Vertical jump (ie, jump height [JH]) is one of the most important indicators of performance and is significantly related to various athletic abilities, such as sprint running1 and change of direction.2 JH is typically defined as the displacement of the body’s center of mass (COM) between COM height at the takeoff instant and that at the apex of the jump.3 In particular, countermovement jump (CMJ) height is used to assess neuromuscular status and holds utility as a parameter for planning recovery strategies and adjusting training volume.4 Consequently, it would be useful for practitioners to have a simple method available for measuring vertical JH in the field. Furthermore, the accurate measurement of JH will facilitate optimal training techniques for many coaches and athletes.
The gold standard for calculating JH is the impulse–momentum method (IM).3 This method determines JH by calculating the impulse from vertical ground reaction force–time data measured using force plates and calculating the takeoff velocity from the impulse–momentum relationship.3 IM is a considerably more accurate method because it has fewer error factors compared with other JH calculation methods, and the takeoff velocity is considered a reliable variable.3 However, the force plates required for IM are expensive and difficult to carry and require specialized analytical knowledge, which makes it difficult to use them in the field.5 Therefore, the flight time method (FT) is commonly used as an alternative and more convenient JH calculation method.3 The benefit of FT is that it only requires the flight time after takeoff, which enables JH to be measured conveniently (eg, with smartphones) without expensive devices.6 As a result, smartphone applications (eg, My Jump Lab) for measuring JH by FT have become widely used in both research and the field.6 However, when measuring JH using FT, if the posture at takeoff and landing changes, measurement errors may occur.7 Normally, because the lower extremity is fully extended at takeoff and slightly flexed at landing,7 several studies7–9 have suggested that FT overestimates JH. For example, Loturco et al8 found that FT significantly overestimated unloaded CMJ height by about 3 cm compared with IM. Another study7 found that the shank and foot segment significantly contributed to the overestimation of JH using the FT. Thus, although FT can readily measure JH, there is a problem that JH is affected by lower-extremity flexion at landing.
When calculating JH using a smartphone application, the jumping motion of the participant is recorded using the high-speed camera, and then the flight time is derived based on the instant of foot takeoff and landing.6,10 However, this method assumes that body posture remains constant during the flight phase, leading to potential overestimation or underestimation of JH when there are disparities between the vertical displacements of the foot and COM.7 Consequently, developing alternative methods for calculating the flight time based on other body segments rather than solely relying on the foot is necessary. Recently, Yamashita et al7 reported that the lower trunk segment, including the greater trochanter, did not significantly contribute to the measurement error of JH when using FT. Based on this finding, calculating the flight time using the displacement of the greater trochanter, instead of the foot, may eliminate the risk of overestimating JH when using FT, while maintaining the convenience of FT.
Therefore, in the present study, we proposed a new method (ie, FT modified [FTM]) using a smartphone application (named: JumpEye, 500 yen at the time of writing) to overcome the FT problem described above and to test its concurrent validity, intraday, intraobserver, and interobserver reliability.
Methods
Subjects
Twenty-four healthy, physically active men (mean [SD]: age 21.8 [4.8] y, height 1.73 [0.06] m, body mass 70.2 [5.9] kg) participated in this study and were free of any musculoskeletal pain or injury that could compromise testing. All of the subjects experienced CMJ testing, traditional resistance exercise, and plyometric training. After explaining the purpose of the study as well as the procedures, risks, and benefits, written informed consent was obtained before participation. The study was conducted based on the principles of the Declaration of Helsinki and was approved by the ethics committee of Keio University (22-012).
Study Design
The experimental protocol in the current study was conducted a single testing session. The participants completed a standard 10-minute warm-up consisting of jogging, lower body dynamic stretches, and vertical jumps. Next, they performed 6 CMJs on dual force plates (PASCO, PS-3229)5 while being recorded with the high-speed camera mode of an iPhone 12 (Apple Inc) at 240 frames·s–1, which was mounted on a tripod at a height of 1 m and a distance of 3 m from the right front of the force plates.6,11,12 This setting was established to ensure that the takeoff of the participant’s feet and the right greater trochanter marker were readily visible in the video. Furthermore, to examine the effect of lower limb flexion at landing on the accuracy of jumping height calculated by the proposed FTM, the 6 CMJs consisted of 3 conditions (ie, control [CON], extension [EXT], and flexion [FLEX]), with different instructions on the landing posture (Table 1). The participants performed 2 jumps for each condition. The order of verbal instructions for each condition was counterbalanced to eliminate the possibility of order effects, and the instructions were reread prior to each trial. The participants were allowed a 1-minute rest interval between trials under the same conditions and a 2-minute rest interval between each condition.
Verbal Instructions Given in the Control, Extension, and Flexion Conditions
| Condition | Verbal instructions |
|---|---|
| Control | “Jump as fast and high as possible without focusing on anything about landing posture.” |
| Extension | “Jump as fast and high as possible, landing with the hips and knees as extended as possible and the ankle joints as plantar flexed as possible.” |
| Flexion | “Jump as fast and high as possible, landing with the hips and knees as flexed as possible and the ankle joints as dorsiflexed as possible.” |
Data Analyses
The vertical ground reaction force data for all CMJs were sampled at a frequency of 1000 Hz.13 Signals from the force plate were filtered using a fourth-order Butterworth low-pass filter with a 50-Hz cutoff.14 Before each jump, the subjects were weighed over 3 seconds with a 0.4-kg wood bar placed on their shoulders to measure the total system weight. The movement initiation of the jump was defined as the time point of 30 milliseconds before the vertical ground reaction force exceeded the threshold (the total system weight − 5 SD).13 For each jump, the COM velocity was calculated using the trapezoid rule, and the net vertical ground reaction force was calculated as the amount of force exceeding the system weight divided by the system mass to determine acceleration.13 Acceleration was numerically integrated to provide instantaneous COM velocity. The takeoff and landing thresholds were identified from 5 SD during the flight phase across a 0.3-second period based on a previous study.15 The takeoff and landing instants were identified as the first force value greater than the force threshold.
—Flight-time method modified using the smartphone application JumpEye. (A) Selection of takeoff frame and alignment of the horizontal line, which can be scrolled up and down with a finger, to the greater-trochanter marker. (B) Video progression after takeoff. (C) Selection of landing frame (under the control condition). (D) Typical example of a landing frame under the extension condition. (E) Typical example of a landing frame under the flexion condition.
Citation: International Journal of Sports Physiology and Performance 20, 1; 10.1123/ijspp.2024-0063
To determine the intraobserver reliability of the FTM, the videos were reanalyzed using FTM 7 days later (day 8) by the same observer.16 In addition, to determine the interobserver reliability of FTM, 2 independent observers (observer 1 and observer 2) analyzed the videos using FTM.10
Statistical Analyses
Statistical analyses were performed using IBM SPSS statistical 29 software. P ≤ .05 was considered statistically significant. Normality was analyzed using the Shapiro–Wilk test. The intraclass correlation coefficient (2-way mixed effects, absolute agreement, and single observer/measurement),17,18 coefficient of variation,19 and standard error of measurement20 were calculated to analyze jump measurement reliability. Coefficient of variations < 10% were considered acceptable.21 To complement the intraclass correlation coefficient analyses, Bland–Altman plots were generated, providing a comprehensive representation of the agreement between methods.22 Heteroscedasticity was assessed using White test. The relationships between JHs were evaluated using Pearson (r) or Spearman (ρ) correlation tests in the absence of normal distributions.23 For pairwise comparisons, paired-sample t tests were conducted, or nonparametric Wilcoxon tests were employed when normal distributions were not observed. The average of 2 trials was used in the analysis when comparing conditions in JHIM. To compare JHs between methods or conditions, a 1-way analysis of variance or nonparametric Friedman test was employed when the data were nonnormally distributed. If the assumption of sphericity was violated according to Mauchly test of sphericity, the Greenhouse–Geisser correction was implemented. When a significant main effect was identified, the Bonferroni post hoc test was conducted using pairwise comparisons. Comparisons between methods (ie, IM, FT, and FTM) were performed using the combined data from each condition (ie, CON, EXT, and FLEX), which is the “All” condition, as well as within each condition. The effect size was determined using Cohen d for parametric data and Cliff delta24 for nonparametric data.
Results
Friedman test indicated a significant main effect (P < .001) of the used methods on the JHs (ie, All, CON, and FLEX conditions), except for the EXT condition (P = .297). Post hoc pairwise comparisons revealed that JHFT was significantly higher compared with JHIM (Table 2) under the All (Cliff delta = 0.238), CON (Cliff delta = 0.253), and FLEX (Cliff delta = 0.448) conditions (P < .001), but not under the EXT condition (Cliff delta = 0.037, P = 1.000); however, JHFTM was not significantly different from JHIM in the All (Cliff delta = −0.006), CON (Cliff delta = −0.012), EXT (Cliff delta = −0.009), and FLEX (Cliff delta = −0.003) conditions (P = 1.000).
Comparison Among Jump-Height Calculation Methods and Reliability of Measured Outcomes
| Condition | Method | Jump height, m, median (IQR) | ICC (95% CI) | CV (95% CI) | SEM, m |
|---|---|---|---|---|---|
| All | IM | 0.364 (0.089) | .952 (.924–.969) | 3.04 (2.61–3.63) | 0.013 |
| FT | 0.394 (0.108)a,b | .959 (.936–.974) | 2.98 (2.56–3.57) | 0.016 | |
| FTM | 0.366 (0.095) | .946 (.915–.966) | 3.00 (2.58–3.59) | 0.015 | |
| Control | IM | 0.374 (0.079) | .966 (.924–.985) | 2.38 (1.85–3.34) | 0.012 |
| FT | 0.405 (0.106)a,b | .975 (.944–.989) | 2.04 (1.59–2.87) | 0.012 | |
| FTM | 0.376 (0.091) | .961 (.913–.983) | 2.62 (2.03–3.67) | 0.013 | |
| Extension | IM | 0.360 (0.084) | .951 (.890–.978) | 3.22 (2.50–4.51) | 0.013 |
| FT | 0.362 (0.095) | .928 (.842–.968) | 3.90 (3.03–5.47) | 0.018 | |
| FTM | 0.363 (0.082) | .948 (.884–.977) | 3.03 (2.36–4.25) | 0.014 | |
| Flexion | IM | 0.366 (0.097) | .939 (.904–.981) | 3.51 (2.73–4.93) | 0.015 |
| FT | 0.414 (0.108)a,b | .957 (.904–.981) | 3.00 (2.33–4.21) | 0.016 | |
| FTM | 0.366 (0.098) | .929 (.844–.968) | 3.36 (2.61–4.71) | 0.017 |
Abbreviations: CV, coefficient of variation; FT, flight-time method; FTM, flight-time method modified; ICC, intraclass correlation coefficient; IM, impulse–momentum method; IQR, interquartile range; SEM, standard error of measurement.
aSignificantly different from jump height calculated using IM in the corresponding condition. bSignificantly different from jump height calculated using FTM in the corresponding condition.
JHFTM, compared with JHFT, showed stronger, perfect, and significantly positive correlations with JHIM (Figure 2). Bland–Altman plots (Figure 3) also revealed that JHFTM, compared with JHFT, exhibited a higher agreement with JHIM, and no significant proportional bias or heteroscedasticity was identified (P > .05). Friedman tests revealed a significant main effect of conditions (ie, CON, EXT, and FLEX) on the differences between JHFT and JHIM (P < .001). Post hoc pairwise comparisons revealed that the difference between JHFT and JHIM under the FLEX condition was significantly higher compared with that under the CON and FLEX conditions (Cliff delta = 0.476, P = .003; Cliff delta = 0.795, P < .001; respectively) and that under the CON condition was significantly higher compared with that under the EXT condition (Cliff delta = 0.622, P < .001).
—Correlations between JH calculated using the flight-time method (dashed line and empty dots) and JHIM, as well as between JHFTM (straight line and filled dots) and JHIM. (A) Combined data for the CON, EXT, and FLEX conditions. (B) Data for the CON condition. (C) Data for the EXT condition. (D) Data for the FLEX condition. *Above 95% CI observed from JH calculated using the flight-time method. CON indicates control; EXT, extension; FLEX, flexion; JH, jump height; JHFTM, JH calculated using the flight-time method modified; JHIM, JH calculated using impulse–momentum method.
Citation: International Journal of Sports Physiology and Performance 20, 1; 10.1123/ijspp.2024-0063
—(A–D) Bland–Altman plots showing the agreement between JHFT and JHIM. (E–H) Bland–Altman plots showing the agreement between JHFTM and JHIM. (A and E) Combined data for the CON, EXT, and FLEX conditions. (B and F) Data for the CON condition. (C and G) Data for the EXT condition. (D and H) Data for the FLEX condition. CON indicates control; EXT, extension; FLEX, flexion; JHFT, jump height calculated using the flight-time method; JHFTM, jump height calculated using the flight-time method modified; JHIM, jump height calculated using the impulse–momentum method.
Citation: International Journal of Sports Physiology and Performance 20, 1; 10.1123/ijspp.2024-0063
Repeated-measures analysis of variance revealed a significant main effect of conditions on JHIM (partial η2 = .228, P = .003). Post hoc pairwise comparisons revealed that JHIM in the EXT condition was significantly lower compared with that in the CON and FLEX conditions (d = −0.229, P = .005; d = −0.186, P = .035; respectively). Under the EXT condition, the absolute value of the difference from JHIM was significantly smaller for JHFTM compared with JHFT (Cliff delta = 0.396, P < .001).
Intraclass correlation coefficients (ie, intraday reliability) for the JHs demonstrated almost perfect reliability, including fully acceptable coefficient of variations (Table 2). The intraobserver and interobserver reliability of the FTM (Figure 4) were acceptable. JHFTM calculated on day 1 and day 8 were not significantly different (Cliff delta = −0.032, P = .910) and were completely equal in 93 out of 144 trials (approximately 65%). JHFTM calculated by observer 2 was significantly lower compared with that calculated by observer 1 (Cliff delta = −0.044, P = .005). JHFTM calculated by observer 1 and observer 2 were equivalent in 87 out of 144 trials (approximately 60%).
—Scatter plots and Bland–Altman plots showing the agreement between JHFTM and jump height calculated using the impulse–momentum method, which indicates the intraobserver (A and C) and interobserver (B and D) reliability of FTM. ICC indicates intraclass correlation coefficient; FTM, flight-time method modified; JHFTM, jump height calculated using the FTM.
Citation: International Journal of Sports Physiology and Performance 20, 1; 10.1123/ijspp.2024-0063
Discussion
Herein, a new method (ie, FTM) was established to overcome the problem of FT, in which flexing the lower limb at landing results in an overestimation of JH. Moreover, its concurrent validity and intraday, intraobserver, and interobserver reliability were tested. JHFT significantly overestimated JHIM, which was consistent with previous studies.8,9,25 However, JHFTM was comparable to JHIM, correlated more strongly with JHIM compared with JHFT, and had a very high intraday, intraobserver, and interobserver reliability. These findings indicate that FTM is a reliable and more accurate method to evaluate JHIM compared with the traditional method (ie, FT).
Without the subject’s attention to landing posture (ie, the CON condition), the magnitude of overestimation (ie, an average of 0.030 m) of JH when using FT was comparable to that of previous studies.8,25 For example, Loturco et al8 and Aragón25 reported that a significant overestimation (an average of 0.03 and 0.041 m, respectively) of JH occurred when using FT, and they did not provide instructions to the subjects with respect to the landing posture. In addition, Kibele9 reported an overestimation of JHIM while using FT without instructions regarding the landing for all subjects except for one. Given these findings, when both the observer and the subject do not pay attention to the landing posture, it appears that the FT overestimates the JH by approximately 0.03 m.
In addition, subjects were provided different instructions (ie, CON, EXT, or FLEX) for landing posture to determine whether the validity of the FTM is affected by lower-extremity flexion at jump landing (Table 1). FTM did not significantly overestimate JHIM under all conditions, which indicates that JHFTM is not affected by lower-extremity flexion at landing (Table 2, Figure 3). Conversely, FT significantly overestimated JHIM under CON and FLEX conditions, but not under the EXT condition, in which participants were instructed to extend the lower extremity as much as possible when landing (Table 2, Figure 3). Furthermore, the magnitude of overestimation of JHIM, when JH was calculated using FT, was the highest under the FLEX condition of the 3 conditions (Figure 3). These results indicate that attention to the landing posture markedly influences the overestimation of JH when using FT. Furthermore, these facts emphasize the importance of providing subjects with strict instructions regarding landing posture when attempting to measure JH using FT (eg, jump mat). In a previous study by Pérez-Castilla et al,26 in which the subjects were instructed to “land with the hips and knees extended and the ankle joints in plantar flexion,” significant overestimation of JH when using FT did not occur. However, when measuring JH, the instructions, such as those given for the EXT condition, do not appear to be recommended. For example, Purevsuren et al27 revealed that ankle plantar flexion is a factor in lateral ankle sprain. Thus, the instructions that encourage ankle plantar flexion on jump landing may increase the risk of lateral ankle sprain. In addition, the instructions provided for the EXT condition may impede the subject’s maximum performance. In the present study, JHIM in the EXT condition was significantly lower compared with that under CON and FLEX conditions. Therefore, in situations in which the practitioner wants to correctly assess the participant’s intrinsic maximum jumping ability, it is important to avoid instructions regarding landing posture (especially for the EXT condition). In addition, because the absolute value of the difference from JHIM in the EXT condition was significantly smaller for JHFTM compared with that for JHFT, FTM may be a more accurate means of measuring JH (ie, a closer value to JHIM) than FT with a controlled landing posture. Based on these suggestions, FTM appears to be more appropriate than FT as a safe and valid method for measuring JH.
The law of the conservation of momentum may explain the high agreement between JHFTM and JHIM. The total momentum and angular momentum of the system remain constant unless an external influence acts. Thus, when a segment moves relative to the COM, the other segments must move to compensate. This suggests that, when lower-extremity flexion occurs after takeoff, upper body flexion (ie, forward tilt) concomitantly occurs. Assuming a simplified segmental model, these movements occur with the hip joints (the greater trochanter when viewed from the sagittal plane) as the axis. This suggests that the greater trochanter is a strong marker of vertical displacement of the COM, which may explain the high agreement between JHFTM and JHIM. These mechanisms were not directly evaluated in the present study and should be clarified in the future.
The results showed a high intraobserver and interobserver reliability for FTM (Figure 4). In particular, intraobserver reliability is important for detecting meaningful longitudinal changes in JH.16 Therefore, FTM is useful as a practical method to accurately evaluate jumping ability, neuromuscular status longitudinally, and cross-sectionally in the field. Although a significant difference in JHFTM was observed between observers, attributed to the large sample size (n = 144), the measured difference was minimal (0.2 cm). Moreover, JHFTM calculated by one observer was consistent with that by the other observer for more than half (ie, 60%) of the trials (Figure 4). Therefore, JHFTM may be interchangeable between observers.
As indicated earlier, the usefulness of FTM in simply and accurately evaluating JH was demonstrated; however, some limitations exist. First, the FTM proposed in this study calculated the flight time based on the displacement of the right greater trochanter in the videos taken from the right front (Figure 1). Therefore, when the right greater trochanter moves on the frontal plane relative to the whole-body COM following takeoff, there is a risk of overestimation or underestimation of JHIM. In vertical jumping, however, because movement occurs primarily in the sagittal plane, significant movement rarely occurs in the frontal plane.28 In fact, the measurement error that may have been caused by this factor was small and negligible (Figure 3). Nevertheless, because of this risk, when measuring JH using FTM in the field, it may be necessary to ensure that no significant movement in the frontal plane (eg, extreme asymmetry in foot landing timing) occurs during the flight phase. Second, the FTM used a smartphone device (ie, iPhone), which has an upper sampling rate limit of 240 frames·s–1. Although this may have affected the JH measurement accuracy, a previous study29 using My Jump reported that sampling rates higher than 240 frames·s–1 did not improve measurement accuracy. Therefore, the effect of the sampling rate was also considered negligible. Third, FTM requires more time and procedures (eg, fixing a smartphone with a tripod) compared with FT using a smartphone (Figure 1); however, these additional steps are easy to implement and appear necessary given the remarkable improvement in measurement accuracy. In addition, compared with devices that provide real-time feedback of JH, FTM is slightly time consuming. Therefore, FTM can be the best option for practitioners who spend time with each person in the field and intend to measure JH accurately without expensive devices (eg, force plate or jump mat). Finally, this study did not directly compare FTM with conventional FT using a smartphone application (eg, My Jump); however, when applying traditional FT, the smartphone-based method is inaccurate compared with the force-plate-based method used in this study.10 Consequently, it is reasonable to interpret FTM as a more accurate JH calculation method than the conventional smartphone-based FT.
Practical Applications
This study demonstrated that FTM using the smartphone application JumpEye outperforms the traditional method (ie, FT) using force plates in measuring vertical JH, indicating that FTM is a more valid method than the traditional approach based on foot takeoff and landing when employing smartphone video analysis to obtain flight time for JH measurement. Furthermore, this study established FTM as a highly reliable method. Consequently, practitioners should consider using FTM as a convenient, cost-effective, reliable, and more accurate method for measuring JH in the field.
Conclusion
The new method proposed in this study exhibited superior concurrent validity and high reliability compared with the traditional method in measuring vertical jump height from flight time. Moreover, this new method was unaffected by lower-extremity flexion at landing from the vertical jump.
Acknowledgment
We are grateful to Mr Hikaru Ono, who developed the JumpEye application.
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