Line 319, 322-327). The authors should consider removing this part of the text to avoid repetition and improve the "fluidity" of the discussion.

Line 397. Please consider replacing "have" before "previously" with "has".

Line 407-437. This paragraph is too long. I recommend the authors to shorten it or divide it into multiple paragraphs.

Line 479. "All FV-variables depend on the measurement condition, including equipment, exercise type, resistance modality and push-off distance." What are the practical applications from this? I believe the discussion could be shortened and provide a more "applied" perspective.

Line 483-521. This paragraph is too long. I recommend the authors to shorten it or divide it into multiple paragraphs.

Line 509. Please consider replacing "is" before "used" with "are".

Line 532. Strengths and limitations. Another important limitation is related to the fact that, for the aggregated analysis, force plates with different sampling frequencies were used. This must be acknowledged in the manuscript and its implications for the results must be briefly addressed (one sentence would suffice).

Line 526. The argument used regarding the "ecological validity" of the study is greatly affected by the fact that athletes whose training regimens do not usually incorporate linear sprint actions (e.g., weightlifting or badminton), where tested for 30-m sprint performance. For this reason, the authors should re-consider the analysis made. The data presented herein is really interesting and address important aspects related to athlete profiling. I consider that publishing such data would be important for the sport science community. It would be relevant, for example, to include some discussion related to this issue, emphasizing that athletes from non-running/sprint-based sports should not perform sprint-based tests, as this is “not rational from a logical standpoint”. Therefore, I strongly advise making the previously mentioned adjustments as it would greatly improve the quality of the data.

Line 574. Please consider replacing "was" before "performed" with "were".

547-549."The jumps in this study were performed with free weights where it was difficult to accurately standardize the center of mass of the jumps using only thigh depth or knee angle as a reference." Although I understand what the authors mean here, I am not sure if performing the exercises with free weights is an actual limitation of the study. Most athletes train with free-weights, so that increases the "ecological validity" of the data reported. Moreover, it is really important for coaches to understand that calculating FV-parameters using free weights affects test-retest reliability due to the reasons mentioned throughout the manuscript. It is not a limitation, but rather an “unavoidable” phenomenon that occurs is real-world training settings.

Conclusions and practical applications

The conclusions seem appropriate and based on the results obtained.

**********

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Reviewer #1: No

Reviewer #2: No

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Submitted filename: Valenzuela (2020) Reliability fv parameters.pdf

 10.1371/journal.pone.0245791.r002 Author response to Decision Letter 0 Submission Version 1

30 Nov 2020

We would like to thank the reviewers for a thorough and excessive job of reviewing this manuscript. The

inputs and suggestions from the referees have been taken under consideration and detailed responses to

reviewers are given in the attached file: Response to Reviewers

Submitted filename: Response to Reviewers.pdf

 10.1371/journal.pone.0245791.r003 Decision Letter 1 Boullosa Daniel Academic Editor 2021 Daniel Boullosa This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Submission Version 1

23 Dec 2020

PONE-D-20-29309R1

Force-velocity profiling in athletes:

Reliability and agreement across methods.

PLOS ONE

Dear Dr. Lindberg,

Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.

Please, address ASAP the revisions suggested by the reviewers to proceed with the acceptance of the manuscript.

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We look forward to receiving your revised manuscript.

Kind regards,

Daniel Boullosa

Academic Editor

PLOS ONE

[Note: HTML markup is below. Please do not edit.]

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation.

Reviewer #1: (No Response)

Reviewer #2: All comments have been addressed

**********

2. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Yes

Reviewer #2: Yes

**********

3. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: Yes

Reviewer #2: Yes

**********

4. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: (No Response)

Reviewer #2: Yes

**********

5. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #1: Yes

Reviewer #2: Yes

**********

6. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: I would like to thank the authors for addressing most of my previous comments. I think the manuscript would benefit from revising some minor typos (please, see some examples below), but is overall acceptable for publication. It would be good if an English native speaker revises the writing (given that PLOS One does not copyedit accepted manuscripts).

Last line of abstract and conclusion: “as well as OF THE differences across measurement methods…” The of is missing.

Introduction. Line 63. Controversy “exists”. The “s” is missing.

Introduction. Line 67. Reference number 19 assessed between-session reliability, not within-session reliability.

Methods, Line 163-164: A protocol of…”was used”. Is the verb referring to “protocol” or to “the loads”?

Methods, Line 164: The increase in loads “was” then individually determined, or loads “were” then individually determined.

Methods, line 186-191: Please be consistent with the verb tense (past simple), i.e., "was gradually increased..."

Results, line 277: the typical error...was, or the typical errorS (in plural)...were

Discussion, Line 366 The correct citation would be Valenzuela et al. (Pedro L. is the name, not the surname). Also applicable in the reference list.

Discussion, Line 424: No need to mention the journal (PeerJ) here. Please, revise the citation.

Reviewer #2: Manuscript: PONE-D-20-29309R1

GENERAL COMMENTS: I would like to congratulate the authors for their effort to address the points raised. I believe that the quality of the paper has greatly improved to the level expected for its publication. The authors have reformulated their discussion which allows for a better understanding of the phenomenon being studied. This manuscript adds to the recent and compelling evidence questioning the reliability of the FV variables which has great implications for coaches and sport scientists. I am happy to endorse the publication of the manuscript. However, the authors should adjust the following minor details:

Tables 3 and 4. Tables 3 and 4. For consistency concerning the rest of the manuscript, please report the ICC values as "0.81" instead of ".81".

Line 366 (consider the line numbers of the manuscript version without marked changes). Please note, that the author is "Valenzuela et al. [19]" and not "Pedro L. et al." Also, this reference should be corrected in the reference list.

Line 424. The reference “(Helland et al 2020 PeerJ)” must be corrected so per journal style. In addition, I was not able to find this reference in the reference list.

Line 529. Please replace "This variations" with "These variations".

**********

7. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #1: No

Reviewer #2: No

[NOTE: If reviewer comments were submitted as an attachment file, they will be attached to this email and accessible via the submission site. Please log into your account, locate the manuscript record, and check for the action link "View Attachments". If this link does not appear, there are no attachment files.]

While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com/. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email PLOS at figures@plos.org. Please note that Supporting Information files do not need this step.

 10.1371/journal.pone.0245791.r004 Author response to Decision Letter 1 Submission Version 2

7 Jan 2021

Thank you for the useful comments. Please se the attached revised manuscript and response letter

Submitted filename: Response to Reviewers.docx

 10.1371/journal.pone.0245791.r005 Decision Letter 2 Boullosa Daniel Academic Editor 2021 Daniel Boullosa This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Submission Version 2

8 Jan 2021

Force-velocity profiling in athletes:

Reliability and agreement across methods.

PONE-D-20-29309R2

Dear Dr. Lindberg,

We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements.

Within one week, you’ll receive an e-mail detailing the required amendments. When these have been addressed, you’ll receive a formal acceptance letter and your manuscript will be scheduled for publication.

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Kind regards,

Daniel Boullosa

Academic Editor

PLOS ONE

Additional Editor Comments (optional):

Reviewers' comments:

 10.1371/journal.pone.0245791.r006 Acceptance letter Boullosa Daniel Academic Editor 2021 Daniel Boullosa This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

21 Jan 2021

PONE-D-20-29309R2

Force-velocity profiling in athletes: Reliability and agreement across methods.

Dear Dr. Lindberg:

I'm pleased to inform you that your manuscript has been deemed suitable for publication in PLOS ONE. Congratulations! Your manuscript is now with our production department.

If your institution or institutions have a press office, please let them know about your upcoming paper now to help maximize its impact. If they'll be preparing press materials, please inform our press team within the next 48 hours. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information please contact onepress@plos.org.

If we can help with anything else, please email us at plosone@plos.org.

Thank you for submitting your work to PLOS ONE and supporting open access.

Kind regards,

PLOS ONE Editorial Office Staff

on behalf of

Dr. Daniel Boullosa

Academic Editor

PLOS ONE