Validity of a User-Friendly Spreadsheet Designed for an In-Depth Analysis of Countermovement Bipodal Jumps

Abstract

Countermovement bipodal jumps (CMJs), are widely used for health and performance assessment, but the software required for such analyses is often costly. The study aim was to examine the validity of an Excel/VBA spreadsheet for comprehensive CMJ kinetic analysis. The outcomes have been informed from scientific literature, and the spreadsheet includes modules for data filtering and photogrammetric analysis. To evaluate its validity, 21 participants performed CMJs on a dual force platform system, and the primary outcomes were compared with those derived from prestigious software (MARS 4.0). When jump height was calculated based on take-off speed and flight time the Mean Absolute Errors were 1.79 and 0.69 cm and the minimal detectable changes (MCD) were 1.28 and 0.16 cm. For the propulsive impulse, the error was 5.5 N · s and the MCD was 5.41 N · s. The intraclass correlations were 0.932 (0.902–0.953), 0.984 (0.977–0.989), and 0.940 (0.914–0.959), respectively, demonstrating a strong relationship, and residuals exhibited homoscedasticity. Considering the variability reported in previous studies for intra- and inter-subject comparisons, these errors are minimal, highlighting the spreadsheet’s sensitivity. With its exhaustive analytical capabilities and customizable features, this template serves as a valuable tool for trainers, physiotherapists, and academic teaching settings.

1. Introduction

Physical performance and health evaluation are crucial in both high-performance sports and clinical practice. Jump tests are widely recognized as key indicators of an individual’s functional capacity, explosive strength, and neuromuscular status [1,2]. Prominently, health assessment protocols across diverse populations incorporate jump measurements to assess strength and balance—two fundamental elements in fall prevention and longevity promotion [3]. There is also a relationship between jump height, sprint, and muscular strength, suggesting that jump outcomes could be used as an indicator of sport performance [4]. Furthermore, asymmetries in jump performance, where one limb generates more force than the other, often reflect underlying muscular imbalances or compensatory mechanisms that disproportionately overload one limb, thereby exacerbating the risk of injury in sports and other high-intensity physical activities [5]. These studies emphasize the significance of jump tests as essential tools in both athletic and public health evaluations. An in-depth analysis of the countermovement bipodal jump (CMJ) requires analyzing each leg’s variables in isolation, not only taking into account the magnitude of the ground reaction forces but also the temporal offset between each phase of the dominant and non-dominant leg.

In this context, force platforms are frequently regarded as the benchmark instrument for assessing the kinetic and kinematic variables associated with jumping [6,7]. The accuracy and reliability of the data obtained from these platforms are contingent upon the software employed, as the precision of variable calculations hinges on the formulas utilized [8]. A notable example is Measurement, Analysis, and Reporting Software [MARS 4.0], developed by the esteemed brand Kistler. MARS 4.0 is a comprehensive solution that requires no specialized programming knowledge, making it accessible for broad use in both research and practice [9]. This software facilitates the extraction of a wide array of parameters, including kinematical and temporal parameters or kinetics ones [10]. Among these, two of the most widely used in research are jump height calculated via take-off velocity or flight time [8,11,12,13,14] and propulsive impulse [15,16], which directly influences take-off velocity and, consequently, jump height.

One of the primary challenges associated with software specifically designed to evaluate jumps is its prohibitive cost, with most brands exceeding one thousand euros. Consequently, many coaches and research laboratories with limited budgets find it unaffordable. This underscores the need to develop cost-effective solutions for assessing bipodal CMJs, given the considerable amount scientific literature dedicated to this jumping skill. Conventional spreadsheet-based software (such as Microsoft Excel) offers an alternative, given its widespread availability and user-friendly interface and has been used for complex sport sciences applications [17,18]. Furthermore, Excel includes features that are particularly advantageous in academic settings, such as customizable formulas that can be easily modified and automated (even including more sophisticated script in VBA computer programming language). Indeed, few authors have developed spreadsheets enabling the straightforward calculation of bilateral CMJ parameters, including eccentric and concentric phase impulses, as well as jump height derived from flight time or take-off velocity [19,20]. However, there is currently no solution available that facilitates the assessment of CMJ using a dual-platform system, allowing for the isolated analysis of each leg. In this context, the existing literature emphasizes that the choice between unilateral or bilateral jumps should be dictated by the specific objectives of the study: unilateral CMJ provides a more accurate indicator of individual limb performance, whereas bilateral CMJ offers a broader understanding of inter-limb compensatory strategies [20,21].

The present study aimed to compare, in the particular case of the CMJ, the primary outcomes (jump height and propulsive impulse) generated by an ad hoc spreadsheet with those derived from prestigious software (MARS 4.0). It is hypothesised that the error would be small and that the spreadsheet is sensitive enough to capture changes in future intra- and inter-subject studies. Given that the spreadsheet allows a good number of variables to be calculated and that it is customizable, its use can be extended to rehabilitation, sports performance, and academic teaching settings.

2. Materials and Methods

This cross-sectional observational study examined the differences between reliable, valid, and user-friendly software (MARS 4.0; Milwaukee, WI, USA) and a freely available, ad hoc Excel/VBA spreadsheet (Excel version: Microsoft^® Excel^® LTSC MSO [16.0.14332.20824] 64-bit) for the analysis of jumping biomechanics. MARS 4.0 software has demonstrated high intra-subject reliability [9] and has been utilized in studies evaluating the validity of various instruments [22]. Due to its proven reliability and widespread use in the field, MARS 4.0 software could be regarded as a benchmark in biomechanical assessments.

2.1. Sample

This study was conducted with a cohort of 21 healthy and physically active male students from the Faculty of Sports Sciences at the University of Granada, aged between 18 and 25. Participants had to meet the following inclusion criteria: (i) being young, healthy adults aged 18 to 30 years, without musculoskeletal dysfunction. Subjects with any of the following criteria were excluded: (i) surgical interventions in the last six months, (ii) any disability that made it difficult to perform the tests correctly, (iii) any pain that could affect the outcome of the tests, (iv) the technical inability to execute a CMJ jump. None of the participants had experienced any musculoskeletal injury in the three months preceding this study that could potentially impair their jumping ability. Participants were informed of the benefits and risks of the investigation prior to signing an institutionally approved informed consent form. This study adhered to the ethical guidelines outlined in the Declaration of Helsinki for human research and was approved by the Research Ethics Committee of the University of Granada (nº: 687/CEIH/2018).

2.2. Instruments

The tools employed in this study included MARS 4.0 software, an Excel/VBA spreadsheet (including VBA script), and a force platform. Kistler MARS 4.0 (Measurement, Analysis, and Reporting Software) encompasses various kinetic analysis modules, including ones specifically for jump analysis (e.g., CMJ, Squat, Drop Jump, and Hop Jump) [10]. In this study, in addition to the MARS 4.0 analysis itself, the data for each jump were imported into the custom-made Excel/VBA spreadsheet. A selected set of variables was then calculated and compared with the MARS 4.0 outcomes: (i) jump height computed from take-off velocity, (ii) jump height computed from flight time, and (iii) force impulse between maximal force and take-off. This last variable was used as an approximation of the propulsive impulse, since MARS 4.0 does not provide this variable directly, and it was assumed that the propulsive phase begins approximately when the force reaches its maximum positive value. The force platform utilized in this research was a Kistler 9286BA (60 × 40 × 3.5 cm; Winterthur, Switzerland), a portable piezoelectric force platform with a maximum sampling frequency of 1000 Hz, a 16-bit AD converter, and a voltage range of ±10 volts. Kistler is an internationally recognized brand, and its platforms have been employed as benchmark systems in studies validating jump height assessment instruments [8,22].

The following subsection provides a detailed explanation of the use of the ad hoc Excel/VBA spreadsheet, enabling other researchers to effectively implement it. The structure and usage of the spreadsheet will be thoroughly discussed. Additionally, the spreadsheet, accompanied by two video tutorials, some CMJ force data examples (in .txt format), and a pdf document including a list of the variables provided with percentiles (based on the 105 jumps recorded for this study) is available as Supplementary Material.

2.2.1. Structure and Use of the Excel/VBA Spreadsheet

The Excel/VBA tool has several sheets and VBA modules with comments explaining the function of each of these modules. The Excel/VBA tool sheets are as follows: (i) Import data (Sheet 1), were data obtained from a force plate and can be imported (based on VBA open code); (ii) Input (Sheet 2), a sheet that contains the force data from both plates, copied directly from the sheet Import data or pasted by the user; (iii) CMJ analysis (Sheet 3), the sheet containing the formulas and graphs necessary for performing the analysis; (iv) Report (Sheet 4), a sheet that can be printed, and that includes some CMJ outcomes; (v) Percentiles (Sheet 5), for the variables computed by the spreadsheet based on the data of the present manuscript (same as included in Supplementary Material); (vi) Photo analysis (Sheet 6), where a photogrammetric analysis can be performed based on a photo sequence of the jump; (vii) Database (Sheet 7), where the variables extracted from each jump can be stored; and (viii) Help! How to set the landmarks (Sheet 8) and (ix) Help! How to know photo path (Sheet 9), which provide brief instructions for selecting the landmarks (events) required to perform the jump analysis and to select the path of the photo sequence. Sheets 1, 2, and 3 are explained in further detail below, while sheets 4, 5, 7, and 8 do not require user manipulation or are simple to manage. Sheet 6 will be explained in another subsection.

Sheet 1 (Import_data) facilitates the uploading and filtering of data from a .txt file, a common format used by many tools. The sheet is designed to import .txt files from two force data logging software programs, MARS 4.0 and Bioware (V5.4.2.0, Kistler Ibérica SL, Barcelona, Spain). The data are organized according to the .txt file format. For example, the MARS 4.0 software generates a .txt file containing four columns: the time column, which records the time data for each entry; the Fz (N) column, which presents the resultant force values from the two platforms used; the FzLeft (N) column, which displays the force data on the Z-axis of the left-leg force platform; and the FzRight (N) column, which shows the force data on the Z-axis of the right-leg platform. All the forces represent the vertical ground reaction force. If users want to import the data in another format, they have to modify the VBA script (it does not require high level programming knowledge). The Excel/VBA spreadsheet includes a fourth-order zero-phase shift Butterworth low-pass data noise filter with a user-defined cut-off frequency, implemented in VBA by Van Wassenbergh [23] and based on the book of Winter [24].

On Sheet 2 (Input), data from the Import Data sheet is reorganized to derive the kinetic variables of the CMJ. The user must specify the platform’s sampling frequency in cell E1 and the gravitational acceleration value in m · s⁻² in cell E3.

Sheet 3 (CMJ Analysis) is crucial for performing the kinetic analysis of the jump. It relies on Excel formulas and VBA programming. A video demonstrating the tool’s usage and sample files with jump kinetic data are provided as supplementary materials. To assist users in understanding these instructions, different cell ranges (matrices) are color-coded, and plots are outlined in various tones (see Figure 1):

• List of matrices: Orange Matrix (A1:C13), Green Matrix (A19:I5020), White Matrix (J19:K5020), Grey Matrix A (L19:Q5020) and Grey Matrix B (AD1:AY11), Blue Matrix A (R19:W5020) and Blue Matrix B (AD67:AY77), and Red Matrix A (X19:AZ5020) and Red Matrix B (AD132:AY142).
• List of plots: Pink Border Plot (in cells range D1:R14), Black Border Plot (in cells range AD21:AW63), Blue Border Plot (in cells range AD87:AW189), and Red Border Plot (in cell range AD151:AW194).

The first step for the user is to click on the button Manual Calculation (cell B1) to prevent the sheet from performing calculations that could potentially freeze the program when modifying the data in the graphs. After this, in the Pink Border Plot (Figure 2), the following parameters should be determined using the corresponding slider bars located below that plot: (i) the start of the baseline (marker B1), which will facilitate the estimation of body weight; (ii) the end of the baseline (marker B2), which should be approximately two seconds from point B1 (or 2000 samples if the platform records at 1000 Hz); (iii) the start of the jump (marker labelled as Start in the graph), just before the countermovement phase; and (iv) the end of the jump (marker labelled as Finish in the graph), once the force returns to the subject’s weight (or a position close to it). The data selected from the graph between the Start and Finish points will be displayed in the Black Border Plot, Blue Border Plot, and Red Border Plot. Once these four points have been selected, the Automatic Calculation Button can then be clicked.

The user of the Excel/VBA spreadsheet will then mark the start and end of the x-axis on the chart (to calibrate the length of that axis and compute a scaling factor in cell BF2 that transforms pixels into graph coordinates) and the ten key points of the CMJ (Figure 3) [19]:

• Unweighting phase start. The beginning of the CMJ or the start of the negative impulse phase.
• Braking phase start (or positive impulse start). The end of the negative impulse phase.
• Propulsive phase start. The end of the countermovement phase, where the velocity equals zero and the negative phase impulse equals the positive phase impulse.
• Positive impulse finish (the force signal crosses the baseline).
• Flight phase start. The moment when the take-off begins and the platform does not register any force.
• Landing time start (or braking landing impulse start). When contact with the platform is re-established.
• Landing positive impulse start. The start of the positive impulse during landing.
• Braking landing impulse finish (or repositioning phase start). The end of the braking phase (the velocity equals zero).
• Landing positive impulse finish (or unweighting phase start). When the force signal crosses the baseline again.
• Landing unweighting phase end. The end of the CMJ.

To position the key points on the graphs, simply click on the graph at the desired key point location. It is possible to utilize the controls located in cells AW17:AZ17, AW84:AZ84, and AW149:AZ149 to fine-tune the position of the points. In cells AW17, AW84, and AW149 the user selects the point they wish to modify, and in cells AZ17, AZ84, and AZ149, they specify the number of frames the point steps forward or backward on the plot. If there is any previous data, it is possible to delete it by pressing the control near the bottom-right corner, which includes a counter for the number of points selected, ranging from zero to twelve (with two points used for calibration and ten as key points or landmarks).

To check that the key points have been chosen correctly, the user should look at cells AE14, AE17, and AQ15 for the total force, cells AE80, AE83, and AQ82 in the case of the left-leg platform, and cells AE145, AE148, and AQ146 in the case of the right-leg platform. The values in these cells are calculated by subtracting the following: (i) the unweighting phase impulse and the braking phase impulse (cells AE14, AE80, and AE145); (ii) the propulsive positive impulse and the jump break phase impulse (cells AE17, AE83, and AE148); and (iii) the repositioning impulse and the landing unweighting phase impulse (cells AQ15, AQ82, and AQ146). The subtraction of these force impulses must be as close to zero as possible. It will almost never be possible for the value to be zero, due to factors such as sampling frequency (perhaps not sufficient to capture all of the force signal data) or deformation of the shoe sole (causing not all of the force to be applied to accelerate the center of mass). For the selection of the unweighting phase start (event 1) and the take-off time (event 5) the user must also look at cells AJ14, AJ17, AJ80, AJ83, AJ145, and AJ148, where the resultant force (in Newtons) in the unweighting phase start and the difference (in Newtons) between resultant force and half body weight in the flight phase start are displayed. A number of research studies have analyzed the influence of these thresholds on the reliability and magnitude of CMJ outcomes and are recommended to be reviewed for a more precise analysis [25,26].

The pixel data are generated in column BD2:BD13, and the data are then converted into real coordinates in cells BE2:BE13 (based on the scale factor calculated in cell BF2). The user should repeat this procedure to analyze the data for each platform separately in the Blue Border Plot and the Red Border Plot (to analyze the phases of each leg). If the user wants to perform the analysis based on global force data (without considering the data from each platform in isolation), they should paste the data into cells BI and BN. This approach may be useful for studying the contribution of each leg during each phase of the CMJ. If the user wishes to examine the time lag between the two legs, it would be more convenient to perform the analysis separately for each platform.

The computation of both continuous signals and discrete variables is detailed in the following two subsections.

2.2.2. Continuous Kinetic Variables Computation Formulas

The Orange Matrix contains a series of data necessary for calculating the kinetic variables: (i) in cell B4, the acceleration of gravity; (ii) in cells B5 and B6, the time at the start and end of the baseline measurement; (iii) in cells C5 and C6, the force at those moments; (iv) in cells B7 and B8 and C7 and C8, the time at the start and end of the jump and the corresponding force values; and (v) in cells B9 and B13, a series of variables related to body weight:

• Cell B9. The weight in Newtons is calculated based on the values between points B1 and B2 (baseline) on the pink-bordered graph.
• Cell B10. The body mass in kg is determined from the weight (cell B9) and the acceleration of gravity (cell B4).
• Cells B11 and B12 display the weight recorded with an external scale, indicated on the Input sheet, which serves as a confirmatory measure to ensure consistency with the calculated weight value.
• Cell B13 contains half of the body weight.

To calculate the kinetic variables of the CMJ, velocity and displacement at each instant are determined through an integration process based on instantaneous acceleration. This process is explained in detail below. The sheet is designed to accommodate up to 5000 records. If the platform records at 1,000 Hz, this corresponds to a recording duration of 5 s (with each row representing one millisecond). The sampling number is displayed in the Green Matrix, column A. Columns B, C, E, and F contain data from the “Input” sheet. Columns D, F, and H calculate the resultant force: column D shows the resultant force by subtracting the force recorded by the platform from the participant’s weight (column D) or half of the body weight (columns F and H). The White Matrix displays the rows containing the jump data, as selected on the Pink Border Plot. The Grey Matrix shows data from the resultant force (limited to data selected in the Pink Border Plot), the Blue Matrix displays data from the force platform under the left leg, and the Red Matrix includes data from the force platform under the right leg.

Columns L, R, and X display the instantaneous total resultant force, the force recorded on the left platform and the force on the right platform, respectively. Columns M, S, and Y contain the instantaneous acceleration data, calculated by dividing the instantaneous force by the weight. Columns N, T, and Z present the instantaneous velocity, derived from the instantaneous acceleration and the velocity of the preceding row. In columns O, U, and AA, displacement is calculated using the instantaneous velocity and the displacement from the previous row. The instantaneous power (columns P, V, and AB) is determined based on the instantaneous force and velocity. Finally, the instantaneous impulse (columns Q, W, and AC) is computed using the instantaneous force and the sampling frequency. All these calculations are summarized in

Table 1. Computation of the continuous kinetic variables.

Matrix	Variable		Excel Col.		Computation
Grey	Net resultant force		D, L		Subtracting the participant’s weight to the resultant force at each instant
	Acceleration of the GC		M		By dividing the net resultant force at each instant by the weight of the participant
	Velocity of the GC		N		Adding to the instantaneous velocity at previous record, the instantaneous acceleration multiplied by the time of one record
	Displacement of the CG		O		Adding to the instantaneous displacement at previous record, the instantaneous velocity multiplied by the time of one record
	Instantaneous power of the CG		P		Multiplying the net resultant force at each instant by the velocity of the CG at each instant
	Instantaneous impulse of the CG		Q		Multiplying the net resultant force at each instant by the time of one record
Blue A and Red A	Net resultant force of the left/right body side		F, H, R, X		Subtracting half of the body weight to the left or right force at each instant
	Left or right body side acceleration		S, Y		By dividing the net left/right force at each instant by half of the body weight
	Instantaneous velocity of the left or right body side		T, Z		Adding to the instantaneous velocity of the left or right body side in the previous record, the instantaneous acceleration of the left or right body side multiplied by the time of one record
	Displacement of the left or right body side		U, AA		Adding to the instantaneous displacement in the previous record, the instantaneous velocity of the left or right body side multiplied by the time of one record
	Instantaneous power of the left or right body side		V, AB		Multiplying the net resultant force of the left or right body side at each instant by the velocity of the left or right body side at each instant
	Instantaneous impulse of the left or right body side		W, AC		Multiplying the net resultant force of the left or right body side at each instant by the time of one record

.

2.2.3. Discrete Kinetic Variables Computation Formulas

In the Grey Matrix B, several variables related to the quality of the jump are calculated, taking into account the resultant force. Columns AE and AF list the names and numbers of each key event of the jump. The AG column indicates the row number or sample in which the event appears, while the AH column specifies the second in which the event occurs. Further important discrete variables are detailed in

Table 2. Computation of the discrete kinetic variables.

Matrix	Variable		Excel Column		Computation
Grey B, Blue B, and Red B	Partial impulses		AJ		Sum of the instantaneous impulses between the two selected events
	Propulsive average velocity and braking average velocity		AL		Averaging the velocity values between the start of the propulsive phase and the start of the flight phase and between the start of landing and the end of the braking phase
	Average Force		AN		Dividing the impulse of each phase by the phase duration
	Average Power		AO		Multiplying the average force in each phase by the average velocity in each phase

.

The total analysis time of a CMJ using this tool is under five minutes, as demonstrated in the Supplementary Video that explains the use of this spreadsheet. The Excel spreadsheet produces a report table containing several computed parameters (

Table 3. Report generated by the Excel/VBA spreadsheet (example of a CMJ).

General Measures		Phase Delays (ms)
Excentric impulse (N · s)	113.5	Unweighting phase start	−51
Propulsive impulse (N · s)	194.0	Braking phase start delay	35
Impulse ratio	0.585	Positive impulse finish	−5
Take-off speed (m/s)	2.62	Flight phase start	−5
Jump height with initial velocity (cm)	35.14	Landing time start delay	−5
Flight time (Sec)	0.57	Landing positive impulse start delay	0
Jump height with flight time (m)	39.94	Braking landing impulse finish delay	−289
Propulsive relative power (W/kg)	14.8	Landing positive impulse finish delay	−282
Landing positive impulse (N · s)	308.6	Landing unweighting phase end delay	−15
Landing peak force (N)	1117.9	Phase duration differences (ms)
Left-leg negative impulse (N · s)	−61.6	Unweighting phase start	86
Right-leg negative impulse (N · s)	−47.2	Braking phase start delay	−30
Inter-leg negative impulse asymmetry (R-L) (%)	26.5	Positive impulse finish	0
Left-leg positive impulse (N · s)	106.6	Flight phase start	0
Right-leg positive impulse (N · s)	200.2	Landing time start delay	5
Inter-leg positive impulse asymmetry (R-L) (%)	−61.0	Landing positive impulse start delay	−289
Left-leg landing positive impulse (N · s)	58.76	Braking landing impulse finish delay	7
Right-leg landing positive impulse (N · s)	230.7	Landing positive impulse finish delay	267
Inter-leg landing PI asymmetry (R-L) (%)	−118.8	Landing unweighting phase end delay	0
Landing force peak Left leg (R-L) (N)	343.6
Landing force peak Right leg (R-L) (N)	791.0
Landing force peak asymmetry (R-L) (%)	−78.9

) included in the MARS 4.0 software, many of them are extensively used in the literature [27].

2.2.4. Performing a Photogrammetric Analysis

As mentioned above, the Excel/VBA template allows for an additional photogrammetric analysis in Sheet 6, Photo analysis. This can be useful to check that the CMJ has been performed correctly, to provide feedback to the participant being evaluated, to check that the events have been marked correctly, or for educational purposes, to show the start and end frame of each phase.

This analysis requires recording a photo sequence of the CMJ, which must be saved in the computer folder where the Excel file is located. Each photo should be numbered as Photo (1), Photo (2), etc. This is easily performed in the Window environment by selecting all the photos and naming the first one as Photo (1). Once this is performed, the user should modify cells C1 (selecting the variable number from the range A3:A7, which will be synchronized with the photo frame in the graph on the right), I1 (it is recommended to see Sheet 9 Help! How to know the path of the photo), I2, I4, and Q3 (selecting the frame of the associated folder where the take-off of the CMJ takes place). Next, the user must modify the maximum value of scroll bar 1 by right-clicking on it and setting the maximum value equal to the number of photos in the associated folder. Finally, it is possible to navigate between frames by clicking on the rotate button or the scroll button. In the graph on the right there is a red dot corresponding to the CMJ photo frame (Figure 4).

2.3. Procedures to Analyze the Validity of the Spreadsheet

After a standardized warm-up—comprising five minutes of continuous running, a protocol of five minutes of dynamic stretching targeting the muscles most engaged during the jumps, and five CMJs—the participants undertook the jumping protocol. The data were recorded using MARS 4.0 software, which provides several variables semi-automatically. The raw force data was also imported into the ad hoc Excel/VBA spreadsheet, filtered with a cut-off frequency of 100 Hz [28] and analyzed. Jump height, determined from take-off velocity or flight time, and propulsive impulse outcomes were compared between MARS 4.0 and the ad hoc spreadsheet.

Prior to the jump, the following instruction was given: “Jump as high as you can, initiating the jump from an upright stance and with hands on the hips and performing a countermovement”. The CMJ should be performed involving a rapid downward movement followed by an upward movement (countermovement) to utilize the elastic component of the musculature for achieving a greater jump height. The participants were instructed to hold a static position for approximately two seconds before the jump to establish a baseline for calculating body weight. Each participant performed five jumps, with a two-minute rest between each. If the subject mistakenly performed arm swings during the jump, it was repeated.

2.4. Statistical Analysis

All the statistical analyses were conducted using Microsoft Excel 2018. All the data were tested for normality with a visual inspection of the QQ-plots and of the histograms. To compare the results from the Excel/VBA spreadsheet with those from the MARS 4.0 software, the following statistical issues were analyzed for each of the variables: (i) the residual homoscedasticity via Bland–Altman plots including the regression lines for the residuals; (ii) the magnitude of the error in both absolute and relative terms with the Mean Absolute Errors (MAE), Standard Error of Measurement (SEM), and Percentage Mean Absolute Error relative to the average measurement obtained with the MARS 4.0 software (PMAE); (iii) the level of agreement based on the Lin’s intraclass correlation coefficient (Lin CCC) with the 95% confidence intervals. The strength of agreement for the Lin CCC was categorized as follows: > 0.8, very strong; 0.6–0.8, strong; 0.4–0.6, medium; 0.2–0.4, weak; <0.2, very weak [29]. Finally, to determine the magnitude of change that would exceed the threshold of measurement error [30], the minimal detectable change (MDC) as a 90% and 95% confidence interval (MCD₉₀ and MCD₉₅) was calculated. It was performed with the following formulas: MCD₉₀ = SEM ⋅ √2 ⋅ 1.65 and MCD₉₅ = SEM ⋅ √2 ⋅ 1.96.

3. Results

The means and standard deviations of the height obtained with MARS 4.0 and with the ad hoc Excel/VBA spreadsheet were 36.5 ± 7.3 cm and 37.2 ± 7.2 cm when calculated using take-off velocity and 36.5 ± 6.6 cm and 35.8 ± 6.6 cm when calculated using flight time. The mean propulsive impulse was 207 ± 20 N ⋅ s and 209 ± 20 N ⋅ s.

For jump height calculated based on take-off velocity, the MAE was 1.79 cm (PMAE was 4.92%). In contrast, for jump height calculated based on flight time, the MAE and PMAE were lower, 0.69 cm and 1.89%, respectively. For the propulsive impulse, the MAE was 5.5 N ⋅ s (PMAE = 2.66%). All Lin’s CCC values indicated a very strong relationship. The statistical parameters, including the 95% confidence interval for the Lin CCC, the SEM, and the minimal detectable changes, are included in

Table 4. Statistical parameters used to evaluate the spreadsheet’s validity.

Variable		Statistical Parameter
		Reliability		Error (cm)			* MCD (cm)
		Lin CCC (95% CI)		MAE	SEM		MDC90	MDC95
Jump height from take-off velocity		0.932 (0.902–0.953)		1.79	0.55		1.28	1.52
Jump height from flight time		0.984 (0.977–0.989)		0.69	0.07		0.16	0.19
Propulsive impulse		0.940 (0.914–0.959)		5.5	1.95		4.55	5.41

* Lin’s concordance correlation coefficient with the lower and upper ends of the 95% confidence interval; * MDC: minimal detectable change; MAE: Mean Absolute Error; SEM: Systematic Error of Measurement.

.

Residuals depicted in the Bland–Altman plots appeared homoscedastic for all three variables (and the associated regression lines did not exhibit any linear relationship), indicating that the differences between MARS 4.0 and the ad hoc Excel/VBA spreadsheet were not dependent on the magnitude of the measurement (see Figure 5, Figure 6 and Figure 7).

4. Discussion

This study introduces a custom Excel/VBA spreadsheet designed specifically for the analysis of dual platform countermovement bipodal jumps, offering a cost-effective and accessible alternative to high-end software solutions. The manual identification of key events during the jump, which can be completed in less than five minutes, allows for the extraction of a wide range of biomechanical variables. These variables are summarized in a printable format, integrating data from both force platforms while also allowing for the individual analysis of each leg’s function during the jump. The comparison between the ad hoc Excel/VBA spreadsheet and the prestigious software (MARS 4.0), recognized as a benchmark in biomechanics laboratories, revealed small differences. The difference in jump height estimated using flight time was less than one centimeter, and less than two centimeters when estimated using take-off velocity, corresponding to relative errors of approximately 2% and 4%, respectively. The propulsive impulse showed a difference of approximately 5 N ⋅ s, with a relative error of about 2.5%. These findings suggested that the custom spreadsheet provided accurate results, making it a viable option for laboratories and researchers with limited resources.

When assessing the magnitude of these errors, it is essential to consider the typical between-group and within-subject differences reported in the literature. In other words, coaches and scientists must avoid measurement errors larger than the differences they intend to measure [31,32]. For example, a researcher intending to use the ad hoc Excel/VBA spreadsheet for a specific aim should carefully consider the magnitude of error relative to the differences found in similar studies. Regarding jump height, a difference of approximately 1.8 cm was observed when using take-off velocity for estimation and of 0.7 cm when using flight time. Some scientific literature results are discussed below, in which the use of the ad hoc Excel/VBA spreadsheet would be recommended or not. In a study by Markström and Olsson [11] comparing jump performance between throwers and sprinters, the sprinters exhibited a jump height approximately 10 cm greater (35 cm vs. 45 cm). Similarly, in a study by Mihalik et al. [13], a four-week training program incorporating resistance and plyometric exercises, with a frequency of two days per week, demonstrated improvements in jump height ranging from 3 to 5 cm after three weeks. Both examples show differences larger than the spreadsheet errors of 1.8 cm when using take-off speed to estimate jump height and 0.7 cm when using flight time, indicating that it is sensitive enough to accurately detect these variations. In addition, a shoe with higher bending stiffness improved jump height by an average of 1.7 cm [14]. While this improvement exceeds the 0.7 cm error associated with the Excel/VBA spreadsheet using flight time, it is very close to the 1.8 cm error observed when using take-off speed, suggesting that the latter method may not be suitable for such studies. Moreover, Markovic [33] assessed the effects of plyometric and concentric exercise programs lasting between 6 and 12 weeks, finding jump height improvements of approximately 5% to 10% (equating to 2–6 cm). These percentage increases are substantially higher than the percentage error for jump height obtained with the Excel/VBA spreadsheet using flight time, confirming its adequacy for such assessments. However, when take-off speed is used, the percentage error (≈4%) is lower than that reported in most studies included in the meta-analysis but is comparable to those with the smallest improvements. In these latter cases, the use of take-off speed for estimation is not recommended. In a study examining within-subjects jump height changes across sessions, systematic biases of 1.3 cm were found [12]. These biases exceed the Standard Error of Measurement (SEM) of the ad hoc Excel/VBA spreadsheet, whether using take-off velocity or flight time to estimate jump height. The MCD₉₀ and MCD₉₅ confirm that the spreadsheet is capable of detecting most of the changes discussed, as it can detect changes in jump height of 1.28 or 1.52 cm and 0.16 or 0.19 cm when using the take-off velocity or the flight time, respectively.

Regarding propulsive impulse, fewer studies have focused on this variable, possibly due to the relative ease and interpretability of measuring jump height. Since the MARS 4.0 software does not provide a propulsive impulse measurement directly, the force impulse from maximal force to take-off was used as an approximation. Given that propulsive impulse directly determines take-off velocity and consequently flight height, it is arguably a more direct and potentially less error-prone variable than flight time [34]. An observational study reported propulsive-concentric impulses of 171.18 ± 38.6 N · s in females and 254.1 ± 37.46 N · s in males [35], so the ad hoc Excel/VBA spreadsheet could detect these differences, because it showed a margin of error of 5 N · s. In other related research, the platform recorded concentric impulse values of approximately 230 ± 50 N · s in CMJs [16]. This standard deviation (50 N · s), encompassing both random and systematic errors, is significantly higher than the Excel/VBA spreadsheet’s 5 N · s error, indicating that this can be considered a minimal error. Furthermore, the use of arm swing on concentric impulse allows for a gain in propulsive impulse of about 30 N · s [15], a difference also detectable by the Excel/VBA spreadsheet. In this case, the MDC₉₀ and the MDC₉₅ indicated that a change greater than 4.55 or 5.41 N · s would be required to be certain that the change is not due to measurement error when using the spreadsheet. These values are also below the differences in the means of the studies used as examples, confirming the sensitivity of the measurement.

The present study was not exempt from limitations. Firstly, this study’s focus on young, healthy male participants limits its applicability to other groups. Although the Bland–Altman plots did not show any kind of tendency on the residuals, it would be necessary to study whether the template is still accurate with lower jump heights, achieved, for example, by children or sedentary people or even with athletic jumpers reaching greater jump heights. Although no statistical power study was conducted, the sample size was similar to that of studies analysing jumping assessment instruments or procedures [8,25,26,28]. In addition, the events are marked based on visual observation of the signal and there exists a human error that has to be considered. Manual marking of CMJ phases could introduce subjectivity and inconsistencies, particularly for inexperienced users. Such error can be assessed by comparing the marking of events with a fully automatic system and also by performing intra- and inter-rater reliability studies. Nevertheless, the sheet includes calculations that attempt to minimize such error. In particular, three subtractions of force impulses are calculated which should be the closest possible to zero, explained at the end of the Section 2.2.1. On the other hand, considering its wide use in research, only one brand and one force platform software (Kistler and MARS 4.0) was used, and it would be interesting to analyse whether other systems could provide similar accurate results. Finally, a fourth-order, zero-phase-shift Butterworth low-pass filter was selected, based on a previous study [28], but perhaps other types of filters would have been more appropriate (e.g., an adaptive filter [23] or a residual-based filter).

Despite these limitations a notable advantage of the custom Excel/VBA spreadsheet is its adaptability and ease of use. Unlike more complex mathematical software (e.g., MATLAB or Python), it does not require extensive programming expertise, making it accessible to a broader range of users, including those in educational settings (i.e., in university degrees such Sports Science, Kinesiology, or Physiotherapy). The flexibility of the spreadsheet allows researchers to tailor the analysis to specific research questions or educational objectives, enhancing its utility in both research and teaching environments. This is particularly valuable in settings where the budget for specialized software is limited, yet there is a need for reliable and valid biomechanical analysis tools. Furthermore, the spreadsheet’s ability to analyze each leg separately during bipodal jumps offers insights into inter-limb coordination and asymmetries. This feature is crucial for identifying compensatory strategies or imbalances that could predispose athletes to injury [35,36]. While the current study focused on jump height and propulsive impulse, future research could expand the validation of this tool to include other kinetic variables, such as rate of force development, explore its reliability across different populations and conditions, or compare the accuracy with that of systems such as 2D and 3D photogrammetry or inertial sensors. The spreadsheet could also provide several physical outcomes useful for training or rehabilitation purposes such as (i) muscle power, (ii) rate of force development, (iii) impact peaks upon landing, (iv) outcomes related to the degree of muscle recovery, or (v) the improvements in muscle strength or jumping ability following an intervention program. It can also be utilized to assess specific research issues such as (i) the effect of different plyometric jump programs on asymmetries [37]; (ii) the inter-limb coordination during jumping, which can also be used as a measure of neuromuscular fatigue e.g., generated by competition [38]; (iii) the effects of shoe soles designed to minimize energy dissipation and improve the jumping performance [14]; or the relation between inter-limb asymmetries and jumping performance [39]. Additionally, inter-rater and intra-rater reliability studies could further establish the robustness of this tool, ensuring its broader applicability in diverse research contexts. Moreover, it is noteworthy that, in the past, the high cost of force plates often restricted their accessibility, compelling modest laboratories to rely on photogrammetric systems or contact mats for jump evaluations. However, with the recent availability of force plates priced under USD 1,000, the utilization of conventional spreadsheets becomes increasingly relevant.

5. Conclusions

This study presented a user-friendly and customizable Excel/VBA spreadsheet designed for detailed jump kinetic analysis using a dual force platform system. The results demonstrated that the spreadsheet produced small errors in calculating jump height—whether based on flight time or take-off velocity—and in estimating propulsive impulse. These small errors, coupled with high intraclass correlation coefficients and homoscedastic residuals, suggest that the tool is adequate for a number of practical applications.

While further validation is required, the custom spreadsheet offers a robust, cost-effective alternative to commercial software for analyzing dual-platform, bipodal jumps. Its accessibility, adaptability, and precision make it a valuable resource for trainers, researchers, and educators.