Temporal Stability and Practical Relevance of Velocity and Velocity-Loss Perception in Back Squat

Abstract

The aim of this study was to investigate the accuracy and stability of both Perception of Velocity (PV) and Perception of Velocity Loss (PVL) over four weeks, without any feedback regarding velocity during training sessions. Fifteen subjects performed six training sessions: four sessions familiarized the athletes with PV and PVL and the final two sessions assessed the accuracy and stability of PV and PVL, with one conducted 48 h after the familiarization and the other after 4 weeks. To assess PV and PVL, two loads (60% 1RM and 80% 1RM) and two velocity losses (20% VL and 40% VL) were employed. PV accuracy was measured by the DeltaScore, the difference between perceived velocity (Vp) and the velocity provided by the encoder (Vr): DetlaScore = Vp − Vr. PVL was measured by the Vscore, the difference between repetitions where the subject perceived the target %VL (Np) and repetitions that actually met it (Nr): Vscore = Np − Nr. The analysis performed revealed no differences in DeltaScore nor in Vscore between the two test sessions performed 4 weeks apart (p > 0.05). On the other hand, the effect of load on both DeltaScore and Vscore was significant in both sessions (p < 0.05). PVL and PV accuracy are stable throughout time. PVL may be used to prescribe and monitor velocity-based training. Conversely, when prescribing training sessions based on PV, it is essential to pair PV with a perception scale and incorporate an encoder when possible.

1. Introduction

Proper resistance training (RT) prescription is fundamental for optimizing performance improvements and enhancing health outcomes [1,2,3]. RT programs are developed by manipulating several variables, with intensity and volume being two of the most crucial [2]. Historically, the most common method for prescribing RT has been percent-based training (PBT) [4]. PBT determines the intensity as a percentage of the one-repetition maximum (%1RM) and prescribes the training volume based on that intensity [5]. The main limitation of PBT is that it does not consider daily fluctuations in 1RM, which could lead to a less precise training prescription [5]. Velocity-based training (VBT) [5] instead, uses the velocity of the barbell during the concentric phase of the movement to modulate the intensity, and the percentage of velocity loss (VL) within the sets to prescribe training volume [5]. VBT shifts the focus from the absolute load lifted to the measurement of movement velocity [5]. This approach is based on the close inverse relationship between the lifted load and the average propulsive velocity, which makes it possible to create a general or individual load-velocity profile [6,7]. Through the load-velocity profile, which is exercise- [6] and sex-specific [7], 1RM can be accurately estimated [6,7,8,9]. Therefore, barbell velocity can be used to account for daily readiness and fatigue, which allows day-by-day adjustments to optimize the training session [10,11]. However, despite these advantages, the main issue in VBT is the cost of the devices used for monitoring velocity. Indeed, the most reliable devices, linear position transducers (LPTs) [12,13], are quite expensive, with prices ranging from ~400$ for the cheaper ones to ~2000$ for those considered as the gold standard [13]. For this reason, in recent years, many studies have investigated the accuracy of perceiving barbell velocity, with the goal of using the velocity perception (PV) for training whenever LPTs are unavailable [14,15,16,17,18,19,20,21,22].

PV is the ability to estimate the velocity of a single repetition during exercise [16,19]. Previous studies have demonstrated that, after a period of familiarization with the combined use of LPT and a PV scale, the subjects’ perceived velocity becomes substantially closer to the real barbell velocity, measured by devices [18,19]. The accuracy of PV is assessed using a Delta Score (Ds), calculated as the difference between perceived velocity (Vp) and real velocity (Vr) (Ds = Vp − Vr). Therefore, a Ds closer to 0 indicates a more accurate PV [18,19]. Previous studies reported that a Ds for medium (40–70% 1RM) intensities is more accurate than that for low (<40% 1RM) and high (>70% 1RM) intensities, where Vp tends to be overestimated and underestimated, respectively [14,15]. However, increasing the familiarization period has been shown to increase PV accuracy at all intensities [16,19]. Furthermore, a familiarization period consisting of four sessions over two weeks (i.e., two sessions per week) [17,18] appears sufficient to yield results comparable to those observed following a five-week familiarization period with the same weekly session frequency [16]. Lastly, it has been proven that PV is a stable parameter even under both physical and mental fatigue conditions [17,18].

Another aspect that has been investigated is the ability to perceive changes in barbell velocity [20,21,22,23,24], which has been examined in three different ways [20,21,22]. Firstly, perception of velocity loss (PVL) accuracy has been assessed by asking participants to verbally report, starting from the second repetition, the perceived change in barbell velocity, expressed as a percentage of the first repetition [20,22]. In these studies, the difference between the perceived and the actual change in velocity reflects PVL accuracy [20,22]. Meanwhile, Dello Iacono et al. asked participants to verbally report when they thought their velocity, compared to the first repetition, had dropped by 20% and 40% [21]. PVL accuracy was calculated as the difference between the number of repetitions at which the participant reported 20% and 40% PVL and the actual repetitions corresponding to those velocity losses [21]. Lastly, da Silva et al. asked participants to stop the sets when they thought their %VL was between 15% and 30% and thereafter calculated the percentage of sets stopped correctly [24]. As with PV, it has been proven that PVL accuracy also increases after familiarization, although the familiarization protocols used were shorter than those used for PV [22]. Finally, PVL accuracy seems to be related to the number of repetitions performed, where an increase in repetitions corresponds to an increase in the PVL error [20,21,22]. Despite these issues, some studies conclude that PVL can be implemented as a VBT monitoring tool whenever LPTs are limited or not available [21,24].

Although the research conducted so far is encouraging, no study has explored the possibility of combining PV and PVL simultaneously. Thus, it is important to highlight that using both velocity and %VL in combination is essential for accurately prescribing VBT. Therefore, the first aim of this study was to investigate the possibility of using both PV and PVL simultaneously, and whether the combined use of these two parameters influences the accuracy of one (PV), the other (PVL), or both. Furthermore, as mentioned previously, it is well established that familiarizing subjects with PV and PVL enhances accuracy levels; however, it remains unclear whether these improvements are maintained over time and, if so, for how long. Therefore, the second aim of the present study was to assess whether the accuracy of PV and PVL remains stable after four weeks, during which participants trained using classical PBT rather than velocity-based training, and without receiving any form of velocity feedback during their sessions.

2. Materials and Methods

2.1. Participants

The present study included 15 well-trained subjects (8 males, 7 females, age: 22.6 ± 1.8 years, height: 1.78 ± 0.10 m, body weight: 77.05 ± 12.04 kg, 4.7 ± 2.4 years of experience; 1RM/BW 1.5 ± 0.2). The study’s inclusion criteria required participants to have at least two years of experience in RT, regularly perform the back squat in their training routine, be aged between 18 and 35 years, and have no current or prior injuries for a minimum of two years. After being thoroughly informed about the study’s procedures, risks, ethical considerations, and provided with a copy of the explanatory information sheet, participants signed informed consent and data processing forms. The study protocol was developed in accordance with the latest revision of the Helsinki Declaration, which ensures the protection of the rights, integrity, and well-being of individuals participating in experiments, and received approval under CAR 165/2023. Participants were free to withdraw from the study at any time, either at their own request or that of the staff, without needing to provide a reason and without facing any consequences.

2.2. Experimental Design

A test–retest reliability design was used to analyze the effect of time on PV and PVL accuracy. Each participant completed a total of six training sessions, performing two or three sessions per week, with at least 48 h between sessions. During the first four sessions, participants were accustomed to VBT, focusing on the velocity performed during each repetition and the VL across each set. In the final two sessions, conducted 48–72 h after the last familiarization session and four weeks apart, participants performed four sets of squats at 60% and 80% of their 1RM, with both loads executed at 20% and 40% VL. The sets were performed in a randomized order, and the weights were concealed during all sets to ensure that participants were unaware of the loads on the barbell. For each set, participants reported the velocity of the first repetition. They were then instructed to stop the set when they believed they had reached either 20% or 40% VL, depending on the condition (Figure 1). Participants were not informed about the number of loads or the aforementioned randomization. Finally, at the beginning of each set, participants were reminded to perform each repetition with maximal intent during the concentric phase of the movement. However, no verbal encouragement was provided to avoid influencing their perceived exertion.

2.3. Familiarization Session and One-Repetition Maximum Test

During the whole session, a linear position transducer “Vitruve” (SPEED4LIFTS S.L., Madrid, Spain) was utilized to measure mean propulsive velocity (MPV). The first three familiarization sessions were designed to help participants become acquainted with PV and PVL. During the initial testing session, participants provided informed consent and allowed for data processing prior to the beginning of data collection. Information regarding their height, body weight, age, and experience in RT was subsequently gathered. During the first three sessions, after a standardized warm-up (i.e., 5 min of self-selected intensity cycling followed by 5 min of joint mobility exercises), participants performed six or seven sets of squats per session, with a rest period of 3 to 5 min between sets. On each occasion, the first two sets (three on the first day) were designated as warm-up sets, with participants selecting their own loads. They were instructed to progressively increase the load with each successive warm-up set. After the warm-up, four sets of squats were completed during every familiarization session. On the first day, participants performed four sets of back squats using heavy loads, characterized by a MPV < 0.50 m·s⁻¹. On the second day, the four sets of back squat were executed with moderate loads (MPV < 0.80 m·s⁻¹ > 0.60 m·s⁻¹). The third day included two sets with moderate loads (MPV ~ 0.70 m·s⁻¹) and two more with heavy loads (MPV < 0.50 m·s⁻¹). Each of the loads with a specific target velocity was performed at both 20% and 40% VL. Finally, on the fourth day, participants performed a maximal incremental back squat test to determine their 1RM [16]. During every familiarization session, participants received auditory feedback regarding the velocity achieved during each repetition and another auditory signal was given when the velocity loss threshold required was reached, both signals were given from the encoder. After each set, participants were presented with the validated PV squat scale [19], along with the velocity attained during that set. Participants were instructed to focus on the perceived effort associated with 20%VL or 40%VL rather than the number of repetitions performed.

2.4. PV and PVL Assessment

The final two sessions were performed 4 weeks apart and we assessed PV and PVL. During the four weeks between the test and re-test, subjects continued their regular training using the %1RM to calculate the daily load. During this period, they did not receive any feedback regarding PV or PVL, and did not use the PV scale [19] or LPT.

PV was evaluated using two distinct metrics: the Delta Score (Ds) and the absolute Delta Score (|Ds|). Specifically, Ds is calculated as the difference between perceived velocity and real velocity (Ds = Vp − Vr), thereby preserving the sign of the error and indicating whether PV is overestimated (positive value) or underestimated (negative value). In contrast, |Ds| is derived from the absolute difference between Vp and Vr (|Ds| = |Vp − Vr|) and quantifies the magnitude of the error discarding its direction. This dual approach provides a comprehensive evaluation, with Ds revealing the error’s direction and |Ds| offering a precise measure of its absolute magnitude. To evaluate the accuracy of PVL, a metric called the Vscore was used. In line with the methodology employed by Dello Iacono et al., the Vscore was defined as the difference between the number of repetitions performed by the participant (Np) and the number of repetitions required to reach the prescribed VL threshold (Nr) (Vscore = Np − Nr) [21]. Finally, consistent with the approach used and explained for Ds, the absolute Vscore (|Vscore|) was calculated to provide a more precise quantification of the error magnitude (|Vscore| = |Np − Nr|). During these sessions, participants performed a total of four sets of squats with two different loads (60% and 80% 1RM), each with two VL thresholds (20% VL and 40% VL). The order of the loads and VL thresholds was randomized. During the sets, the weights on the barbell were concealed to ensure they were unidentifiable to the participants. Prior to performing the prescribed four sets, participants were instructed to complete at least three warm-up sets of back squats. They were informed that after the third warm-up set, any load could be used, ranging from very light to very heavy, and were therefore advised to be prepared to lift loads potentially close to their 1RM. Additionally, for safety reasons, participants were instructed to always approach the barbell assuming it was loaded with an extremely heavy weight, emphasizing the importance of being both mentally focused and physically prepared to execute the set. Lastly, participants were instructed to end the set when they believed they had reached the required %VL. If a set was terminated prematurely, the VL slope during the set was used to estimate the number of repetitions needed to reach the prescribed %VL (Nr).

2.5. Statistical Analysis

The data were normally distributed, as confirmed by the Shapiro–Wilk test (p > 0.05). PV accuracy was assessed using the Delta Score (Ds), which represents the difference between Vp and Vr. Ds was analyzed using a two-way repeated-measure ANOVA to examine the effects of load (60% and 80% of 1RM) and time (test–retest session). The agreement between Vp and Vr and their correlation was assessed using Bland–Altman plots and Intra-Class Correlation (ICC), respectively, for both test and re-test sessions. Additionally, simple linear regression between Vp and Vr was performed for each session to determine the coefficient of determination (R²). PVL accuracy was calculated using the Vscore (Np − Nr). A three-way repeated-measure ANOVA was used to analyze the effect of Load (60% and 80% of 1RM), Velocity Loss (20%VL and 40%VL) and Time (test–retest session) and their interaction on Vscore. The relationship between Np and Nr was evaluated through Bland–Altman plots to assess agreement and ICC to determine their correlation, for both the test and re-test sessions. Lastly, for each session, a simple linear regression was performed between Np and Nr to determine the coefficient of determination (R²). The magnitudes of ICC were classified as follows: poor (<0.5), moderate (0.5–0.75), high (0.5–0.75), good (0.75–0.90), and excellent (>0.9) [25]. A priori power analysis was conducted using G*Power 3.1.9.7. An F-test with the “ANOVA: Repeated measures, within–factor” option was selected. A effect size (f = 0.3), an alpha level of 0.05, and a statistical power of 0.8 were used, with two groups and four measurements (2 time × 2 loads), assuming a correlation of 0.7 among repeated measures. The estimated required sample size was 15 participants. Moreover, a posteriori power analysis was conducted for the results identified as significant in order to estimate the power of our findings.

3. Results

3.1. Delta Score and Velocity Perception

The two-way repeated-measure ANOVA showed significant effects for load (F(1) = 11.9, p = 0.02, η² = 0.31), but not for time or load*time interaction (p > 0.05). The results of the Bland–Altman plot are presented in Figure 2. ICC showed good results between Vr and Vp in both the test and re-test sessions (

Table 1. Intra-class correlation coefficient (ICC) and coefficient of determination (R²) between Vp − Vr and Np − Nr.

	Test		Re-Test
	ICC	R2	ICC	R2
Vp − Vr	0.828	0.600	0.837	0.607
Np − Nr	0.980	0.947	0.986	0.923

Vp: perceived Velocity; Vr: real velocity; Np: number of repetitions perceived; Nr: number of repetition where the subject actually reached the required threshold; ICC: Intra-Class Coefficient Correlation; R²: coefficient of determination; Test: Test session 48–72 h after the familiarization protocol; Re-Test: Test session 4 weeks after the test session.

). Linear regressions revealed similar R² values between the pre- and post-test conditions (Table 1). Lastly, the |Ds| between pre- and post-test are reported in Figure 3. We conducted a posteriori power analysis using G*Power 3.1 to evaluate the statistical power of the significant impact of load on PV. In this analysis, we set the test family to F-test and used repeated-measures ANOVA (within factors) with an alpha level of 0.05. Based on our data, the observed effect size (η² = 0.31) from the two-way ANOVA resulted in a power of 0.73 for the load effect on PV. Although the statistical power we observed is relatively low, we strongly believe that increasing the sample size would enhance both the power and robustness of our findings. This is supported by existing literature, which shows that PV accuracy improves with higher loads [20].

3.2. Vscore and Velocity-Loss Perception

The three-way repeated-measure ANOVA revealed significant effects only for velocity loss (F(1) = 33.54, p < 0.001, η² = 0.72), meanwhile a trend for load (p = 0.06, η² = 0.25), and load*velocity loss interaction (p = 0.08, η² = 0.06) was found, indicating that Vscore is influenced mainly by velocity loss. Conversely, time, load*time, velocity loss*time, and load*velocity loss*time interactions were not significant (p > 0.05). The results of the Bland–Altman plot for Np and Nr are presented in Figure 4. ICC showed an excellent correlation between Nr and Np in both the test and re-test sessions (Table 1). Linear regressions revealed similar R² values between the pre- and post-test conditions (Table 1). Lastly, the |Vscore|, categorized by load and velocity loss, are reported in Figure 5. A posteriori power analysis to assess the statistical power of significant results for %VL in PVL was performed. Based on our dataset, we set the test family to F-test and used a repeated-measure ANOVA (within factors) with an alpha level of 0.05. In the three-way ANOVA for %VL, we observed an effect size of η² = 0.72, which corresponded to a statistical power of 0.99. These findings indicate that, despite a small sample size, the statistical power for %VL in PVL was extremely high, suggesting that the limited sample size was not a constraint.

4. Discussion

The aim of this study was to assess the stability of the accuracy of PV and PVL after four weeks during which participants did not receive any feedback on the velocity of the barbell’s movement during their training sessions. Different findings have been observed.

4.1. Delta Score and Velocity Perception

In agreement with previous studies [16,17,19], we found significantly greater PV accuracy for higher loads compared to lower ones, both in the test and re-test session after 4 weeks. Moreover, a very high correlation between Vr and Vp in both test and re-test sessions was found, suggesting that PV is a stable parameter over time. To the authors’ knowledge this is the first study to examine the stability of PV after four weeks without feedback with an encoder or PV scale. Indeed, PV is not only stable over time but, as found by Romagnoli et al., it is also unaffected by mental and physical fatigue [17,18]. Furthermore, the Ds reported in Figure 2 is comparable to what previously reported [16], indicating that the combined familiarization of PV and PVL does not appear to have altered the velocity perception accuracy. However, the Ds, which is the only parameter currently used to evaluate PV accuracy, is influenced by the presence of both positive and negative values (i.e., under or over estimation of the velocity); therefore, to accurately assess the magnitude of the error associated with PV we considered more appropriate to use the absolute difference between Vp and Vr. For the aforementioned reason, it is important to use both Ds and |Ds| to obtain information about the direction of the error as well as an accurate estimate of its magnitude. Since it is not influenced by the presence of both positive and negative values, |Ds| exhibited a slightly higher error than Ds. Therefore, PV accuracy, with an absolute error of approximately 0.11 m·s⁻¹ when using light loads, does not appear sufficiently precise for prescribing VBT intensity, potentially leading to incorrect load selection. Further research is needed to enhance the accuracy of PV across the entire load-velocity spectrum used in VBT sessions. Lastly, the |Ds| exhibited a large standard deviation (i.e., ~0.07 m·s⁻¹), indicating that some subjects achieved high accuracy while others were markedly imprecise. Future studies should explore the underlying mechanisms behind these differences. One possible explanation is that differences in proprioception among subjects may account for variations in PV ability. Proprioception informs force generation and, in tandem with exteroceptive senses such as visual, vestibular, and tactile feedback, may help detect changes in velocity [26]. Moreover, some studies have suggested that proprioception varies based on individual factors such as experience [26], age [27], and sex [28]. Therefore, considering that this study did not account for these differences, future research should investigate this possibility. This could involve proprioceptive training interventions or comparative analyses across groups with known differences in proprioceptive ability, such as athletes versus non-athletes or younger versus older individuals [28,29,30]. Lastly, within the field of neuroscience, the perception of an object’s velocity is considered to be determined by a combination of proprioceptive and exteroceptive afferents, such as vision [26,29,30]. Future studies could also investigate the impact of visual input on PV accuracy.

4.2. Vscore and Velocity-Loss Perception

This was the first study to investigate the consistency of PVL over four weeks. No significant differences in the Vscore were found pre and post the four-week period indicating PVL as stable for at least this time frame. Regarding the level and characteristics of PVL accuracy, some incongruences with previous studies have been found. It is important to note that this study is the first to use such an extended familiarization period before assessing PVL accuracy. In previous research, two studies provided no familiarization at all [15,18], and others performed only a single session [21,24]. Based on our results PVL appears to be primarily influenced by the %VL threshold, with higher thresholds corresponding to increased accuracy. The highest PVL accuracy was observed at the 40% VL threshold with the heaviest load (80% 1RM), where no participant exceeded a one-repetition error even after 4 weeks. Additionally, the |Vscore| for 40% VL at 60% 1RM had an error comparable to that for 20% VL at 80% 1RM. However, these results appear to be in contrast with findings from other studies that reported that an increase in repetitions performed, therefore in %VL is associated with a higher PVL error [20,21,22]. Dello Iacono et al. hypothesized two pathways responsible for this [21]: (1) the time delay after the initial repetition may cause the sensation of velocity perceived during that first attempt to fade, potentially altering PVL, and (2) neuromuscular fatigue, which could lead to discomfort and hinder participants’ ability to perceive velocity. However, our results do not support these hypotheses, as sets with higher %VL turned out to be more precise. We hypothesize that multiple factors may underlie these results. Firstly, two of the previously reviewed studies assessed a parameter that differs slightly from PVL, as those studies focused on the perception of changes in velocity, specifically, verbally reporting the velocity of each repetition [20,22]. Consequently, they did not evaluate the accuracy in identifying the attainment of a specific VL threshold, but rather the ability to perceive variations in repetition velocity within a set. In our view, perceiving the velocity of the final repetition is fundamentally different from recognizing the sensation associated with reaching a given percentage of velocity loss. This distinction may explain the discrepancies between our findings and those of earlier investigations. Furthermore, we suggest that during the familiarization sessions, participants may have begun associating specific %VL thresholds with distinct sensations of fatigue and proximity to momentary failure. Therefore, while Dello Iacono et al. hypothesized that PVL accuracy deteriorates over time due to the increasing temporal and mechanical separation between the first and last repetitions, our findings indicate the opposite trend: as the number of repetitions increases (i.e., higher %VL), accuracy improves, possibly because participants are progressively approaching failure. This interpretation is supported by evidence from previous research on repetitions in reserve (RIR), which shows that the closer individuals are to failure, the more accurate their RIR estimations tend to be [31]. Consequently, the 40% VL threshold at 80% 1RM yielded the highest precision and proximity to failure compared to other load and %VL combinations. Regarding the importance of load in PVL, results in the literature are conflicting [21,24]. da Silva et al. [24] found higher accuracy with heavy loads compared to lower ones. On the other hand, Dello Iacono et al. [21], found that PVL was more accurate with loads between 50 and 60% of 1RM compared to heavier ones [21]. The present investigation shows only a trend (p = 0.06) in line with the result of da Silva et al. [24]. Therefore, based on these results, it seems that PVL is a reliable parameter, also stable over time. Considering an error of 1 repetition negligible [21], in our opinion PVL could be used to prescribe VBT volume with loads of 80% 1RM at both 20% and 40% VL or even with loads of 60% 1RM if a 40% VL threshold is used.

5. Conclusions

This is the first study that evaluated the stability of PV and PVL accuracy over a four-week period. The main finding is that both parameters remained stable. PVL appears to be an acceptable metric for prescribing VBT volume in high-intensity and/or high-volume training, even four weeks after familiarization. Finally, PVL was found to be highly reliable at high loads with both 40% VL and 20% VL, but less reliable at medium loads with 20% VL. Future studies should investigate PVL accuracy at lower velocity-loss thresholds and with closer threshold ranges, particularly at medium intensities, to better understand its feasibility under various conditions. Conversely, PV accuracy, with an absolute error of approximately 0.11 m·s⁻¹ when using light load, does not appear sufficiently precise for prescribing VBT intensity. An error of 10% 1RM could shift the focus of training away from the specific purpose [2], and a variation in velocity of ~0.10 m·s⁻¹ corresponds to a difference of about 10% 1RM [32]; therefore, we consider acceptable error to be below 0.09 m·s⁻¹. In light of these results, it is important, when prescribing training based on PV, to consistently use PV in conjunction with a PV scale and, whenever possible, to integrate the use of an encoder.