Free-fall normalised peak braking velocity for countermovement jump monitoring

Abstract

Background

Peak braking velocity (PBV) during the countermovement jump (CMJ) is used to describe descent strategy, but its interpretation is affected by countermovement depth. This study introduced free-fall normalised peak braking velocity (PBVFF), a dimensionless index expressing PBV relative to the displacement-specific theoretical free-fall velocity limit, and evaluated its reliability, performance associations and ranking consequences.

Methods

Seventy injury-free male academy footballers (18.7 ± 1.6 years) performed three maximal hands-on-hips CMJs on dual force plates. Using retrospective observational routine monitoring data, one representative testing day per athlete was analysed. Two PBVFF variants were examined: PBVFF normalised to countermovement depth (PBVFF_CMD) and PBVFF normalised to displacement at PBV (PBVFF_{PBV_d}). Reliability was assessed using coefficient of variation and two-way mixed-effects intraclass correlation coefficients. Associations with modified reactive strength index (mRSI) and jump height (JH) were assessed using Pearson correlations, Benjamini–Hochberg false discovery rate correction and partial correlations controlling for JH. Ranking effects were examined using Spearman rank correlations, Kendall’s coefficient of concordance and absolute rank shifts.

Results

PBVFF_CMD showed reliability comparable to raw PBV, with a pooled coefficient of variation of 5.81% versus 6.75% and three-trial intraclass correlation coefficients of 0.865 versus 0.888, respectively. PBVFF_CMD was more strongly associated with mRSI than raw PBV (r = 0.573 versus r = 0.231). After controlling for JH, the association between raw PBV and mRSI reversed direction (partial r = − 0.266), whereas the association for PBVFF_CMD remained positive (partial r = 0.531). PBVFF_{PBV_d} showed similar but weaker associations with mRSI (r = 0.430; partial r = 0.438). Switching from raw PBV to PBVFF_CMD reclassified 46% of athletes by at least 10 ranking positions.

Conclusions

PBVFF provides a depth-contextualised interpretation of CMJ descent strategy without compromising within-session reliability. PBVFF_CMD appears particularly practical because it can be derived from commonly exported variables and may improve athlete monitoring by reducing misinterpretation driven by countermovement-depth and anthropometric differences. It should complement, rather than replace, established force–time and performance metrics.

Trial registration

Not applicable.

Introduction

Objective monitoring is now embedded in contemporary performance and rehabilitation practice. The force plate-based countermovement jump (CMJ) test remains among the most frequently used assessments for inferring acute changes in lower-body neuromuscular function because it provides high-frequency data and enables phase-specific force–time analysis beyond a single outcome such as jump height [4, 6, 32]. In parallel, commercial ecosystems have reduced barriers to force plate monitoring through portable hardware and automated analytics. This increased accessibility is valuable, but it also increases the risk that complex, integration-derived variables are treated as interchangeable dashboard outputs without explicit reporting of their definitions, assumptions, and processing choices.

Many CMJ variables are not directly measured, but are obtained by transforming vertical ground reaction force into centre-of-mass (COM) acceleration, velocity, and displacement through force-integration procedures [27, 29]. Consequently, decisions regarding quiet-standing weight estimation, movement-onset detection, filtering, integration constants, and phase definitions can alter the resulting CMJ outcomes. Direct comparisons between commercial automated analyses and custom workflows indicate that reported variables can differ across processing pipelines [14, 30, 37–39, 42]. These realities support recent calls to rationalise CMJ reporting and prioritise variables that are mechanistically interpretable and robust under typical applied constraints [1, 4]. Therefore, the challenge is not simply to decide which CMJ outputs should be reported, but to determine how retained variables should be contextualised so that their interpretation remains mechanically coherent.

Within this context, peak braking velocity (PBV), defined as the magnitude of the peak negative vertical COM velocity during the countermovement descent at the transition from unweighting into the braking phase, represents a particularly relevant example of the broader challenge surrounding integration-derived CMJ strategy variables [15, 29, 31]. Strategy variables describe how the jump is executed, rather than only the final outcome it produces, and include phase-specific kinetic, kinematic, and derived mechanical descriptors from the unweighting, braking, and propulsive phases. However, they should be distinguished from net propulsive impulse and take-off velocity, which directly reflect the impulse–momentum determinants of jump height. Fatigue-related changes in CMJ performance may be expressed through altered movement strategy or lower-limb biomechanics even when headline outcomes change only modestly, supporting the use of mechanics-related variables alongside outcome measures in fatigue monitoring [20, 41, 44]. In this context, alternative analytical approaches suggest that phase-specific CMJ descriptors may complement global outcomes by contextualising jump-execution variables, particularly eccentric and temporal features; however, they should not be interpreted as stand-alone evidence of fatigue or as direct evidence of a specific altered movement strategy [17].

In practice, PBV is interpreted as the athlete’s downward COM velocity at the onset of active deceleration, with the braking phase defined as the portion of the countermovement in which vertical ground reaction force exceeds the system-weight baseline. Accordingly, PBV is commonly used to contextualise trial execution quality, including whether the athlete generated sufficient downward COM velocity before braking, which may indirectly reflect movement intent, as well as the vertical deceleration requirements imposed during the subsequent braking phase. The importance of this downward velocity is supported by evidence that greater PBV is associated with more efficient CMJ performance in trained athletes [16, 18]. Mechanically, PBV magnitude reflects the downward change in COM velocity generated by the net unweighting impulse relative to system mass. However, PBV shares the general methodological vulnerabilities of integration-derived CMJ variables, including sensitivity to weighing accuracy, movement-onset detection, integration drift, and event identification [1, 43]. Thus, although PBV may be a useful descriptor of countermovement behaviour, its raw value should not be interpreted as an isolated marker of movement quality or neuromuscular function; rather, it should be interpreted in relation to the broader execution strategy used to archive it.

A key source of this context dependence is countermovement depth (CMD), defined as the magnitude of maximal downward COM displacement relative to movement onset (t₀). A deeper countermovement increases the displacement available for the COM to accelerate downward before it must be arrested, and depth manipulations can alter downward velocity and force–time characteristics even when neuromuscular capacity is unchanged [40]. CMD selection and PBV magnitude can also meaningfully shift several important CMJ-derived variables, including force, velocity, and power outputs, jump height, reactive strength index modified (mRSI), and force–time curve shape. Because mRSI is a composite ratio partly driven by jump height and time to take-off, it is included here not as an independent construct-validating outcome, but as an example of how force plate metrics can be substantially influenced by countermovement strategy [35, 36]. Anthropometry further complicates interpretation because CMD and related kinematics are influenced by body size, segment lengths, and joint configurations. Therefore, between-athlete PBV comparisons or fixed PBV thresholds may be systematically biased when athletes differ substantially in stature or range-of-motion availability [28].

This issue is particularly relevant because fixed PBV targets have been proposed in applied settings. For example, [8] suggested that PBV values of 0.6 m/s in the unilateral CMJ and 1.2 m/s in the bilateral CMJ may be considered minimum acceptable targets. In our view, translating such fixed PBV benchmarks into clinical or sport performance cut-offs is problematic because PBV is influenced by multiple modifiable and non-modifiable factors. Reliance on any single threshold may therefore increase the risk of misclassification, inappropriate athlete or patient evaluation, and the inadvertent promotion of movement strategies that improve the metric without necessarily reflecting meaningful underlying functional improvement.

Importantly, this does not imply that negative phase CMJ characteristics are meaningless or merely incidental. Evidence suggests that these characteristics are trainable neuromuscular qualities that contribute to improved stretch–shortening cycle performance rather than purely self-selected movement features [10, 11]. Higher downward COM velocity reflects greater unweighting/negative acceleration and imposes a greater requirement to develop braking force rapidly to arrest and reverse the movement [11, 33]. Thus, PBV remains a potentially useful descriptor of countermovement behaviour, provided that it is interpreted alongside CMD and direct braking force–time variables rather than as a standalone proxy for neuromuscular function.

The purpose of the present paper is therefore to introduce free-fall normalised peak braking velocity (PBVFF), a dimensionless index that expresses PBV as a fraction of the maximum downward velocity theoretically attainable under gravitational acceleration over a specified negative COM displacement. Contextualising countermovement performance using PBVFF may reduce misinterpretation driven by depth strategy and range-of-motion availability, support more equitable comparisons across athletes and sessions, and provide a simple quality-control criterion for identifying implausible values. Specifically, PBVFF values greater than 1 indicate that the observed PBV magnitude exceeds the displacement-specific theoretical free-fall maximum and should therefore be treated as a likely processing, integration, or event-detection artefact. In the following section, we derive the free-fall limit and define two PBVFF formulations: (1) normalisation to trial CMD, and (2) normalisation to displacement at the PBV event (PBV_d). We then provide guidance on computation and reporting, and present worked examples contrasting PBVFF with raw PBV. Finally, we evaluate the framework using two complementary approaches—illustrative hypothetical examples and a retrospective dataset of CMJ trials from an applied athletic cohort—to examine reliability, relationships with CMJ performance, and whether PBVFF changes athlete rankings relative to raw PBV.

Aims. This paper introduces a physically constrained, displacement‑contextualised interpretation of peak braking velocity (PBV) using a free‑fall normalisation (PBVFF).

Applied evaluation. Using routine CMJ monitoring data, we examined (1) within‑session reliability of PBVFF variants relative to PBV, (2) associations with jump height and modified reactive strength index (mRSI), and (3) whether it influences athlete ranking.

Hypotheses. We hypothesised that PBVFF normalisation would provide a clearer, objective way of quantifying countermovement performance and would alter rank ordering relative to PBV.

Methods

Free‑Fall Normalised Peak Braking Velocity (PBVFF)

The authors propose PBVFF as a dimensionless index that expresses PBV relative to the maximum downward velocity theoretically attainable under gravity over the same displacement. During the countermovement, the athlete remains in contact with the force plate. Acceleration of the COM is therefore:

which implies a(t) ≤ g as long as Fz(t) ≥ 0. Consequently, for a given downward displacement (s) starting from rest, the maximum achievable downward velocity under this constraint occurs when a(t) = g throughout the displacement (i.e., when Fz approaches zero and the athlete experiences an effective free-fall-like condition while maintaining contact). Under constant acceleration g, the kinematic relationship is:

1

PBVFF is then defined as the ratio between the observed magnitude of PBV and this displacement-specific free-fall limit:

2

Importantly, s can be operationalised in two complementary ways, each with a different mechanistic emphasis and different practical requirements.

Strategy-normalised PBVFF using CMD (PBVFFCMD)

If s is set equal to the athlete's self-selected CMD, the free-fall limit becomes VFF_max_CMD, and PBVFF is:

2a

This version is attractive for applied settings because PBV and CMD are frequently exportable summary metrics in many commercial force plate ecosystems, enabling implementation without access to full, raw time-series data. Conceptually, PBVFF_CMD contextualises PBV within the athlete's overall depth strategy (displacement at which unweighting and braking occur).

Event-specific PBVFF using displacement at PBV (PBVFF_{PBV_d})

PBV, however, is an event that occurs before the bottom of the countermovement, whereas CMD is the maximum negative countermovement displacement (where velocity has returned toward zero), and represents the transition from downward to upward movement. Therefore, normalising PBV to the full CMD necessarily includes displacement over which the subsequent braking phase occurs (from PBV to the bottom). To avoid embedding this additional post-PBV displacement in the denominator, d can instead be defined as the COM displacement at the instant PBV is recorded, denoted PBV_{_d}.

where s(t) is COM displacement, t0 is movement onset, and t_PBV is the time of peak negative COM velocity. PBVFF is then:

2b

By construction, PBVFF_{PBV_d} normalises PBV to the displacement over which PBV is actually developed (i.e., the pre-PBV descent), without incorporating the additional displacement associated with braking to zero velocity at the bottom. This event-specific formulation is therefore more closely aligned with the mechanics that generate PBV (primarily the unweighting net impulse), while remaining grounded in the same free-fall upper-bound rationale.

For both formulations, PBVFF is dimensionless and, under the assumptions above, should typically fall between 0 and 1.

PBVFF answers a different question than PBV. PBV asks: "What was the peak downward COM velocity during the descent?" In contrast, PBVFF asks: "What fraction of the displacement-specific free-fall limit did the athlete express?" In practice, PBVFF_CMD is best interpreted as a strategy-contextualised index that is easy to deploy from common exports, whereas PBVFF_{PBV_d} is a more event-specific index that excludes the braking phase displacement from the normalisation term, albeit at the cost of requiring PBV_d information (typically from raw time-series analysis or expanded export options).

PBV event location within the countermovement (PBV_loc)

Because PBV occurs before the bottom of the countermovement, it is also informative to quantify where within the negative displacement the PBV event is expressed. We therefore define the relative PBV location as:

3

PBV_loc is also dimensionless and typically ranges between 0 and 1. Unlike PBVFF, PBV_loc does not describe the magnitude of downward velocity; instead, it describes the timing on the displacement axis (i.e., the fraction of the total CMD completed at the instant PBV occurs). As a result, PBV_loc provides complementary information to both PBVFF formulations.

Mechanistically, PBV_loc partitions the negative phase into (1) the pre-PBV descent (distance PBV_d), over which downward velocity is developed, and (2) the post-PBV braking distance (approximately CMD − PBV_d), over which velocity is reduced back toward zero at the bottom. Expressed in relative terms, the available braking displacement after PBV is:

This matters in practice because two jumps can show similar PBV or PBVFF values yet differ substantially in the remaining displacement available to decelerate the COM after PBV. For example, a high PBVFF coupled with a high PBV_loc indicates that a large fraction of the displacement-specific free-fall velocity potential was expressed and that relatively little distance remained to brake to zero velocity at the bottom, which may imply greater relative braking demands. Conversely, a low PBV_loc indicates that PBV occurs early, leaving more displacement to dissipate momentum. Thus, PBV_loc is not a substitute for PBVFF_{PBV_d} ​; instead, it contextualises PBVFF by describing how the available negative displacement is allocated between velocity development and subsequent braking. Figure 1 illustrates the free-fall reference together with the key CMJ events (PBV, PBV_d, CMD) on the force–time, velocity–time, and displacement–time traces.

Fig. 1.

Conceptual illustration of PBVFF using a kinematic model and CMJ force–time, velocity–time, and displacement–time traces. Legend: A Movement onset (algorithm-detected), marking the start of the unweighting phase and the entire jump. B Attainment of PBV, defining the end of the unweighting phase and the onset of the braking phase. C Attainment of CMD, marking the end of the braking phase and the onset of the propulsive phase. D VFF_max_{PBV_d}. E VFF_max_CMD. F PBV. G CMD. H Peak positive displacement (maximum upward displacement; jump height). I Quiet phase (pre-jump weighing). J Unweighting phase. K Braking phase. Colour coding: blue labels indicate markers describing lines spanning the three time-normalised traces; red labels indicate markers describing instantaneous events; green labels indicate markers describing the vertical-jump sub-phases

Worked examples

To describe how PBVFF_CMD changes interpretation relative to raw PBV, Table 1 presents illustrative scenarios for two hypothetical athletes with different anthropometry: a shorter female athlete (1.60 m) and a taller male athlete (1.95 m). For each athlete, the authors model a baseline self‑selected CMJ, a high‑fatigue condition characterised by increased CMD and reduced PBV magnitude, and two coached conditions that manipulate CMD while holding PBV constant. For each scenario, VFF_max_CMD is computed from Eq. 1 and PBVFF_CMD from Eq. 2.

Table 1.

Exemplary CMD, PBV, VFF_max_CMD, and PBVFF_CMD across CMJ strategies

Athlete	Condition	CMD [m]	PBV [m/s]	VFF_maxCMD [m/s]	PBVFFCMD
Short female (1.60 m)	Baseline (self-selected)	0.30	− 1.20	2.43	0.49
Short female (1.60 m)	High fatigue (deeper CM, slower descent)	0.38	− 1.10	2.73	0.40
Short female (1.60 m)	Coached shallow-fast	0.24	− 1.30	2.17	0.60
Short female (1.60 m)	Coached deep	0.42	− 1.30	2.87	0.45
Tall male (1.95 m)	Baseline (self-selected)	0.40	− 1.20	2.80	0.43
Tall male (1.95 m)	High fatigue (deeper CM, slower descent)	0.48	− 1.10	3.07	0.36
Tall male (1.95 m)	Coached shallow-fast	0.32	− 1.30	2.51	0.52
Tall male (1.95 m)	Coached deep	0.55	− 1.30	3.28	0.40

These examples highlight three applied points. First, identical PBV values do not imply equivalent descent intensity when CMD differs. PBV = − 1.20 m/s yields PBVFF_CMD = 0.49 at CMD = 0.30 m, but PBVFF_CMD = 0.43 at CMD = 0.40 m. Therefore, a universal PBV threshold used to infer good intent could systematically penalise athletes who naturally adopt deeper countermovements (often taller athletes) and over‑credit athletes who adopt shallow CMD. Second, fatigue‑related increases in CMD can mask decrements in PBV: both athletes show a modest PBV reduction (− 1.20 to − 1.10 m/s), yet PBVFF_CMD decreases more clearly because the denominator increases with depth. Third, coached manipulations demonstrate that PBV alone cannot distinguish shallow‑fast from deep descent strategies when PBV magnitude is held constant; PBVFF_CMD changes because the available depth changes.

PBVFF enables displacement-specific, practically attainable PBV targets via reverse engineering (e.g., using an athlete’s recent 5-test CMD baseline) rather than relying on a single absolute velocity cutoff. By rearranging the PBVFF relationship, practitioners can translate a chosen benchmark into a CMD-adjusted negative velocity goal that respects the athlete’s movement strategy. This approach helps set realistic PBV targets that align with normative PBVFF ranges while remaining achievable within the athlete’s typical depth profile.

These worked examples (Table 2) highlight three applied points when PBV is normalised to the PBV_d​, rather than to the full CMD. First, identical PBV values do not imply equivalent descent intensity when PBV_d​ differs. For example, PBV = − 1.20 m/s yields PBVFF_{PBV_d}​​ = 0.64 when PBV_d​ = 0.18 m (with an event‑specific free‑fall upper bound VFF_max_{PBV_d} = 1.88), but only PBVFF_{PBV_d}​​ = 0.58 when PBV_d​ = 0.22 m (VFF_max_{PBV_d} = 2.08). Therefore, a universal absolute PBV threshold used to infer good intent could systematically penalise athletes who reach PBV later/deeper (larger PBV_d​, higher VFF_max​) and over‑credit athletes who reach PBV earlier/shallower (smaller PBV_d​, lower VFF_max​), despite identical measured PBV.

Table 2.

Exemplary CMD, PBV_d, PBV_loc_, PBV, VFF_max_{PBV_d}, and PBVFF_{PBV_d} across CMJ strategies

Athlete	Condition	CMD [m]	PBV_d[m]	PBV_loc	PBV [m/s]	VFF_maxPBV_d [m/s]	PBVFFPBV_d
Short female (1.60 m)	Baseline (self‑selected)	0.30	0.18	06.0%	− 1.20	1.88	0.64
Short female (1.60 m)	High fatigue (deeper CM via prolonged braking; PBV_d unchanged)	0.38	0.18	47.4%	− 1.10	1.88	0.59
Short female (1.60 m)	Coached shallow‑fast (earlier PBV depth)	0.24	0.15	62.5%	− 1.30	1.72	0.76
Short female (1.60 m)	Coached deep entry (later PBV depth)	0.42	0.22	52.4%	− 1.30	2.08	0.63
Tall male (1.95 m)	Baseline (self‑selected)	0.40	0.22	55.0%	− 1.20	2.08	0.58
Tall male (1.95 m)	High fatigue (deeper CM via prolonged braking; PBV_d unchanged)	0.48	0.22	45.8%	− 1.10	2.08	0.53
Tall male (1.95 m)	Coached shallow‑fast (earlier PBV depth)	0.32	0.18	56.3%	− 1.30	1.88	0.69
Tall male (1.95 m)	Coached deep entry (later PBV depth)	0.55	0.27	49.1%	− 1.30	2.3	0.56

Second, the table illustrates how fatigue‑related increases in CMD can be disentangled from pre‑PBV descent behaviour using PBVFF_{PBV_d} In the fatigue scenarios, CMD increases (e.g., 0.30 → 0.38 m and 0.40 → 0.48 m) while PBV_d​ is held constant (0.18 m and 0.22 m), representing a deeper overall countermovement driven primarily by the subsequent braking portion rather than by a longer acceleration‑into‑PBV distance. Under these assumptions, the denominator of PBVFF_{PBV_d}​​ (i.e., VFF_max_{PBV_d}) remains unchanged, so the observed decrease in PBVFF_{PBV_d}​​ tracks the reduction in PBV itself (e.g., − 1.20 → − 1.10 m/s). Importantly, the PBV_loc column provides additional context: as CMD increases while PBV_d​ remains stable, PBV occurs at a smaller fraction of total depth (e.g., 0.60 → 0.47 and 0.55 → 0.45), suggesting a larger proportion of the countermovement is allocated to the post‑PBV braking phase.

Third, coached manipulations demonstrate that PBV alone cannot distinguish early‑versus‑late PBV timing (i.e., differences in where PBV occurs within the descent) when PBV magnitude is similar. When PBV is held constant at − 1.30 m/s, PBVFF_{PBV_d}​​ changes substantially as PBV_d​ changes: for example, a shallow‑fast entry with PBV_d​ = 0.15 m yields PBVFF_{PBV_d}​​ = 0.76 (VFF_max = 1.72), whereas a deeper entry with PBV_d​ = 0.22 m yields PBVFF_{PBV_d}​​ = 0.63 (VFF_max = 2.08). The PBV_loc further clarifies strategy, indicating whether PBV occurs relatively early or late within the athlete’s chosen depth. Likewise, the ratio of unweighting-phase duration to braking-phase duration may offer a similar lens on strategy by quantifying how long the athlete accelerates downward relative to the time spent decelerating.

Accordingly, the present study moves beyond simulation by evaluating the framework in real-world CMJ testing performed in 70 academy footballers.

Participants

Seventy injury-free male academy football players (n = 70; age 18.7 ± 1.6 years; height 178.3 ± 7.4 cm; body mass 67.8 ± 8.8 kg) from a national-level (central) football academy, representing U-16 to U-21 squads (U-16 n = 17, U-17 n = 27, U-19 n = 12, and U-21 n = 14), were included and were integrated into the academy’s routine monitoring programme; during the testing period, all participants reported no pain-related symptoms. The study was conducted in accordance with the principles of the Declaration of Helsinki. The analysis was based on retrospective data from routinely performed diagnostic and training assessments, and ethical clearance was obtained from the Research Ethics Committee at the Jan Długosz University in Częstochowa (Resolution No. KE-U/9/2026, 19 January 2026). Written informed consent to participate and for the use of anonymised assessment data for scientific purposes was obtained from all participants prior to inclusion in the study. For participants under 18 years of age, written informed consent was obtained from a parent or legal guardian, and assent was obtained from the participant. Participants were informed that their results could be used for scientific analyses and that they had the right to refuse or withdraw consent for data use at any stage, without any sporting or organisational consequences. All data were processed to ensure confidentiality and protect participant identity.

Study design, data extraction, and eligibility filtering

This investigation used a retrospective observational design based on routinely collected CMJ monitoring data from the 2024/2025 season. Following completion of the monitoring window, the full longitudinal CMJ dataset was exported from the Hawkin Dynamics Cloud in and csv format for offline processing.

To improve comparability and reduce the influence of sporadic or incomplete monitoring, the exported dataset was filtered using predefined criteria prior to statistical analysis. Only athletes who completed ≥ 3 complete testing days were retained, with a complete testing day defined as a session containing three valid CMJ trials (i.e., one set of three jumps performed within a single monitoring occasion). Athletes who did not meet this minimum exposure threshold were excluded from further analysis.

For each eligible athlete, one representative observation day was selected to standardise the dataset to a single measurement per athlete and avoid pseudoreplication in inferential analyses. The daily mean mRSI was calculated for each available testing day, and the day yielding the highest value was retained as that athlete's index observation. Where ties in the daily mean mRSI occurred, the chronologically earliest qualifying day was used. This selection strategy was intended to identify each athlete’s highest available post-familiarisation performance, thereby retaining trials that more likely reflected maximal, reliable execution rather than early familiarisation-related variability. The resulting post-selection dataset — comprising one observation day (three trials) per athlete — was collated in Microsoft Excel (Microsoft Corp., Redmond, Washington, USA) and checked for completeness and internal consistency prior to export. This post-selection file constitutes the deposited dataset and the basis for all subsequent statistical analyses, which were conducted in Python 3.12 (see Statistical analysis section).

Testing procedures

CMJ vertical ground reaction forces were recorded at 1000 Hz using a wireless, dual force plate system (Hawkin Dynamics, Westbrook, Maine, USA). Signals were transmitted during testing to the Hawkin Dynamics Cloud through the Hawkin Capture Android application (Hawkin Dynamics, Westbrook, Maine, USA). During the data-collection period, software and mobile operating system updates were performed as part of routine maintenance and version releases. The device has demonstrated strong validity and reliability for CMJ assessment when compared with laboratory-grade force platforms [3, 13].

Testing was conducted at a consistent time during the training day: it was performed first, immediately after a standardised preparatory pre-session routine applied identically across squads. Athletes began in an upright stance, with feet approximately shoulder-width apart and hands on their hips to eliminate arm swing. Following the manufacturer-recommended default procedure, players stood still for the software-defined quiet-standing baseline period until the tablet interface provided the default audio-visual readiness prompt indicating that the system was ready to record the trial. They then performed a countermovement jump with a self-selected CMD and maximal vertical effort. Each testing occasion consisted of three maximal CMJ efforts. Between attempts, athletes were given a short inter-trial recovery period (~ 5–10 s) to reposition and prepare while maintaining the same session flow. This approach was intended to reflect routine applied monitoring conditions in sport settings, where testing time is often limited and practitioners aim to collect multiple performance indicators within a constrained session. However, the use of short inter-trial recovery periods should be acknowledged as a potential limitation, as incomplete recovery or insufficient preparation time may have influenced trial quality and within-session variability. Verbal instructions prioritised maximal intent (i.e., “jump as high and fast as possible”). Immediately after each attempt, athletes received performance feedback in the form of jump height. Force plates were re-zeroed at regular intervals throughout testing to support measurement stability.

Derivation of PBVFF from raw signal exports

The PBVFF_{PBV_d} index was recalculated offline using raw data exports. For each athlete’s selected observation, two raw. csv files were used: displacement–time and velocity–time. These files were combined using their shared time base (time column alignment), generating a single time-synchronised dataset.

The event PBV_d was operationally defined as the point corresponding to the most negative value of the velocity signal prior to propulsive phase. Once PBV_d was located on the time axis, the corresponding velocity and associated displacement at PBV_d was extracted and used to compute PBVFF_{PBV_d} for each athlete. The recalculated PBVFF_{PBV_d} values were then appended to the Excel dataset, along with other CMJ-derived variables, for later statistical analysis.

PBVFF_CMD was derived from the software’s standard. csv export—using the routinely reported PBV and CMD variables—and no separate post-processing of raw signals was performed.

Statistical analysis

All analyses were conducted at two levels to match the monitoring workflow and to avoid pseudoreplication. (1) Within‑session (trial level) analyses used the three CMJ trials performed within the selected session for each athlete to quantify absolute and rank‑order reliability. (2) Between‑athlete (daily‑mean level) analyses used athlete‑level daily means (mean of the three trials) from the selected observation day (highest daily mean mRSI), yielding one observation per athlete (n = 70) for inferential associations and ranking comparisons. Peak braking velocity was analysed as the magnitude of the most negative COM velocity (|PBV|).

Descriptive statistics are presented as mean ± SD and range. Analyses were performed on complete cases (no missing data for the analysed variables) without imputation.

No PBVFF values greater than 1 were observed in the analysed dataset.

Reliability

Within-session absolute reliability was quantified using the coefficient of variation (CV%). For each metric, an individual CV% was calculated for each athlete across the three trials as CV%ᵢ = (SDᵢ/Meanᵢ) × 100, where SDᵢ and Meanᵢ are the within-athlete standard deviation and mean across the three trials. From these 70 individual CV% values, we computed the mean CV% (± SD), median and interquartile range across athletes, together with non-parametric 95% confidence intervals for the mean (bootstrap percentile method, 10 000 resamples; seed 42). To summarise group-level absolute stability, a pooled CV% was additionally computed as Pooled CV% = (SDw/GrandMean) × 100, where SDw is the pooled within-athlete standard deviation obtained by pooling individual within-athlete variances (SDw = √(ΣSDᵢ²/n)), and GrandMean is the mean across all athletes/trials for that metric. Acceptability criteria. Within-session absolute reliability (CV%) was pre-specified as acceptable when ≤ 10% and as good when < 5%, consistent with commonly adopted thresholds in team-sport neuromuscular monitoring [9], with classifications based on point estimates rather than the 95% confidence intervals. Rank-order reliability was interpreted using the framework of [21]: ICC < 0.50 poor, 0.50–0.75 moderate, 0.75–0.90 good, and > 0.90 excellent. Analyses were performed in Python 3.12 using pingouin 0.6.1 (ICC, partial correlations), scipy 1.11 (Pearson and Spearman correlations, bootstrap resampling), statsmodels 0.14 (Benjamini–Hochberg FDR correction), pandas 2.1/numpy 1.26 (data handling), and matplotlib 3.8/seaborn 0.13 (visualisation). Full analytical code and data exports are available in the public repository10.5281/zenodo.18910863.

Associations with performance outcomes

Associations between PBV‑derived metrics (PBV, CMD, PBVFF_CMD, PBVFF_{PBV_d}, PBV_d, PBV_loc) and performance outcomes (mRSI and jump height) were evaluated using Pearson product‑moment correlations on athlete‑level daily means (n = 70). Two‑tailed p‑values were computed, and 95% confidence intervals for correlation coefficients were derived using Fisher’s r‑to‑z transformation. To control multiplicity across the targeted association tests (6 metrics × 2 outcomes = 12 correlations), p‑values were adjusted using the Benjamini–Hochberg [5] false discovery rate procedure; FDR‑adjusted q‑values are reported alongside correlations. Because mRSI is a ratio-derived variable that directly includes jump height in its numerator (mRSI = jump height/time to take-off), univariate associations between PBV-derived metrics and mRSI are susceptible to shared variance and mathematical coupling through the height component [2, 7, 24]. To isolate the portion of mRSI variance not attributable to jump height, partial Pearson correlations r (mRSI, X | jump height) were computed for each of the six PBV-derived predictors using pingouin.partial_corr, and the resulting six p-values were adjusted with the Benjamini–Hochberg procedure [5]. In addition, full exploratory correlation matrices (Pearson r and Spearman ρ) across the exported CMJ metrics were computed on athlete‑level daily means; the corresponding p‑values and FDR‑adjusted q‑values are provided in the public repository.

Ranking concordance and reclassification

To examine practical consequences of metric choice, athletes were ranked using daily‑mean scores for PBV, PBVFF_CMD, and PBVFF_{PBV_d.} Pairwise agreement between scoreboards was quantified using Spearman rank correlation (ρ), and overall agreement across the three rankings was assessed with Kendall’s coefficient of concordance (W). Reclassification magnitude was quantified for each athlete as the absolute rank shift between two metrics: |rank(B) − rank(A)|, summarised by mean, median, maximum shift, and the proportion of athletes shifting by ≥ 10 positions. Depth‑driven reclassification was further explored by relating signed rank change (rank_PBVFF_CMD − rank_PBV) to CMD.

Results

Following data cleaning, the final dataset comprised 70 male academy football players, each completing three CMJ trials (210 trials total). Inferential analyses were performed on athlete-level daily means (mean of three trials) from the selected observation day. On these daily means, mRSI was 0.602 ± 0.116 (range 0.385–0.907) and jump height was 0.379 ± 0.055 m (0.274–0.526). Peak braking velocity is reported as the magnitude of the most negative COM velocity (PBV): PBV = 1.380 ± 0.161 m/s (0.993–1.745). The free-fall normalised indices were PBVFF_CMD = 0.588 ± 0.054 (0.470–0.735) and PBVFF_{PBV_d} = 0.775 ± 0.070 (0.625–0.913). Displacement at the PBV event was PBV_d = 0.164 ± 0.030 m (0.109–0.248), and relative PBV location within the countermovement was PBV_loc = 0.578 ± 0.036 (0.483–0.701). A full correlation matrix and heatmap for all metrics are provided in the public repository.

Within the full correlation matrix (athlete-level daily means; Pearson’s r), the strongest associations involving the new indices (defined here as |r|≥ 0.60) clustered around braking-phase force and power variables, with clear evidence of construct overlap between some indices. PBVFF_CMD was highly collinear with PBVFF_{PBV_d} (r = 0.936) and showed strong positive correlations with braking power/force metrics, including peak relative braking power (r = 0.894), average relative braking power (r = 0.862), average relative braking force (r = 0.857), peak braking power (r = 0.799), average braking power (r = 0.737), PBV (r = 0.681), and average braking velocity (r = 0.631). PBVFF_{PBV_d} followed a similar but attenuated pattern, correlating strongly with peak relative braking power (r = 0.752), average relative braking power (r = 0.703), peak braking power (r = 0.674), PBV (r = 0.638), and average braking power (r = 0.605), reinforcing that both PBVFF-based indices primarily reflect braking-phase power/force characteristics. In contrast, PBV_d aligned more with movement strategy and impulse–time structure, particularly CMD (r = 0.948), relative propulsive impulse (r = 0.867), time to takeoff (r = 0.730), and relative braking impulse (r = 0.704), while PBV_loc exhibited fewer strong correlations overall, with |r|≥ 0.60 observed mainly for peak relative braking force (r = 0.665), relative force at minimal displacement (r = 0.655), braking rate of force development (RFD) (r = 0.621), and an inverse association with braking phase duration (r = − 0.621).

The depth dependence of PBV and the rationale for CMD normalisation are illustrated in Fig. 2. Across athletes, the same PBV value could correspond to meaningfully different PBVFF_CMD values depending on CMD, highlighting that raw PBV alone does not uniquely characterise relative descent intensity when CMD varies.

Fig. 2.

PBV vs CMD with iso-lines of PBVFF_CMD. Legend: Scatterplot showing the relationship between CMD and PBV across athletes (daily means; n = 70). Solid curves denote iso-lines of constant PBVFF_CMD (0.4–0.7), calculated as PBV/√(2·g·CMD) (g = 9.81 m/s.²). The iso-lines show that identical PBV magnitudes can represent different relative descent intensities depending on self-selected CMD. Each point represents one athlete (mean of three trials from the selected observation day)

Within-session reliability outcomes are summarised in Fig. 3. All metrics demonstrated pooled CV% values below 10% (PBV 6.75%; CMD 6.21%; PBVFF_CMD 5.81%; PBVFF_{PBV_d} 6.84%; PBV_d 7.77%; PBV_loc 5.59%). Individual mean CV% values (± SD) [bootstrap 95% CI for the mean; percentile method, 10 000 resamples] were: PBV 5.90 ± 3.93% [5.03, 6.86]; CMD 5.59 ± 2.96% [4.91, 6.29]; PBVFF_CMD 4.95 ± 3.33% [4.21, 5.74]; PBVFF_{PBV_d} 5.44 ± 4.50% [4.45, 6.53]; PBV_d 6.91 ± 3.86% [6.05, 7.83]; PBV_loc 4.53 ± 3.60% [3.74, 5.39]. In rank-order terms, PBV and PBVFF_CMD showed similarly high single-trial ICC values and both improved substantially when averaging three trials, supporting their use for athlete profiling from routine three-jump sets. PBVFF_{PBV_d} displayed lower rank-order reliability than PBV and PBVFF_CMD, consistent with its greater dependence on event/displacement identification. Notably, PBV_loc combined relatively low CV% with low single-trial ICC, indicating limited discriminative reliability despite apparent absolute stability.

Fig. 3.

Within-session reliability of PBV_-derived metrics: CV% thresholds and ICC. Legend: Boxplots show within-session coefficient of variation (CV%, three trials) across athletes (n = 70) for PBV, CMD, PBVFF_CMD, PBVFF_{PBV_d,} PBV_d, and PBV_loc. Horizontal dashed reference lines indicate commonly used practical thresholds for acceptable variability (5% and 10% CV). Values displayed above each box represent rank-order reliability as ICC(1,1)/ICC(1,k) (one-way random-effects, absolute), where ICC(1,1) reflects single-trial reliability and ICC(1,k) reflects reliability of the daily mean of three trials. Boxes indicate median and interquartile range; whiskers extend to 1.5 × IQR; points indicate outliers

Associations with performance outcomes are shown in Fig. 4. PBV behaved primarily as a jump height correlate (PBV vs jump height r = 0.460), while evidence for association with mRSI was weaker and not robust after FDR correction (PBV vs mRSI r = 0.231; qFDR = 0.065). In contrast, PBVFF_CMD exhibited the strongest alignment with mRSI (r = 0.573; qFDR = 3.0 × 10⁻⁶) while maintaining a smaller but significant association with jump height (r = 0.346; qFDR = 0.00576). PBVFF_{PBV_d} and PBV_loc were also moderately associated with mRSI (r = 0.430 and r = 0.410, respectively), whereas PBV_d was unrelated to mRSI (r = − 0.147) but showed a moderate association with jump height (r = 0.356). Overall, these patterns indicate a functional divergence: PBV was more jump-height centric, whereas PBVFF_CMD (and to a lesser extent PBVFF_{PBV_d} and PBV_loc) was more strongly aligned with mRSI. Because mRSI contains jump height in its numerator by construction [24], univariate PBV-derived ↔ mRSI associations were re-evaluated using partial Pearson correlations controlling for jump height, r(mRSI, X | jump height) (Table 3). Once jump height was statistically controlled, the PBV–mRSI association reversed sign (partial r = − 0.266, qFDR = 0.032), indicating that the weak positive univariate link was driven by shared variance with jump height rather than by a direct mechanistic relationship. By contrast, the PBVFF_CMD–mRSI association remained strongly positive (partial r = + 0.531, qFDR < 0.001), and PBVFF_{PBV_d}–mRSI was similarly preserved (partial r = + 0.438, qFDR < 0.001). CMD and PBV_d showed strongly negative partial correlations with mRSI once jump height was held constant (partial r = − 0.857 and − 0.786, respectively), consistent with the role of depth and time in determining mRSI's denominator. PBV_loc, which was moderately associated with mRSI univariately, lost statistical significance after adjustment (partial r = + 0.218, qFDR = 0.072). Collectively, these results indicate that PBVFF_CMD carries mRSI-relevant variance beyond that attributable to jump height, supporting its construct validity as an index of descent strategy rather than a proxy for vertical jumping performance.

Fig. 4.

Associations of PBV_-derived metrics with mRSI and jump height. Legend: Forest plots of Pearson correlations (r) between PBV_-derived metrics and (A) mRSI and (B) jump height, using athlete-level daily means (n = 70). Points indicate Pearson’s r and horizontal bars denote 95% confidence intervals; the vertical dashed line indicates r = 0. q-values shown adjacent to points are Benjamini–Hochberg FDR-adjusted across the targeted tests. Metrics are labelled according to manuscript nomenclature: PBV, CMD, PBVFF_CMD, PBVFF_{PBV_d}, PBV_d, and PBV_loc

Table 3.

Univariate and partial Pearson correlations with mRSI (n = 70). Partial correlations control for jump height, r (mRSI, X | jump height). Univariate qFDR adjusted across 12 targeted tests; partial qFDR adjusted across the 6 partial tests (Benjamini–Hochberg, 1995

Predictor	Univariate r	95% CI	Univariate qFDR	Partial r | JH	95% CI	Partial qFDR
PBV	+ 0.231	[− 0.004, 0.442]	0.065	− 0.266	[− 0.470, − 0.030]	0.032
CMD	− 0.287	[− 0.489, − 0.056]	0.024	− 0.857	[− 0.910, − 0.780]	< 0.001
PBVFFCMD	+ 0.573	[0.391, 0.712]	< 0.001	+ 0.531	[0.340, 0.680]	< 0.001
PBVFFPBV_d	+ 0.430	[0.217, 0.604]	< 0.001	+ 0.438	[0.220, 0.610]	< 0.001
PBV_d	− 0.147	[− 0.369, 0.091]	0.224	− 0.786	[− 0.860, − 0.670]	< 0.001
PBV_loc	+ 0.410	[0.193, 0.588]	0.001	+ 0.218	[− 0.020, 0.430]	0.072

Legends: Bolded rows highlight the primary comparison: whereas PBV's mRSI association reverses after partialling out jump height, PBVFFCMD retains a large positive association

Practical consequences of metric choice were evident in the athlete scoreboards (Figs. 5–6). Although overall agreement across PBV, PBVFF_CMD, and PBVFF_{PBV_d} rankings was high (Kendall’s W = 0.830), PBV-based ordering differed from PBVFF-based ordering.

Fig. 5.

Reclassification magnitude when switching metrics. Legend: Boxplots show the distribution of absolute rank shift (positions) across athletes (n = 70) when switching between scoreboards: PBV vs PBVFF_CMD, PBV vs PBVFF_{PBV_d} and PBVFF_CMD vs PBVFF_{PBV_d} Absolute rank shift was calculated as |rank(metric 2) − rank(metric 1)| for each athlete. Larger values indicate greater practical reclassification between metrics. Boxes indicate median and interquartile range; whiskers extend to 1.5 × IQR; points indicate outliers

Fig. 6.

Depth-driven reclassification: PBV vs PBVFF_CMD. Legend: Scatterplot showing the relationship between CMD and signed rank change when switching from PBV to PBVFF_CMD, computed as (PBVFF_CMD rank − PBV rank) across athletes (daily means; n = 70). Negative values (blue points) indicate an improved rank under PBVFF_CMD relative to PBV, whereas positive values (orange points) indicate a worse rank under PBVFF_CMD. The horizontal dashed line denotes zero rank change

Consistent with this, Spearman rank associations were ρ = 0.703 for PBV vs PBVFF_CMD (p = 1.17 × 10⁻¹¹) and ρ = 0.598 for PBV vs PBVFF_{PBV_d} (p = 4.73 × 10⁻⁸), whereas PBVFF_CMD and PBVFF_{PBV_d} were tightly aligned (ρ = 0.934, p = 5.00 × 10⁻³²). These results suggest that PBVFF-based scoreboards are not simply rescaled PBV rankings, but may provide an alternative interpretation of the same countermovement behaviour once descent velocity is normalised to depth.

Mean absolute rank shift was 11.83 positions for PBV vs PBVFF_CMD (median 9; max 45) and 14.03 positions for PBV vs PBVFF_{PBV_d} (median 12; max 44), with 46–54% of athletes moving by ≥ 10 ranking positions (Fig. 5). In contrast, PBVFF_CMD and PBVFF_{PBV_d} rankings were closely aligned, with a smaller average reclassification (mean 5.00; median 3; max 27). Depth-driven reclassification is illustrated in Fig. 6: signed rank change (PBVFF_CMD rank − PBV rank) showed a clear CMD-related pattern, supporting the practical rationale for CMD-normalised PBV monitoring when comparing athletes and interpreting longitudinal strategy drift.

Taken together, the new indices — particularly PBVFF_CMD — demonstrated absolute reliability comparable to PBV (pooled CV 5.81% vs 6.75%) and three-trial rank-order reliability of similar magnitude (ICC(1,k) 0.865 vs 0.888, both good per [21]. Single-trial rank-order reliability was slightly lower for PBVFF_CMD than for PBV (ICC(1,1) 0.681 vs 0.726), but both values remained within the moderate range. Against this reliability profile, PBVFF_CMD showed substantially stronger transfer to mRSI (PBVFF_CMD–mRSI r = 0.573, qFDR = 3.0 × 10⁻⁶ vs PBV–mRSI r = 0.231, qFDR = 0.065), at the cost of being less tightly coupled to jump height than PBV.

This combination—adequate reliability, stronger mRSI alignment, and demonstrably different ranking behaviour—supports the practical usefulness of CMD-normalised PBV monitoring for athlete profiling when reactive strength strategy is the construct of interest.

Discussion

This study demonstrated that the PBVFF is characterised by similar repeatability to the traditional PBV, while being more strongly correlated with one of the output performance indices–mRSI. Furthermore, PBVFF increased the ranking of some athletes and lowered that of others relative to PBV alone, indicating that this novel variable captures information not conveyed by PBV in isolation.

Practical implications

PBVFF may provide practitioners with a simple way to interpret PBV relative to CMD and g. Through this normalisation process, athletes can be compared on a common 0–1 scale, or expressed more intuitively as percentage points after conversion to a 0–100% scale. This may make countermovement strategy easier to communicate, track, and compare across athletes, sessions, and groups. In applied settings, PBVFF may support the development of scoreboards and internal normative databases, helping practitioners and athletes better understand countermovement strategy. Such outputs may also improve athlete engagement by making technical execution more visible, interpretable, and competitive within training environments. PBVFF may also support real-time cueing during testing, allowing practitioners to provide immediate feedback when an athlete’s countermovement strategy does not reach the intended intensity (i.e., when they use only a limited fraction of the velocity potential available within their self-selected displacement). This may lead to shorter and more specific coaching cues. PBVFF may also provide a more defensible foundation for developing benchmarks, thresholds, and, with appropriate validation, return-to-sport guidance. By expressing downward velocity relative to the available displacement and the constant of gravity, the proposed indices place PBV within a clearer mechanical context. The small reliability differences observed between raw PBV and PBVFF should not, at this stage, be considered sufficient to meaningfully alter applied practice, as both metrics demonstrated acceptable reliability in the present cohort. The observed relationships between PBVFF and established CMJ metrics further suggest that these indices may offer useful complementary information when interpreted alongside stable force–time and performance variables, and, with further validation, may support the development of reliable proxy indicators for selected outcome scores.

Minimal monitoring set and reporting logic

In contemporary high-performance settings, the rapid delivery of reliable information is paramount for optimising training and therapeutic processes. Consequently, because the two proposed indices appear to provide highly overlapping information, we recommend pre-selecting one formulation—either PBVFF_CMD or PBVFF_{PBV_d}—as the primary descriptor of negative phase strategy, thereby minimising redundancy in reporting and interpretation. However, robust decision-making mandates a multi-parametric approach; therefore, this kinematic descriptor must be complemented by stable mechanical variables effectively characterising braking, propulsive, or landing phases and should not function as a standalone decision-making factor.

Trial quality screening

In routine monitoring, athletes often produce technically valid trials that are not comparable to their typical pattern (e.g., overly cautious descent, altered rhythm, protective strategies, lack of familiarisation or inconsistent adherence to instructions). PBVFF can serve as a quick comparability check: when PBVFF is unusually low relative to an athlete’s baseline under stable instructions or to the normative dataset, subsequent braking and propulsive variables should be interpreted cautiously, and repeating the trial may be warranted. The proposed indices may help determine whether the athlete reached a sufficiently demanding braking context; only under such conditions can practitioners make a more robust interpretation of force and power expression during the braking phase. This is particularly relevant because verbal cues and coaching constraints can shift phase-specific behaviour without necessarily improving overall performance [25]. Importantly, out-of-range PBVFF values (> 1) should be treated as a data-quality flag rather than interpreted physiologically. Under the simplified point-mass framework used here, PBVFF > 1 indicates that the observed PBV magnitude exceeds the displacement-specific free-fall limit, which is not mechanically plausible for the whole-body COM in a standard hands-on-hips CMJ. Such values are therefore most likely to reflect processing or measurement issues, including movement-onset misidentification, weighing error, integration drift, event misdetection, or signal artefact. Segmental motion and active unweighting may influence the timing, posture, and organisation of movement during the countermovement, but they do not invalidate the external-force constraint on whole-body COM acceleration that underpins the free-fall reference.

Distinguishing strategy drift from performance change

In monitoring practice, changes in raw PBV may reflect either altered neuromuscular function or a change in how the athlete performed the countermovement. PBVFF helps interpret these changes by expressing descent velocity relative to the available countermovement depth. For example, if raw PBV magnitude decreases while PBVFF remains stable, the change may primarily reflect a shallower or otherwise altered countermovement strategy rather than a reduction in relative descent intensity. In contrast, if PBVFF decreases despite stable CMD, this may suggest that the athlete used a smaller fraction of their depth-specific velocity capacity. In this way, PBVFF can help contextualise whether changes in raw PBV are more likely to reflect strategy drift or changes in psychophysiological readiness or preparedness.

Clinical monitoring and rehabilitation context

Force plate monitoring is increasingly applied to track deficits and recovery following lower limb injury, particularly after anterior cruciate ligament reconstruction [22, 23, 26]. However, valid interpretation of mechanical output requires ensuring that the mechanical demands of the test reflect injury-relevant conditions. Given that non-contact injuries frequently occur during high-velocity eccentric or quasi-isometric braking actions [12, 19, 34], effective benchmarking necessitates that the patient demonstrates the confidence to generate high deceleration demands. In this context, PBVFF may serve as a requisite check for test validity. A downward fluctuation in PBVFF relative to the patient's baseline warrants extended clinical evaluation, as it often signals pain, discomfort, or kinesiophobia limiting the willingness to explore the negative range of motion or limit negative velocity itself. Consequently, any concurrent plateau or decline in braking and propulsive metrics should be interpreted with caution; these likely reflect a protective strategy rather than a long-term regression in physiological capacity. Therefore, PBVFF may act not only as a rehabilitation target itself, but as a contextual indicator—confirming that the patient has entered a sufficiently high-intensity zone to allow for a valid evaluation of their neuromuscular potential. When available, PBVFF values may also be interpreted against internal, population-specific normative data, such as reference ranges stratified by injury type, rehabilitation stage, sport, sex, or competitive level.

Taken together, PBVFF is most useful when embedded within an explicit monitoring framework: (i) standardise the protocol and data processing; (ii) establish individual baselines; (iii) develop normative benchmarks; and (iv) interpret PBVFF alongside reliable braking and propulsive descriptors.

Limitations and future research recommendations

The present findings are population- and protocol-specific, and the characteristics of the cohort and testing approach may have influenced the obtained results. Therefore, the present PBVFF values should not be treated as universal normative scores or assumed to transfer to female athletes, younger or older populations, or non-football cohorts without population-specific validation and reference data. More broadly, the selected methodology limits the generalisability of the overall concept, and future studies should evaluate this new index in larger and more diverse cohorts.

A further limitation concerns the single-observation selection rule. Retaining, for each athlete, the day with the highest daily mean mRSI selected an extreme rather than a typical daily value, and because that same day informed both the reliability scores and the mRSI associations, it may have biased the within-session CV% and the observed correlations. The reported results may therefore not generalise to unselected, routine testing days and could differ under alternative selection rules.

PBVFF should also not be interpreted as a direct marker of eccentric capacity. The index contextualises the magnitude of PBV relative to a depth-dependent theoretical bound, but it does not quantify how the athlete subsequently decelerates and reaccelerates the COM. Two athletes may display similar PBVFF values while presenting different braking mechanical characteristics and load-tolerance profiles. In addition, motivation, familiarisation, fear, pain-related guarding, and instruction effects may alter countermovement strategy independently of structural or neuromuscular capacity, and these behavioural, perceptual, and contextual factors cannot be distinguished from the athlete’s level of athletic preparedness using this index alone. Accordingly, PBVFF is best interpreted as a descriptor of the conditions under which the athlete enters the braking phase, rather than as an isolated measure of eccentric neuromuscular function.

PBVFF also inherits the vulnerabilities of integration-derived CMJ variables. Weight estimation, onset detection, filtering, integration constants, and event definitions can materially influence derived velocity and displacement signals [30]. In addition, variability in CMJ protocols and reporting conventions limits comparability across force plate systems and studies [4]. PBVFF should therefore be reported alongside transparent processing descriptions and routine quality-control procedures.

Interpretation of the PBVFF–mRSI associations also requires caution. mRSI is a ratio-derived metric, calculated as jump height divided by time to take-off, and ratio variables may propagate measurement error from both components or change because of the numerator, denominator, or both. Therefore, a univariate PBVFF–mRSI association should not be treated as strict construct validation. To reduce this concern, partial correlations controlling for jump height were additionally computed. Under this adjustment, the PBV–mRSI association reversed sign (partial r = − 0.266, qFDR = 0.032), whereas PBVFF_CMD–mRSI remained strongly positive (partial r = + 0.531, qFDR < 0.001). This approach is consistent with methodological recommendations concerning mathematical coupling and ratio-variable artefacts [2, 24], and supports the interpretation that PBVFF_CMD captures mRSI-relevant strategy information beyond shared jump-height variance. Nevertheless, PBVFF and mRSI are embedded within the same CMJ time–displacement trajectory, so part of their covariance may reflect shared task structure, particularly depth and timing strategy, rather than a unique mechanistic link to negative phase quality.

It is worth noting that the relative PBV_loc index, while providing complementary insight into the timing of descent, showed limited between-athlete reliability in our data (low ICC despite a low CV). Thus, PBV_loc may be better suited as a descriptive metric than for individual monitoring, and its practical utility warrants further investigation.

These limitations motivate a focused research agenda. Priority questions are not whether PBVFF is mathematically valid, but whether it improves reliability, interpretability, and decision quality in real monitoring workflows. Future work should therefore establish the reliability and sensitivity of PBVFF_CMD and PBVFF_{PBV_d} under standardised protocols. Construct validity should be tested by examining PBVFF responses to distinct fatigue mechanisms, familiarisation effects, assessor’s cueing, and deliberate strategy manipulations, while concurrently assessing well-established mechanical performance variables. Future studies should also evaluate the incremental value of PBVFF in multivariate monitoring, asking whether PBVFF_{PBV_d} and/or PBVFF_CMD improves inference beyond existing metrics representing the unweighting, braking, and propulsive phases when predicting or assessing fatigue states, levels of athletic preparedness, injury-related guarding, return-to-play milestones, or potential injury risk. A further research direction may be to examine PBVFF as a potential proxy index for other important neuromuscular abilities or sport-specific manoeuvres. This should be accompanied by an assessment of its applied feasibility, as PBVFF_{PBV_d} may be less straightforward to implement in routine practice due to the limited availability of the required variables in common commercial force-plate systems. Finally, reference and normative data should be developed across athlete and patient groups with explicit protocol control.

Conclusions

The results of this study support the utility of PBVFF. Its reliability was comparable to that of PBV, it exposed player-profile differences not evident in raw PBV-based classifications, and it related more strongly to the commonly used headline outcome−mRSI. Although PBV is an appealing descriptor of descent strategy, it is intrinsically context-dependent and, when interpreted in isolation, may lead to athlete misclassification, especially when CMD or timing varies across sessions. This interpretation is further complicated by the athlete’s anthropometric profile, which may influence the PBV values observed for a given countermovement strategy. PBVFF addresses this limitation by expressing PBV as a fraction of the maximum downward velocity theoretically attainable under gravitational acceleration over a specified negative COM displacement. It should not be interpreted as a standalone diagnostic marker of fatigue or capacity, but as a contextual indicator intended to reduce depth-driven misinterpretation, improve comparability, and stimulate further research on benchmarking and reference data. We propose two complementary operationalisations: PBVFF_CMD, which is typically derivable from standard exports and reflects overall depth strategy, and PBVFF_{PBV_d}, an event-specific normalisation that requires more detailed data and robust event detection.

Abbreviations

CMJ

Countermovement jump (bilateral)

CMD

Countermovement depth / peak negative displacement

COM

Centre-of-mass

PBV

Peak braking velocity (peak negative COM velocity)

PBV_d

Displacement at the instant of PBV (from movement onset)

PBV_loc

PBV location within CMD (PBV_{_d/}CMD)

VFF_max

Free‑fall maximum velocity magnitude for a given displacement

VFF_max_CMD

Free‑fall maximum velocity magnitude for a given displacement (strategy-normalised)

VFF_max_{PBV_d}

Free‑fall maximum velocity magnitude for a given displacement (event-specific)

PBVFF

Free‑fall normalised peak braking velocity

PBVFF_CMD

Free‑fall normalised peak braking velocity (strategy-normalised)

PBVFF_{PBV_d}

Free‑fall normalised peak braking velocity (event-specific)

mRSI

Modified reactive strength index

CV

Coefficient of variation

ICC

Intraclass correlation coefficient

RFD

Rate of force development

Authors’ contributions

Conceptualization: K.K.; Methodology: K.K.; Validation and statistical analysis: K.K., M.N.; Investigation: K.K., M.N.; Resources: K.K., M.N.; Data curation K.K.; Ethics: M.N.; Writing—original draft preparation: K.K., M.N.; Writing—review and editing: K.K., A.R., J.L., M.N.; Visualization: K.K., M.N., Supervision: A.R., J.L.; Project administration: K.K., M.N. All authors read and approved the final version of the manuscript.

Funding

This study received no specific funding. 10.5281/zenodo.18910863

Data availability

During peer review, access is provided through the private reviewer link included in the submission system; the repository will be made publicly available upon acceptance/publication. 10.5281/zenodo.18910863

Declarations

Ethics approval and consent to participate

The study was conducted in accordance with the principles of the Declaration of Helsinki. The analysis was based on retrospective data from routinely performed diagnostic and training assessments, and ethical clearance was obtained from the Research Ethics Committee at the Jan Długosz University in Częstochowa (Resolution No. KE-U/9/2026, 19 January 2026). Written informed consent to participate and for the use of anonymised assessment data for scientific purposes was obtained from all participants prior to inclusion in the study. For participants under 18 years of age, written informed consent was obtained from a parent or legal guardian, and assent was obtained from the participant. Participants were informed that their results could be used for scientific analyses and that they had the right to refuse or withdraw consent for data use at any stage, without any sporting or organisational consequences. All data were processed to ensure confidentiality and protect participant identity.

Consent for publication

Not applicable.

Competing interests

This study was conducted using the Hawkin Dynamics force plate system and associated software/cloud platform. J.L. has served as a scientific consultant for Hawkin Dynamics. This relationship had no influence on the study design, data collection, data processing/analysis, interpretation of the results, or manuscript preparation. All other authors declare no conflicts of interest.