## 1 Introduction  
Soccer requires players to execute short linear sprints interspersed with periods of passive rest or low to moderate activity. These sprints are often followed by active or passive rest periods longer than one minute, allowing complete or near-complete recovery [1]. While some studies report a decline in performance during repeated sprints, they suggest that this decrease is relatively small and that players are able to recover well between sprints [2], others indicate that linear sprints performed with short rest intervals (i.e., less than 30 s) may negatively impact sprint performance [3]. This potential decline in linear sprint performance can be attributed to repeated sprint ability (RSA). RSA refers to an athlete's capacity to perform short sprints (less than 6 s) with brief rest periods (less than 30 s), and it may influence the high-intensity efforts required during critical moments in competitions, such as counter-attacks and defensive recovery [4]. Several factors may influence RSA, including the muscle power output [5]. A previous study reported a moderate correlation (\(r=0.51\) to \(0.54\), \(p=0.01\) to \(0.02\)) between leg strength and the maximum RSA in soccer players [6]. Furthermore, a recent systematic review indicated that increasing strength levels could enhance soccer players' RSA, including the best, mean, and total times [7]. Previous studies have suggested that improving strength levels can positively impact soccer players' RSA. Consequently, various warm-up protocols designed to enhance soccer players' performance have garnered significant attention from strength and conditioning coaches [8]. One such warm-up protocol is post-activation performance enhancement (PAPE), which aims to develop strength by utilizing different intensities of one-repetition maximum (1 RM) with external loads [9]. PAPE is defined as an acute increase in human voluntary movement performance, including maximal force, power, and speed following preloading [10]. While some researchers have presented their views on the mechanisms underlying the post-activation potentiation (PAP) effect in the literature, it is theoretically anticipated that PAP should result in PAPE. The mechanisms that support PAPE have not been fully elucidated, suggesting that further studies are necessary [11]. Additionally, researchers argued that the need for further exploration of PAPE arises partly from the lack of observed effects when PAP is significant (e.g., within 3-4 min post-contraction) [12]. Notably, the temporal profile of myosin light chain phosphorylation, a key mechanism underlying \"classical\" PAP, rarely aligns with the temporal profile of voluntary force enhancement. Furthermore, unlike PAP, changes in muscle temperature, muscle/cellular water content, and muscle activation may contribute at least partially to voluntary force enhancement. Consequently, this enhancement has been recently termed PAPE [11]. Several preloading methods have been applied to achieve PAPE. Although heavy resistance exercises are commonly performed as preloading, studies have also been conducted on pyometric jumps, weight tests, isometric contractions, and electromyostimulation (EMS) applications [13; 14]. A recent systematic review and meta-analysis indicated that resistance training, compared with pyometric exercises and complex training, has a more pronounced effect on athletes' jumping and sprinting performance [15]. Previous studies demonstrate and widely support the efficacy of maximal or near-maximal contractions (greater than 80% of dynamic or isometric maximal voluntary contraction) in optimization [16; 17]. Some studies have indicated that maximal or near-maximal preloading is one of the most effective ways to elicit PAPE [14]. In a previous study examining the effects of preload on repeated sprint performance, significant improvements were observed in the repeated sprint performance of elite athletes after performing squats at 90% of their 1 RM.