# Temporal Stability and Practical Relevance of Velocity and Velocity-Loss Perception in Back Squat
## 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 (%1 RM) and prescribes the training volume based on that intensity [5]. The main limitation of PBT is that it does not consider daily fluctuations in 1 RM, 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], 1 RM 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 \(\sim\)400% for the cheaper ones to \(\sim\)2000s 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% 1 RM) intensities is more accurate than that for low (<40% 1 RM) and high (>70% 1 RM) 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, [PERSON] et al.