1. Introduction
The countermovement jump (CMJ) is routinely used by both practitioners and researchers to monitor acute and long-term changes in athlete performance. The CMJ offers a non-invasive assessment that can be performed in a time efficient manner, making it an attractive field measure to evaluate neuromuscular performance [
1]. In addition, the CMJ involves the dynamic muscle action known as the stretch-shortening cycle (SSC), which is a key component in many sporting events [
2]. More specifically, the CMJ has been associated with slow-SSC (>250 ms in duration) performance, which has been related to sprint acceleration, where ground contact time is longer [
3,
4]. This makes the CMJ assessment a fundamental tool in appraising key performance indices among basketball athletes, which require frequent acceleration and deceleration.
Two protocols are regularly employed when performing the CMJ. One protocol is performed without an arm swing (CMJ NAS), which requires the athlete to maintain hand placement on their hips or grasping a practically-weightless implement (e.g., polyvinyl chloride pipe or wood dowel) positioned on their shoulders during the CMJ [
5,
6,
7,
8,
9]. The CMJ NAS method isolates lower extremity force production by mitigating the influence of the arm swing. Alternatively, the second CMJ method incorporates the use of the arm swing (CMJ AS), with previous literature advocating the inclusion of the arm swing as it may reflect a greater degree of sport specificity and familiarity among skilled jumpers [
10,
11,
12,
13]. Previous literature has supported the intra- and inter-session reliability of the majority of CMJ variables during both CMJ protocols, especially in skilled jumpers [
5,
7,
10,
14,
15]. However, the arm swing appears to positively influence performance during the CMJ, such as increasing jump height and velocity at take-off, when compared to the CMJ NAS [
16,
17,
18,
19]. These noted increases in performance may allude to an athlete’s absolute maximal capacities, which could provide additionally pertinent information during an athlete’s needs analysis useful in directing a training program.
Reactive Strength Index Modified (RSI
Mod) and the Flight Time to Contraction Time Ratio (FT:CT) are two common variables of interest during CMJ analysis. Adopted from the Reactive Strength Index during the drop-jump, RSI
Mod assesses an athlete’s ability to create maximal vertical impulse in a minimal amount of time during the CMJ, while being credited as a valid measure of lower extremity explosiveness as it includes factors of both force and speed [
3,
20,
21]. RSI
Mod is calculated by dividing jump height (JH) by contraction time (CT) [
16]. JH can be computed via the flight time method, where the time the athlete is in flight is measured to determine jump height, and then used to generate RSI
ModFT, or by quantifying JH from the impulse-momentum method, which required the use of force platforms and used to produce RSI
ModIMP [
20,
22]. CT is defined as the duration (ms) from jump initiation (start of movement) to take-off [
10]. Similarly, FT:CT compares the ratio of an outcome variable (FT) and a process variable (CT) in an effort to evaluate an athlete’s jumping strategy, ultimately alluding to neuromuscular readiness [
20]. Previous literature has utilized both RSI
Mod and FT:CT to evaluate athlete performance and monitor neuromuscular functional status [
23,
24,
25]. In fact, RSI
Mod and FT:CT are oftentimes utilized over traditional gross output measures (i.e., force, power, jump height, etc.), as they may provide more relevant information reflecting changes in movement strategy in an attempt to meet the gross output desired [
5]. However, the similarities in computation between the two metrics may make their simultaneous inclusion in analysis redundant for athlete monitoring and performance testing. Nevertheless, previous literature has yet to compare performance differences in RSI
Mod and FT:CT between CMJ protocols, nor the relationship in performance within each variable between the CMJ NAS the CMJ AS. Understanding the relationship within each variable between protocols may aid coaches in determining which CMJ protocol to use for athlete assessment, while also providing context for practitioners when comparing an athlete’s performance profile characteristics with respect to normative data [
26].
Recent work by McMohan et al. [
20] demonstrated a strong correlation between the variables of FT:CT and RSI
Mod when performing the CMJ NAS in a cohort of sport science graduate students. However, the maintenance of this relationship during the CMJ AS, where differences in mechanical events of the CMJ are notably different, and among a cohort of skilled jumpers remains unknown. In addition, previous literature has yet to explore differences in RSI
ModFT, RSI
ModIMP, and FT:CT between the CMJ NAS and CMJ AS protocols. Therefore, the primary purpose of the present investigation was to evaluate differences in RSI
ModFT, RSI
ModIMP, and FT:CT during the CMJ NAS compared to the CMJ AS, while additionally exploring the relationship within each variable between jump protocols. In addition, a secondary purpose sought to explore the relationship among RSI
ModFT, RSI
ModIMP, and FT:CT during both the CMJ AS and the CMJ NAS. It was hypothesized RSI
ModFT, RSI
ModIMP, and FT:CT would be significantly greater during the CMJ AS, while exhibiting moderate to large correlations between CMJ protocols. Secondarily, it was hypothesized RSI
ModFT, RSI
ModIMP, and FT:CT would demonstrate strong positive correlations during both CMJ NAS and CMJ AS, while more specifically, the relationship between RSI
ModFT and RSI
ModIMP would produce enhanced limits of agreement during the CMJ NAS compared to the CMJ AS.
3. Results
The descriptive statistics are outlined in
Table 1. Data normality was confirmed and is presented as the mean of the three jumps performed during each condition from Test Session 1 and Test Session 2. The inter- and intra-session reliability of the variables in the present study are reported elsewhere [
10].
There was a significant condition (CMJ AS vs. CMJ NAS) effect, with RSIModFT (d = 0.67; p < 0.001), RSIModIMP (d = 0.66; p < 0.001), and FT:CT (d = 0.52; p < 0.001) all significantly greater during the CMJ AS compared to the CMJ NAS. However, there were no significant differences revealed across time (p > 0.05) and no significant condition × time interactions (p > 0.05) for any variable.
When comparing the relationships between the CMJ AS and CMJ NAS within each variable, during each test session, there was a very large significant positive correlation of RSIModFT (Test Session 1: r = 0.803, p < 0.001; Test Session 2: r = 0.783, p < 0.001) and a very large significant positive correlation of RSIModIMP (Test Session 1: r = 0.789, p < 0.001; Test Session 2: r = 0.722, p < 0.001), while there was a significantly large positive correlation of FT:CT (Test Session 1: r = 0.669, p < 0.001; Test Session 2: r = 0.621, p < 0.001).
There was a significant positive correlation between RSIModFT and RSIModIMP during both the CMJ AS (Test Session 1: r = 0.878, p < 0.001; Test Session 2: r = 0.925, p < 0.001) and CMJ NAS (Test Session 1: r = 0.986, p < 0.001; Test Session 2: r = 0.980, p < 0.001). There was a significant positive correlation between RSIModFT and FT:CT during both the CMJ AS (Test Session 1: r = 0.958, p < 0.001; Test Session 2: r = 0.951, p < 0.001) and CMJ NAS (Test Session 1: r = 0.969, p < 0.001; Test Session 2: r = 0.965, p < 0.001). There was also a significant positive correlation between RSIModIMP and FT:CT during both the CMJ AS (Test Session 1: r = 0.864, p < 0.001; Test Session 2: r = 0.910, p < 0.001) and CMJ NAS (Test Session 1: r = 0.961, p < 0.001; Test Session 2: r = 0.960, p < 0.001).
There were no significant differences between RSI
ModFT and RSI
ModIMP during either the CMJ NAS or the CMJ AS (
p > 0.05). The Bland-Altman Plot in
Figure 1 outlines an average measurement bias of 0.008 ± 0.02 during the CMJ NAS. Measurements of RSI
Mod by the flight time method (RSI
ModFT) ranged between −0.038 less and 0.054 greater than measurement by the impulse-momentum method (RSI
ModIMP) for 95% of individuals assessed during the CMJ NAS.
As illuminated by the Bland-Altman Plot in
Figure 2, the average measure bias between RSI
ModFT and RSI
ModIMP during the CMJ AS was −0.028 ± 0.12. In addition, measurements of RSI
Mod by the flight time method (RSI
ModFT) varied between −0.265 less and 0.209 greater than measurement by the impulse-momentum method (RSI
ModIMP) for 95% of individuals assessed during the CMJ AS.
4. Discussion
The main findings of the present study were (a) a significant increase in RSIModFT, RSIModIMP, and FT:CT during the CMJ AS compared to the CMJ NAS; (b) a large correlation within RSIModFT, RSIModIMP, and FT:CT between jump protocols; (c) a large significant positive correlations among RSIModFT, RSIModIMP, and FT:CT, during both the CMJ AS and the CMJ NAS; and (d) RSIModFT and RSIModIMP demonstrated superior limits of agreement during the CMJ NAS compared to the CMJ AS.
The present study performed a novel comparison of RSI
ModFT, RSI
ModIMP, and FT:CT outcomes during the CMJ NAS compared to the CMJ AS. As hypothesized, the present study illuminated statistically significant increases, all of the medium effect sizes, in RSI
ModFT, RSI
ModIMP, and FT:CT during the CMJ AS compared to the CMJ NAS. Improvements in performance during the CMJ AS compared to the CMJ NAS is persistent throughout the literature [
15,
16,
17,
18,
19], such as the increase in jump height of 10–12% [
35]. Likewise, the velocity at take-off has been shown to be 6–10% greater during the CMJ AS [
16,
18,
36]. Similarly to prior literature, the present investigation observed increases of 20%, 24%, and 11%, in RSI
ModFT, RSI
ModIMP, and FT:CT, respectively during the CMJ AS. While a variety of theories have been postulated as responsible for the improvements in performance during the CMJ AS, enhancements are likely the result of several mechanisms operating simultaneously. Early work by Payne [
37] proposed the ‘transmission of force’ theory in which the upward acceleration of the arm swing increases reciprocal downward forces exerted through the body, increasing ground reaction forces and ultimately leading to a greater vertical velocity of the center of mass. While intuitive, this theory is likely an oversimplification, as newer work by Lees et al. [
18] offers a more complex explanation, involving a series of events that allows the arms to build energy early in the jump and transfer that energy to the rest of the body in the later stages of the jump. Alternative theories include the eccentric stretching phase perhaps leading to a potentiation effect, with an increase in myoeletric activity during the subsequent concentric contraction [
16], while others have speculated the significant increase in tension during the onset of the concentric contraction may result in enhanced chemical energy availability for force generation [
35]. Regardless of the mechanisms at play, the observed increase in performance during the CMJ AS in the present study offers novel insight into maximal capacities that may be more directly related to performance during sport, beneficial to applied practitioners and researcher.
Importantly, the present study identified only a large correlation, suggesting only about 38–64% of the shared variance between the CMJ protocols. The increase in the performance variables of RSI
ModFT, RSI
ModIMP, and FT:CT during the CMJ AS compared to the CMJ NAS, while lacking very large, or nearly perfect, correlations between jump performances indicates different information may be captured from the CMJ AS force-time signature not acquired from the CMJ NAS. Although much of the previous literature has used the CMJ NAS protocol to assess RSI
ModFT, RSI
ModIMP, and FT:CT [
5,
26,
38], the present data suggests the inclusion of the CMJ AS protocol may identify alterations in maximal performance capacities. In addition, the CMJ AS may provide information independent from that obtained during the CMJ NAS and may relate more closely to the athlete’s expression of performance capabilities during the actual sporting event tasks, especially in sports incorporating a large vertical component. Furthermore, recognizing differences in performance between the CMJ NAS and CMJ AS will be essential in developing and comparing reference RSI
Mod and FT:CT values among various athletic populations [
26].
Ultimately, these data suggest it may be necessary for practitioners to perform both CMJ protocols when assessing an athletes’ physical capacities. For example, practitioners may employ the CMJ NAS to evaluate acute changes in neuromuscular readiness, as previous literature has established less error of measurement. The CMJ AS may be more useful in to quantitating long-term changes in performance, such as changes in performance after a training program or alterations in performance between training phase, allowing coaches and practitioners to identify the changes in maximal performance capacities and where differences in performance are likely to be greater than acute changes.
The present study illuminated significant and strong positive relationships among RSI
ModFT, RSI
ModIMP, and FT:CT during the CMJ NAS, but uniquely identified a similar association among the variables during the CMJ AS. The findings of the present study support recent work by McMahon et al. [
20] that also observed nearly identical Pearson’s correlation coefficients between RSI
ModFT and RSI
ModIMP (r = 0.980,
p < 0.001), between RSI
ModFT and FT:CT (r = 0.947,
p < 0.001), as well as between RSI
ModIMP and FT:CT (r = 0.944,
p < 0.001) during the CMJ NAS. Moreover, these shared findings further endorse a significant and almost perfect positive relationship among RSI
Mod and FT:CT regardless of the computation method. Similarly, the relationship between RSI
ModFT and FT:CT during the CMJ AS paralleled the results of the CMJ NAS, in an almost perfect fashion, which was expected considering the extensive use of congruent parameters to compute the variable. In contrast, the relationship between RSI
ModFT and RSI
ModIMP, as well as between RSI
ModIMP and FT:CT during the CMJ AS were still positively correlated and very large, however their relationship did not parallel to the same degree as the aforementioned relationships. The small relational disparities observed, especially during Test Session 1, coincide with observations of less reliability when using the impulse-momentum method to calculate jump height during the CMJ AS [
10], however the variables remain strongly related.
The present study found no significant differences between RSI
ModFT and RSI
ModIMP during the CMJ NAS or the CMJ AS. Important to note, these findings are in contrast to the recent findings by McMahon et al. [
20] which observed a significant difference between variables using the CMJ NAS protocol, but only a trivial effect (
d = 0.14). No differences between RSI
ModFT and RSI
ModIMP alone would indicate that practitioners could select either variable for player assessment. Interestingly, the CMJ NAS produced superior limits of agreement between RSI
ModFT and RSI
ModIMP compared to the CMJ AS, as visualized by the Bland-Altman Plots in
Figure 1 and
Figure 2. The CMJ NAS demonstrated a smaller average measurement bias and reduction in measurement difference variability. Differences in the limits of agreement are likely due to exaggerated variability in the velocity at take-off during the CMJ AS with the movement occurring at a greater velocity, leading to alterations in the reliability of the impulse-momentum computation of jump height [
10]. Previous literature has identified the consequences of inaccurately pinpointing the instant of take-off by as little as 2–3 ms, which can manipulate an increase in variability of both velocity and displacement by as much as 2% [
22,
39]. The flight time method assumes center of mass is the same during take-off as landing, therefore differences in center of mass during take-off and landing can lead to an over estimation of the jump height calculation. Its speculated that the flight time method overestimates jump height, as the jumper’s center over mass is often higher at take-off than landing [
29]. Previous literature has shown the center of mass is located at a higher relative position at take-off during the CMJ AS compared to the CMJ NAS [
17], which may exacerbate differences in calculations in that the difference in center of mass during take-off are not paralleled upon landing.
In addition, it is likely that the predetermined force thresholds used by the commercially available software influence the discrepancies between RSI
ModFT and RSI
ModIMP, however collecting data at higher sampling frequencies, such as 1000 Hz in the present study is thought to reduce measurement error [
22]. It should be mentioned that, it is also possible participants performed minute increases in hip, knee, or ankle flexion once airborne, not visible to the eye in real-time during the CMJ AS and which then did not occur during the CMJ NAS, resulting in a decreased association between variables within jump protocols [
29,
31]. However, the research team ruled jumps invalid when such characteristics were visible. In accordance with previous literature [
10], these findings suggest the use of the CMJ NAS may be the more suitable protocol for athlete assessments when RSI
Mod is a key variable of interest, especially when evaluating acute day-to-day changes in neuromuscular functional performance. In addition, the enhanced limits of agreement during the CMJ NAS suggests the chosen computational method of RSI
Mod (RSI
ModFT or RSI
ModIMP) when utilizing the CMJ NAS will likely exert a negligible influence on the RSI
Mod values.
Important to note, the present study found no differences between Test Session 1 and Test Session 2 and no significant condition by time interactions. These findings further support the inter-session reliability of the variables in the present study, as reported elsewhere [
10].
The present study is not without limitations. This investigation examined a relatively small, homogenous sample of skilled jumpers. In addition, the levels of agreement among variables may be influenced by the software used for analysis. Finally, training loads were not quantitively confirmed with an athlete monitoring technique, such as internal or external training load measures [
6].
In conclusion, the present study offers several key findings useful to applied practitioners using the CMJ with increasingly available commercial force platform technology to evaluate changes in performance and fatigue. The increases in RSIModFT, RSIModIMP, and FT:CT evident during the CMJ AS illuminate the potential use of the CMJ AS to reveal changes in maximal performance that may translate more closely to sport specific tasks, such as assessing performance changes after a training block or between training phases. In addition, the observed relationship within RSIModFT, RSIModIMP, and FT:CT between the CMJ AS compared to the CMJ NAS suggests each jump protocol may provide novel insight valuable to assessing an athlete’s physical capacities. In addition, the present investigation identified the strong relationship among RSIModFT, RSIModIMP, and FT:CT during both the CMJ NAS and CMJ AS. Furthermore, it appears the RSIModFT and RSIModIMP exhibit greater levels of agreement during the CMJ NAS compared to the CMJ AS. Practically, these findings indicate that either RSIMod or FT:CT may be utilized to monitor changes in neuromuscular function and performance, but it is unnecessary to include both, as they may provide similar information about an athlete’s force-time characteristics, conceivably making their simultaneous inclusion during a player assessment redundant.