Enriching Medicine Ball Throw with Anthropometric Information: An Alternative Assessment Method

doi:10.21203/rs.3.rs-8419104/v1

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Enriching Medicine Ball Throw with Anthropometric Information: An Alternative Assessment Method

https://doi.org/10.21203/rs.3.rs-8419104/v1

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Medicine ball throw (MBT) is a simple, fast and cost-effective field measurement method used to assess the explosive strength of the upper body strength based on throwing distance. Body weight and height have been identified as influencing factors of the traditional measure of distance thrown (MBT_T) with advantages for heavier and taller children. We designed three alternative indices taking into account body mass and height (MBT_A1 = MBT_T / (mass × height)), height-to-mass ratio (HMR) (MBT_A2 = MBT_T × HMR), or body mass index (BMI) (MBT_A3 = MBT_T / BMI). The validity of the four MBT indices was examined in linear mixed models (LMMs) and compared to achievements in other standard fitness tests (6-minute run, standing long jump, sideways jump, 4 × 10 m shuttle run, push-ups). The sample consisted of 821 Austrian primary school children, aged 7 to 10 years, from grades 2 and 3. The three anthropometrically enriched MBT_A yielded significantly better goodness of fit than MBT_T; MBT_A1 fitted best among the three MBT_A variants. When, alternatively, MBT measures were included as a covariate rather than a dependent variable in a second set of LMMs, MBT_A2 had the best goodness of fit. Results were replicated in a second sample of 173 secondary-school and 178 high-school students with standing long jump and push-up as physical fitness tasks. We recommend to enrich MBT_T with body weight and body height data to achieve a fair and realistic assessment of the explosive strength of the upper extremities.

General Practice

Pediatrics

Sports Medicine and Kinesiology

Special Education

Health Economics & Outcomes Research

Preventive Medicine

Medicine ball throw

physical fitness

assessment

children

adolescents

fair assessment

Globally, the prevalence of obesity and extreme obesity has risen alarmingly in recent years. (1) Increased body mass index (BMI) values, waist circumference, and body fat percentage are positively correlated with reduced fitness and a higher prevalence of metabolic syndrome later in life. (2) Physical fitness in childhood is considered an important health indicator (3), and childhood obesity is associated with cardiovascular risk factors (4) and coronary heart disease. (5) Strategies are being implemented and interventions launched in schools worldwide with the aim of establishing suitable countermeasures against the spreading obesity pandemic and the associated low levels of physical fitness by improving nutritional awareness and increasing physical activity levels in early childhood. (6, 7) These strategies and interventions, as well as physical development in childhood and adolescence, are monitored and assessed by widespread national and international fitness monitoring systems. (8)

The fitness tests used in these monitoring systems should be reliable, valid, ´easy to carry out, and cost-effective so that they can be used throughout the country. (9) Alongside anthropometric parameters, comprehensive fitness monitoring also includes assessing physical fitness parameters such as endurance, strength, speed, flexibility, and coordination. (10)

In field tests, the parameter “strength” distinguishes between explosive strength and strength endurance, static and dynamic strength, as well as lower and upper body strength. (11) There are a variety of field tests that can be used to assess upper body strength. (11, 12) The feasibility of these tests is a key criterion for their practical implementation, however, some of these tests are less suitable for a wide use as field tests in schools, as they lead to long group test times (holding in the forearm support, holding in the hang), generate high material costs (hand strength measurement with dynamometer), or cannot be carried out everywhere due to a lack of equipment (e.g., pull-ups in primary schools). (13)

Physical fitness (PF) in children is well characterized by a latent construct of tasks comprising endurance, coordination, speed, and leg-muscle power. (14) One of the prime indicators of upper arm muscle power, the medicine ball throw (MBT), however, does not fit to align with performance profile in other physical fitness tasks, specifically cardiorespiratory endurance, lower body strength, body coordination, action speed and upper body muscular endurance. (14) Indeed, it shows a qualitatively different relation to anthropometric indicators such as body height (H_B), body mass (M_B), BMI or HMR. (14) Whereas the former four tasks all show concave functions with strongly decreasing fitness for high values of mass and BMI, MBT performance increases with H_B, M_B, and BMI. (15, 16). Trivially, reasons for this divergence are that MBT favors overweight children due to Newton’s law and is also the only task that does not require to move their own weight during task execution. (15) However, arm muscle power is also an indicator of physical fitness. When compared with the other tasks it is the one that can be assessed with the least effort. Therefore, it is desirable to keep the MBT as a test item in the assessment of children’s physical fitness.

To this end, we propose to enrich the traditional assessment of MBT (MBT_T) with distance thrown with the anthropometric measures of mass and height, yielding alternative indices of MBT enriched with anthropometric information (MBT_A). Thus, the aim of this study was to investigate whether MBT_A aligns better with the BMI-, gender-, and age-related profile of standard fitness tasks (i.e., 6-minute run, standing long jump, jumping sideways, 4 x 10m shuttle run, and push-up) than MBT_T. As a corollary, we also tried to find out whether they serve as a more efficient predictor of performance in these four tasks. The generalizability of the findings was assessed using data from two cross-sectional studies that differed in age range, type of school and tasks assessed.

Study participants

The participants of this secondary analysis were selected from two different study populations (Jarnig et al. 2021 (17) (study population 1 (SP1); N=821)) and Jarnig et al. 2025 (18) (study population 2 (SP2)); N=354). Both studies were approved by the Research Ethics Committee of the University of Graz, Styria, Austria. For all participants included in the analysis, active consent to participate in the study was given by their legal guardians or, in the case of adolescents older than 14 years, by the adolescents themselves, as well as information on age, sex, and type of school (see Figure 1)

Analyses were performed with data from the primary school children participated in SP1. SP2 data from 178 secondary-school and 176 high-school children were used to test the generalizability of findings to older children.

Procedure

Measurements of anthropometric parameters and fitness tasks were carried out by trained members of the research team and took place at schools during physical education classes. All tests were carried out in sport halls with participants wearing standard sports clothing but no shoes (except the 6-minute run (6MR), which was done in sneakers.).

Anthropometrics

Body height (cm) was measured to the nearest 0.1 cm using a stadiometer (SECA 213, Hamburg, Germany), and body weight (kg) was measured to the nearest 0.1 kg using an electronic scale (BOSCH PPW4202/01, Nuremberg, Germany). BMI was calculated by dividing body weight by height in meters squared.

Fitness assessments in SP1

Cardiorespiratory endurance was assessed with the six-minute run (6MR), lower body strength with standing long jump (SLJ), upper body strength with standing1-kg medicine ball chest throw (MBT_SCT-1kg), body coordination with jumping sideways test (JS), and action speed with 4×10-meter shuttle run (4×10SHR). Action speed (m/s) was scored by dividing the total distance run (i.e., 40 meters) by seconds of running time 4×10SHR. All fitness tests were performed according to the methodology described by Jarnig et al. in 2021 (17).

Fitness assessment and age groups in SP2

In SP2, secondary school children (from fifth to eighth grade) up to young people in high school (from ninth to twelfth grade; maximum age: 18 years) completed the medicine ball overhead throw (MBT_SOT-2kg). Children and adolescents stood at the starting line, using both hands to hold a 2 kg medicine ball behind their heads. They then used both hands to throw the ball over their heads as far forward as possible. The shortest distance between the starting line and the point where the ball hit the ground was measured to the nearest centimeter using a tape measure. The participants had two attempts to throw the ball, with the longest attempt being counted.

All children in SP2 also completed the SLJ according to SP1 instructions. In addition, all children attending secondary school performed a push-up test (PU) based on instructions of the German motor test (19). In the starting position, participants lay on their stomachs on the floor and touched one hand with the other (above the glutes near the spine). To perform a push-up correctly, participants had to place their hands next to their shoulders and push their bodies into a fully extended push-up position. In this position, they had to lift one hand off the floor and touch the back of the other hand. Then, they had to place their hand back on the floor and return to the starting position in a controlled manner. Within 40 seconds, participants had to complete as many push-ups as possible, and the number of correctly performed push-ups was included in the analysis.

Standardization and classification

Anthropometrics

Using the international standard reference values for age and sex from the International Obesity Taskforce (IOTF) (20), the standard deviation scores (BMI_IOTF SDS) for BMI were calculated using the LMS method (21). Age- and sex-specific IOTF BMI cut-off values (20) for thinness, normal weight, overweight, obesity, and morbid obesity were used to categorize raw BMI values into a 5-level weight classification.

Fitness test: 6MR, 4×10SHR, JS, SLJ, PU

Standard deviation scores (SDS; z-scores) were calculated based on age- and gender-specific reference values to compare results (raw scores) of the fitness tests with established reference values. Since no national reference values were available for this age groups, international reference values were used. The most recent German percentile tables from the Düsseldorf model ( (22); collected 2011–2018) were used for 6MR and SLJ and the Macedonian standard values from the 2018 “Macedonian fitness meter” (MAKFIT) (23) for the 4 × 10 SHR. Z-scores were derived with the LMS method (21) based on the German (DüMo) and Macedonian (MAKFIT) reference tables. Z-scores for JS and PU were computed based on the German Motor Test (2016 norms (19)) using the usual z-score standardization (24).

Tests of upper body strength: MBT_SCT-1kgand MBT_SOT-2kg

Since no comparable reference values existed for the MBT_A variants and in order to ensure objective comparability, it was necessary to calculate age- and gender-adjusted z-scores for MBT_T and the alternative assessments (MBT_A1, MBT_A2, and MBT_A3) based on the raw values of our own study population using traditional z-score standardization (24).

Anthropometrically enriched measures of MBT (MBT_A)

Traditionally, MBT_T performance is based on the distance thrown with a medicine ball, usually adjusted for gender and age (MBT_Tz). These raw or z-scores ignore that H_B and M_B have been shown (16, 25) to significantly influence MBT_T. The alternative MBT_A assessments proposed here try to “correct” this by taking H_B and M_B into account. We designed three different indices: MBT_A1, MBT_A2, and MBT_A3 to analyze and compare them with the traditional assessment MBT.

MBT_A1. MBT_A1 normalizes the throwing distance on H_B and this result on M_Bor equivalently on the product of H_B and M_B:

MBT_A1 = MBT_T/ H_B / M_B = MBT_T / (H_B × M_B)

As length units (cm) reduce each other in the mathematical fraction = the unit of MBT_A1 is 1/kg (or: kg^-1).

MBT_A2. MBT_A2 normalizes the throwing distance on the ratio of H_B and M_B:

MBT_A2 = MBT_T / (M_B / H_B) = MBT_T × (H_B/ M_B) = MBT_T × HMR

The unit of MBT_A2 is square centimeters per kilogram cm²/kg (or: cm²kg^-1).

MBT_A3. MBT_A3 is a variation of MBT_A2 by setting the throwing distance in relation to BMI (m throwing distance per BMI):

MBT_A3= MBT_T / (M_B / H_B²) = MBT_T × (H_B²/ M_B) = MBT_T / BMI

The unit of MBT_A3 is cubic meters per kilogram: m³/kg (or: m³kg^-1).

Statistical analysis

Descriptives

Continuous variables are reported as means (M) and standard deviations (SD), categorical variables as absolute values (n) and percentages (%) for descriptive statistics. No data imputation was performed.

Statistical inference with linear mixed models (LMMs)

With a first set of LMMs we tested alignment of the three anthropometrically enriched MBT_A variants (MBT_A1,MBT_A2,and MBT_A3) with the four other PF tasks and the traditional MBT_T. For statistical inference, we specified four LMMs including the four PF tasks plus either MBT_T or one of the 3 MBT_A measures as a five-level repeated-measures factor task (i.e., as five dependent variables). Fixed effects comprised quadratic BMI, sex, quadratic age, grade, and region. Child and school were included as random factors with variance components (VCs) and correlation parameters (CPs) for the five repeated measures. Model comparison considered LMMs with more complex and simpler fixed-effect structures. Selection was based on likelihood ratio tests (LRTs) and an Akaike Information Criterion (AIC) with a significant improvement requiring a decrease of more than five units for the more complex model. (26)

The second set of LMMs was a modification of the above first set. Specifically, rather than including one of the four MBTs as a level of the task factor (i.e., as dependent variable), we used it as a predictor of the four other fitness tasks (i.e., as an independent variable). This afforded a comparison of the efficiency of traditional and alternative MBTs in the prediction of standard PF tasks. Other fixed effects and random effect structure were the same as in the first set of LMMs. Model comparison and selection followed the procedure described for the first set of LMMs and led to the same LMM structure of fixed effects and random-effect structure for both sets.

The same analysis strategy was employed for SP2, but only with standing long jump and push up as comparative physical fitness tasks. As children were all from the same school, the fixed effect of region and the random factor school were not included in the models.

Software

For data analyses and graphics, we used mainly tidyverse (version 2.0.3) (27) , and easystats (version 0.7.5) (28) packages in the R language (version 4.5.2) (29). LMMs were estimated with MixedModels.jl (version 5.1.0) (30)in the Julia programming language (version 1.12.2). (31)

Descriptive statistics

Table 1 provides means and standard deviations for anthropometric measures and scores in original metric on fitness tasks in SP1 (top) and SP2 (bottom).

Table 1

Descriptive data on anthropometrics and achievements in fitness tests by sex, grade, and school type.
SP1
Sex	Boys		Girls
Grade/School	2nd/PS	3rd/PS	2nd/PS	3rd/PS
N	206	196	200	219
Age [yrs]	7.7 ± 0.4	8.8 ± 0.5	7.7 ± 0.4	8.7 ± 0.5
Body Mass [kg]	28 ± 5	32 ± 9	28 ± 7	31 ± 7
Body Height [cm]	130 ± 5	136 ± 6	129 ± 6	134 ± 6
MBT [cm]	346 ± 64	403 ± 68	285 ± 55	340 ± 57
6MR [m]	969 ± 157	969 ± 157	845 ± 114	902 ± 129
4×10SHR [m/s]	2.7 ± 0.2	2.8 ± 0.3	2.6 ± 0.2	2.7 ± 0.2
JS[N]	30 ± 7	34 ± 7	30 ± 7	33 ± 7
SLJ [cm]	125 ± 18	134 ± 22	113 ± 17	124 ± 19
SP2
Sex	Boys		Girls
School	SS	HS	SS	HS
N	89	68	89	108
Age [yrs]	12.6 ± 1.2	16.3 ± 1.0	12.4 ± 1.4	16.3 ± 1.0
Body Mass [kg]	53 ± 15	70 ± 12	51 ± 15	61 ± 15
Body Height [cm]	161 ± 12	179 ± 8	156 ± 10	165 ± 6
MBT [cm]	538 ± 144	790 ± 173	440 ± 94	535 ± 119
SLJ [cm]	155 ± 32	193 ± 34	126 ± 21	135 ± 28
PU [m]	12.4 ± 3.6	N.D.	12.4 ± 3.2	N.D.
Note. Data presented are means ± standard deviation. MBT = medicine ball throw; 6MR = six-minute run; 4×10 SHR = 4 x 10-m shuttle run; JS = jumping sideways; SLJ = standing long jump, PU = push up. PS = primary school, SS = secondary school; HS = high school; N.D. = no data.

Alignment of MBT_A vs. MBT_T with four fitness tasks

Analysis of bivariate correlations of z-scores from the six fitness tasks (MBT, 6MR, 4×10SHR, JS, SLJ, PU) showed that MBT_A correlated higher between tasks than MBT_T. Among MBT_A variants, MBT_A2 correlated best with most other fitness tests, with the exception of SP2 and PU, where MBT_A1 correlated best (see supplements Table S1). Zero-order relations for BMI revealed the expected alignment of anthropologically enriched MBT_A1 MBT_A2, and MBT_A3 with 6MR, 4×10 SHR, JS, and SLJ (see Fig. 2A for SP1, 2B for SP2). Except for traditional MBT_T (left panel in second row of Fig. 2A; left panel in first row of Fig. 2B), performance decreased strongly with high BMIz for all measures.

Goodness-of-fit statistics for LMMs using one the four MBT indices in turn as dependent variable PF tasks are shown in the top two blocks of Table 2 for SP1 and SP2. In SP1, the MBT index was used along with four PF tasks, in SP2 with two PF tasks. The bottom two blocks contain corresponding statistics when the MBT indices were used in turn as covariates to predict performance in the four (SP1) or two (SP2) PF tasks, Model comparison strongly favored MBT_A2, particularly in the adolescent group (SP2) and predictive models. The AIC differences indicate that MBT_A2 provides a

substantially superior fit to the data compared to traditional and other alternative methods. It fits best in three of the four LMM sets and only slightly worse than MBT_A1 in the first set comparing alignment with PF tasks in SP1.

Table 2

Goodness-of-fit statistics for alignment LMMs (using MBT as dependent variable) and predictive LMMs (using MBT as covariate) for SP1 and SP2
MBT as .	Data	Index	df	deviance	AIC	BIC
DV	SP1	A1	58	9893	10009	10375
		A2	58	9999	10115	10482
		A3	58	10105	10221	10588
		T	58	10308	10424	10791
	SP2	A1	47	8136	8230	8516
		A2	47	8033	8127	8413
		A3	47	8044	8138	8425
		T	47	8047	8141	8428
Covariate	SP1	A1	24	2132	2180	2295
		A2	24	2098	2146	2261
		A3	24	2120	2168	2283
		T	24	2228	2276	2391
	SP2	A1	18	1297	1333	1410
		A2	18	1239	1275	1352
		A3	18	1246	1282	1359
		T	18	1247	1283	1360
Note. df: degrees of freedom (i.e., number of model parameters). DV: dependent variable. Best fitting models in each set of four are set in bold according to AIC.

Fixed-effect statistics between MBT_A results were similar, but as an ensemble differed qualitatively from MBT_T. Table 3 provides a comparison between MBT_A2 and MBT_T. The qualitative difference is reflected best in a complete reversal of the BMI relationship. While higher BMI predicted better performance in MBT_T (BMI = 0.230), it strongly predicted worse performance in MBT_A2 (BMI = -0.452), aligning MBT with the biomechanical constraints of running and jumping. MBT_A1 and MBT_A3 show comparable differences to MBT_T. Results for MBT_A3 and fixed-effects for all models are documented in the Supplement (Table S2).

Table 3

LMM Fixed-effect estimates BMI, sex, age, and grade on physical fitness in MBT_A2 (left part) or MBT_T (right part) and 6-minute run (6MR), jumping sideways (JS), shuttle run (4x10SHR), and standing long jump (SLJ). Estimates are from SP1.

Task: Parameter	Coef	SE	z	p	Coef	SE	z	p
MBT: BMI	-0.452	0.058	-14.133	< .001	0.230	0.038	6.012	< .001
BMI²	-0.082	0.112	-3.508	< .001	-0.025	0.028	-0.892	0.372
6MR: BMI	-0.272	0.124	-7.195	< .001	-0.273	0.038	-7.212	< .001
: BMI²	-0.144	0.201	-5.196	< .001	-0.143	0.028	-5.173	< .001
4x10SHR: BMI	-0.101	0.062	-3.550	< .001	-0.101	0.028	-3.564	< .001
: BMI²	-0.099	0.032	-4.770	< .001	-0.098	0.021	-4.738	< .001
JS: BMI	-0.102	0.023	-2.140	0.032	-0.103	0.048	-2.151	0.031
: BMI²	-0.068	0.038	-1.939	0.053	-0.067	0.035	-1.915	0.055
SLJ: BMI	-0.150	0.028	-3.787	< .001	-0.150	0.039	-3.801	< .001
: BMI²	-0.121	0.028	-4.195	< .001	-0.121	0.029	-4.171	< .001
MBT: Sex	-0.028	0.021	-0.493	0.622	0.051	0.067	0.764	0.445
6MR: sex	0.132	0.048	2.006	0.045	0.134	0.066	2.025	0.043
4x10SHR: sex	-0.327	0.035	-6.607	< .001	-0.326	0.050	-6.582	< .001
JS: sex	0.332	0.040	3.993	< .001	0.333	0.083	4.006	< .001
SLJ: sex:	0.152	0.029	2.211	0.027	0.154	0.069	2.228	0.026
MBT: age	-0.113	0.056	-2.056	0.040	-0.143	0.062	-2.305	0.021
6MR: age	-0.302	0.066	-4.962	< .001	-0.315	0.062	-5.096	< .001
4x10SHR: age	-0.287	0.050	-5.544	< .001	-0.300	0.053	-5.665	< .001
JS: age	-0.638	0.083	-8.976	< .001	-0.651	0.072	-9.046	< .001
SLJ: age	-0.242	0.069	-3.882	< .001	-0.255	0.063	-4.027	< .001
age²	-0.098	0.055	-2.497	0.013	-0.107	0.041	-2.600	0.009
grade	0.174	0.061	5.261	< .001	0.183	0.035	5.290	< .001
Note. Dependent variables are MBT, 6MR, JS, 4x10SHR, and SLJ; independent variables are BMI, sex, age, and grade. Bold values highlight the alignment of MBT_A2 and misalignment of MBT_T with other fitness tasks. Estimates of MBT_A1 and MBT_A3 are in Supplement Table S2.

Girls scored significantly higher than boys on 4×10 SHR and boys significantly higher on 6MR, JS and SLJ. There were significant negative task-specific linear effects of age and an overall significant concave quadratic age effect. Children in grade 3 scored higher than those in grade 2 (i.e., after adjustment for other covariates such as age). The alignment/misalignment profile of fixed-effect MBT_A and MBT_T, the concave relation with BMT, and boys jumping further than girls were replicated for SP2 (see Table 4).

Table 4

LMM Fixed-effect estimates BMI, sex, age, grade, and region on physical fitness in MBT_A1 (left part) or MBT_T (right part) and push-up (PU) and standing long jump (SLJ). Estimates are from SP2.

Task: Parameter	Coef	SE	z	p	Coef	SE	z	p
MBT: BMI	-0.359	0.040	-9.079	< 0.001	0.317	0.047	6.672	< 0.001
BMI²	-0.106	0.028	-3.765	< 0.001	-0.004	0.034	-0.122	0.903
PU: BMI	-0.076	0.063	-1.210	0.226	-0.080	0.063	-1.266	0.205
BMI²	-0.129	0.044	-2.950	0.003	-0.127	0.044	-2.874	0.004
SLJ: BMI	-0.158	0.047	-3.384	0.001	-0.155	0.047	-3.320	0.001
BMI²	-0.176	0.033	-5.263	< 0.001	-0.175	0.033	-5.243	< 0.001
MBT: sex	0.021	0.087	0.238	0.812	0.180	0.105	1.722	0.085
PU: sex	-0.170	0.138	-1.231	0.218	-0.146	0.139	-1.051	0.293
SLJ: sex:	0.460	0.103	4.467	< 0.001	0.472	0.103	4.591	< 0.00<
MBT: age	-0.068	0.055	-1.221	0.222	-0.083	0.062	-1.325	0.185
PU: age	-0.112	0.074	-1.513	0.130	-0.055	0.081	-0.678	0.498
SLJ: age	-0.105	0.057	-1.843	0.065	-0.092	0.062	-1.477	0.140
age²	0.001	0.010	0.136	0.892	0.011	0.011	0.981	0.327
school	-0.299	0.161	-1.853	0.064	-0.410	0.180	-2.277	0.023
Note. Dependent variables are MBT, PU, and SLJ; independent variables are BMI, sex, age, and school. Bold values highlight the alignment of MBT_A2 and misalignment of MBT_T with other fitness tasks. Estimates of MBT_A1 and MBT_A3 are in Supplement Table S3.

Predictive power of covariates MBT_A1, MBT_A2, MBT_A3, and MBT_T, for fitness tasks

MBT_A1, MBT_A2, and MBT_A3 aligned very well with BMI profiles observed for other fitness tasks and was qualitatively differed from the MBT_T profile. The alternative MBT_A indices were enriched with anthropometric information about height and mass. These measures along with MBT_T can be collected more easily than those of the other four fitness tasks. To test the predictive power of the four assessments, we moved them from the left-hand to the right-hand side in the above LMM equations. Figure 3A for SP1 and Fig. 3B for SP2 show zero-order effects of the four MBT assessments (lines) for each of the four physical fitness tasks (panels). While slopes of MBT_A1, MBT_A2, and MBT_A3 were similar, they were also clearly steeper than traditional MBT_T. As above, the LMMs included BMI, sex, age, and school grade as covariates. The MBT_A-over-MBT_T advantages are due to stronger correlations between low MBT-index values and low scores on PF tasks.

Table 5 contains related fixed effect statistics using in turn one the four MBT indices as covariate for SP1 (top blocks) and for SP2 (bottom blocks). In agreement with Fig. 3 for all four PF tasks of SP1 and for the two PF tasks of SP2, all MBT-covariate slopes were significantly positive, but – except MBT_A1 for SLJ in SP2 – larger for anthropometrically enriched MBT_A1, MBT_A2, and MBT_A3 than traditional MBT_T. Effects of BMI, sex, age, and grade were included as control covariates in the four LMMs. All fixed effects are documented in the Supplement (Table S4 & Table S5).

Table 5

LMM fixed effect estimates for four LMMs varying MBT covariate for SP1 & SP2
Data	Covariate	Task	Coef	SE	z	p
SP1	A1	6MR	0.361	0.045	8.025	< 0.001
		4x10SHR	0.346	0.033	10.516	< 0.001
		JS	0.517	0.056	9.241	< 0.001
		SLJ	0.517	0.045	11.411	< 0.001
	A2	6MR	0.365	0.039	9.327	< 0.001
		4x10SHR	0.349	0.028	12.304	< 0.001
		JS	0.566	0.048	11.836	< 0.001
		SLJ	0.579	0.038	15.284	< 0.001
	A3	6MR	0.331	0.037	8.923	< 0.001
		4x10SHR	0.328	0.027	12.256	< 0.001
		JS	0.510	0.045	11.211	< 0.001
		SLJ	0.543	0.036	15.175	< 0.001
	T	6MR	0.283	0.033	8.572	< 0.001
		4x10SHR	0.296	0.024	12.532	< 0.001
		JS	0.461	0.040	11.483	< 0.001
		SLJ	0.473	0.032	14.837	< 0.001
SP2	A1	PU	0.713	0.080	8.899	< 0.000
		SLJ	0.566	0.057	9.864	< 0.000
	A2	PU	0.588	0.085	6.888	< 0.000
		SLJ	0.725	0.050	14.621	< 0.000
	A3	PU	0.450	0.085	5.290	< 0.000
		SLJ	0.715	0.048	14.859	< 0.000
	T	PU	0.404	0.078	5.176	< 0.000
		SLJ	0.608	0.041	14.794	< 0.000
Note. Other covariates were BMI, sex, age, grade, and school; see Supplement for complete list in Table S4 & Table S5.

Variance components and correlation parameters

Variance components and correlation parameters of the 16 LMMs are documented in the Supplement (Table S6). For young children (i.e., SP1), their child-related CPs were significantly positive. They were always numerically slightly larger with MBT_A2 than with MBT_A1 or MBT_A3 for LMM1 and always numerically slightly smaller for LMM2 Thus, when included as an indicator, MBT_A2 yielded a slightly better defined latent construct of physical fitness than MBT_A1 or MBT_A3. Conversely, these reliable individual differences were reduced (and moved to the fixed effects) when MBT_A2 was used as a covariate. Other CPs were less systematic, presumably because there were only twelve schools for younger children and only three CPs for older children.

Traditional and anthropometrically enriched MBT_A

The medicine ball throw (MBT) is a simple test that can be carried out at low cost and allows assessment of a group (up to 25 participations) in a very short time. It has been used since 1930 to assess the explosive strength of the upper body.(32) Despite its simplicity, it is part of only a few international health-related fitness batteries.(33) One reason for its limited use in test batteries is that MBT is directly related to body mass which reduces its validity in health-related test batteries and biases overall results in performance-related test batteries and talent scouting.(16, 34) There are three main differences between MBT and other PF tasks. First, high body mass confers an inertial advantage (i.e., force = mass x acceleration) whereas it incurs a performance cost in the other five PF tasks (6MR, SLJ, JS, 4×10 SHR, PU) used in our studies. Second, for MBT body mass is not moved whereas for other PF tasks it has to be moved over a defined and/or time-limited or target distance. Third, children with higher body mass often exhibit functional adaptations to habitual load-bearing —effectively 'training' their absolute strength by carrying excess weight during daily activities—which aids for MBT performance but hinders weight-related tasks.(35, 36). Therefore, the strong positive correlations between 6MR, SLJ, JS, 4×10 SHR, and PU and, in contrast, their negative correlations with MBT was to be expected.

All three alternative MBT_A indices fundamentally transform the assessment by penalizing body mass, thereby neutralizing the 'inertial advantage' heavier children possess in projectile tasks. This correction effectively converts the raw metric from a proxy of absolute force into a measure of relative work efficiency, aligning MBT with weight-bearing tasks like running and jumping. However, the indices diverge in their biomechanical treatment of stature. In the first formula (MBT_A1), height is used as a second penalty. In contrast, the second formula (MBT_A2) treats height as a functional asset, not as a liability, and the third (MBT_A3) weighs this asset even more heavily. The positive scaling of height in these latter two indices is physically justified by two constraints: taller children benefit from a higher vertical release point (lengthening the trajectory) and longer levers (arm span), which allow for a longer acceleration path and greater force generation.

While both MBT_A2 and MBT_A3 correctly identify height as an asset, the theoretical preference for MBT_A2 rests on the principles of allometric scaling. Biologically, muscle strength is proportional to muscle cross-sectional area (L²), whereas body mass scales with volume (L³) (37). MBT_A2 accounts for this discrepancy by normalizing the throw (a proxy for force, L²) by the ratio of height to mass (L/L³), resulting in a scale-invariant metric (L² L L^− 3 = 1). In contrast, MBT_A3 normalizes by BMI (M/L²), which scales linearly with height (L). Consequently, MBT_A3 fails to fully eliminate the size advantage, leaving a residual bias that artificially favors taller children (L² / L = L), whereas MBT_A2 provides a mathematically orthogonal measure of relative strength. The empirical superiority of MBT_A2 is in agreement with this theoretical preference.

There is some evidence favoring HMR over BMI in previous research. HMR by itself, not as a scaling factor of performance, was used as an alternative to BMI as a predictor for a range of PF tasks (including also MBT) (38). In this study, the HMR-based model also yielded a slightly better fit than BMI-based models.

Empirically, MBT_A2 achieved the best goodness of fit in three of the four LMM comparisons. There was one exception: MBT_A1 fits marginally better than MBT_A2. One explanation could be that young children (6–9 years) often have a "coordination lag." Being tall is not yet an advantage for them because they cannot control their long limbs effectively. For young kids, "size" is just "bulk”, for adolescents (SP2), "height" becomes "leverage." Therefore, we propose that for longitudinal consistency and biomechanical validity, MBT_A2 offers the most generalizable solution for standardizing upper-body strength assessment.

The empirical superiority of MBT_A2 is in full agreement with the theoretical preference for a scale-invariant metric derived from the square-cube law. Therefore, we recommend MBT_A2 (throwing distance scaled by the height-to-mass ratio) as the standard method for assessing upper-body strength in youth fitness batteries. In the following and in future research, we relabel MBT_A2 as hmrMBT (height-to-mass ratio medicine ball throw).

Implications for children’s PF assessment and sports training in general

It is standard practice to take children’s gender and age into account when assessing their PF. This increases the validity because performance is assessed and interpreted in a more differentiated manner, facilitating the detection of training-related or developmental gains or losses. Trivially, all else being equal, taller children run faster and jump further than smaller children. Therefore, for the same reason we evaluate performance relative to age and gender, we assume that by taking anthropometrics into account we are able to achieve an even more differentiated profile. For example, hmrMBT mitigates the influence of biological growth spurts or, conversely, of delayed physical growth on performance assessment.

Sports training often focuses on different aims (macro, meso, and micro aims). hmrMBT might be useful in the context of strength training with the secondary goal to reduce body mass over a specific time span (micro cycle) (39). The increase in precision of assessment due to indices such as hmrMBT may help to reach specific goals. Weight loss or gain due to illness or injury can be directly considered after returning to training and training-related improvements are easierly detected.

Transparency and objective performance assessments have been shown to increase athletes' personal motivation (40, 41), together with self-assessment of personal performance compared to competitors' performance. Furthermore, externally influenced and self-influenced motivation levels are directly related to dropout rates in sports; as motivation levels rise, dropout rates fall. (42)

In summary, the more precise assessment, the more transparent communication of performance levels and finally the higher participants’ acceptance and motivation may be an important step to (1) increase competition fairness among athletes, (2) increase athletes' understanding of decisions made by coaches or educators, and (3) improve the acceptance of arguments related to performance assessments among athletes and legal guardians. (43)

Limitations

As with any new performance-relevant index, arguments for anthropometrically enriched indices such as hmrMBT bear the risk of erroneous application or even abuse. First, our proposal is limited to considering body mass and height. In principle, other parameters could be integrated as well. For example, sitting height would be relevant for computation of peak-height velocity as a proxy of biological age around puberty.

Second, one index may not suit all PF tasks. For example, a high (Formula Kite) or low (endurance-specific sports) body mass is a factor that determines performance. Thus, some sports may benefit, while another may be negatively affected if specific demands are not considered. Moreover. for some tests, anthropometrics is not essential. For example, anthropometrics might be safely ignored for reaction tasks. Nerve impulses occur at such high speeds that delays caused by differences in body size are usually irrelevant.

Third, methods and workflow of measuring body height and body mass must be carried out with high precision to reduce the rate of measurement errors to a minimum. Measurement errors can have devastating effects, as an incorrect value might substantially affect the assessment (of many individual tests). Fourth, even increased data complexity leads to unusual new data samples such as with MBT_A results, which are displayed by thus far “unusual” mathematical/physical dimensions like kg^− 1, cm²kg^− 1 and m³kg^− 1. Most likely, sometime of explanation and training will be necessary to achieve adequate acceptance among those who are responsible for these test batteries, i.e. especially sports teachers and trainers.

Anthropometrically enriched hmrMBT has the potential to improve the assessment of children’s physical fitness and allows closer and fairer monitoring of athletes’ performance. As further innovation, this consideration of anthropometrics could be extended to other tests of physical fitness, eg. the 6-minute run and the 4 x 10-meter shuttle run. By doing so, increased fairness may contribute to better acceptance and motivation among assessed school children and athletes, but also among assessing teachers and trainers. And may thus also contribute to the implementation of large-scale or even nationwide routine physical fitness tests in school children. With no doubt, in the era of overweight and obesity, such evaluation is urgently needed.

Author Contributions

Conceptualization, G.J. and M.N.M.v.P.; methodology, G.J.; formal analysis, G.J. and R.Kl.; investigation, G.J.; resources, G.J.; data curation, G.J.; writing—original draft preparation, G.J. and R.Kl.; writing—review and editing, G.J., R.Ke., R.Kl. and M.N.M.v.P.; visualization, G.J. and R.Kl.; supervision, M.N.M.v.P.; project administration, G.J.; funding acquisition, G.J. All authors have read and agreed to the published version of the manuscript.

Funding

This research and the Open Access publishing costs were funded by the Austrian Federal Ministry of Education, Science and Research, grant number GZ:2024-0.780.614 and the Austrian Federal Ministry for Arts, Culture, Civil Service and Sport, grant number GZ:2025-0.021.608. The Open Access was funded by the University of Graz. The University of Graz funded open access publishing.

Institutional Review Board Statement

The study was conducted according to the guidelines of the Declaration of Helsinki and approved by the Research Ethics Committee of the University of Graz, Styria, Austria (GZ. 39/68/63 ex 2021/22).

Informed Consent Statement

Informed consent was obtained from all subjects involved in the study.

Data Availability Statement

The data presented in this study are available upon request from the corresponding author. The data are not publicly available due to privacy/ethical restriction.

Conflicts of Interest

The authors declare no conflicts of interest.

NCD Risk Factor Collaboration (NCD-RisC). Worldwide trends in underweight and obesity from 1990 to 2022: a pooled analysis of 3663 population-representative studies with 222 million children, adolescents, and adults. The Lancet 2024, 403 (10431), 1027–1050. DOI: 10.1016/S0140-6736(23)02750-2.
Mintjens, S.; Menting, M. D.; Daams, J. G.; van Poppel, M. N. M.; Roseboom, T. J.; Gemke, R. J. B. J. Cardiorespiratory Fitness in Childhood and Adolescence Affects Future Cardiovascular Risk Factors: A Systematic Review of Longitudinal Studies. Sports medicine (Auckland, N.Z.) 2018, 48 (11), 2577–2605. DOI: 10.1007/s40279-018-0974-5.
Ortega, F. B.; Ruiz, J. R.; Castillo, M. J.; Sjöström, M. Physical fitness in childhood and adolescence: a powerful marker of health. International journal of obesity (2005) 2008, 32 (1), 1–11. DOI: 10.1038/sj.ijo.0803774.
Umer, A.; Kelley, G. A.; Cottrell, L. E.; Giacobbi, P.; Innes, K. E.; Lilly, C. L. Childhood obesity and adult cardiovascular disease risk factors: a systematic review with meta-analysis. BMC public health 2017, 17 (1), 683. DOI: 10.1186/s12889-017-4691-z.
Freedman, D. S.; Khan, L. K.; Dietz, W. H.; Srinivasan, S. R.; Berenson, G. S. Relationship of childhood obesity to coronary heart disease risk factors in adulthood: the Bogalusa Heart Study. Pediatrics 2001, 108 (3), 712–718. DOI: 10.1542/peds.108.3.712.
Wang, Y.; Cai, L.; Wu, Y.; Wilson, R. F.; Weston, C.; Fawole, O.; Bleich, S. N.; Cheskin, L. J.; Showell, N. N.; Lau, B. D.; Chiu, D. T.; Zhang, A.; Segal, J. What childhood obesity prevention programmes work? A systematic review and meta-analysis. Obesity reviews : an official journal of the International Association for the Study of Obesity 2015, 16 (7), 547–565. DOI: 10.1111/obr.12277.
Kriemler, S.; Meyer, U.; Martin, E.; van Sluijs, E. M. F.; Andersen, L. B.; Martin, B. W. Effect of school-based interventions on physical activity and fitness in children and adolescents: a review of reviews and systematic update. Br J Sports Med 2011, 45 (11), 923–930. DOI: 10.1136/bjsports-2011-090186.
Brazo-Sayavera, J.; Silva, D. R.; Lang, J. J.; Tomkinson, G. R.; Agostinis-Sobrinho, C.; Andersen, L. B.; García-Hermoso, A.; Gaya, A. R.; Jurak, G.; Lee, E.-Y.; Liu, Y.; Lubans, D. R.; Okely, A. D.; Ortega, F. B.; Ruiz, J. R.; Tremblay, M. S.; Dos Santos, L. Physical Fitness Surveillance and Monitoring Systems Inventory for Children and Adolescents: A Scoping Review with a Global Perspective. Sports Med 2024, 54 (7), 1755–1769. DOI: 10.1007/s40279-024-02038-9.
Mahar, M. T.; Rowe, D. A. Practical Guidelines for Valid and Reliable Youth Fitness Testing. Measurement in Physical Education and Exercise Science 2008, 12 (3), 126–145. DOI: 10.1080/10913670802216106.
Masanovic, B.; Gardasevic, J.; Marques, A.; Peralta, M.; Demetriou, Y.; Sturm, D. J.; Popovic, S. Trends in Physical Fitness Among School-Aged Children and Adolescents: A Systematic Review. Frontiers in Pediatrics 2020, 8, 627529. DOI: 10.3389/fped.2020.627529.
Castro-Piñero, J.; González-Montesinos, J. L.; Mora, J.; Keating, X. D.; Girela-Rejón, M. J.; Sjöström, M.; Ruiz, J. R. Percentile values for muscular strength field tests in children aged 6 to 17 years: influence of weight status. Journal of strength and conditioning research 2009, 23 (8), 2295–2310. DOI: 10.1519/JSC.0b013e3181b8d5c1.
Pate, R. R.; Burgess, M. L.; Woods, J. A.; Ross, J. G.; Baumgartner, T. Validity of field tests of upper body muscular strength. Research Quarterly for Exercise and Sport 1993, 64 (1), 17–24. DOI: 10.1080/02701367.1993.10608774.
Cruz-León, C.; Expósito-Carrillo, P.; Sánchez-Parente, S.; Jiménez-Iglesias, J.; Borges-Cosic, M.; Cuenca-Garcia, M.; Castro-Piñero, J. Feasibility and Safety of Field-Based Physical Fitness Tests: A Systematic Review. Sports medicine - open 2025, 11 (1), 8. DOI: 10.1186/s40798-024-00799-1.
Fühner, T.; Granacher, U.; Golle, K.; Kliegl, R. Effect of timing of school enrollment on physical fitness in third graders. Sci Rep 2022, 12 (1), 7801. DOI: 10.1038/s41598-022-11710-x.
Bähr, F.; Wöhrl, T.; Teich, P.; Puta, C.; Kliegl, R. Impact of age, sex, body constitution, and the COVID-19 pandemic on the physical fitness of 38,084 German primary school children. Sci Rep 2025, 15 (1), 11300. DOI: 10.1038/s41598-025-95461-5.
Jarnig, G.; van Poppel, M.; Kerbl, R. Adjusting Health-related Fitness Assessment Models in the Context of the Global Obesity Pandemic. Paediatr. Paedolog. Austria 2025, 60 (1), 43–45. DOI: 10.1007/s00608-024-01269-3.
Jarnig, G.; Jaunig, J.; Kerbl, R.; Lima, R. A.; van Poppel, M. N. M. A Novel Monitoring System (AUT FIT) for Anthropometrics and Physical Fitness in Primary School Children in Austria: A Cross-Sectional Pilot Study. Sports 2022, 10 (1), 4. DOI: 10.3390/sports10010004.
Jarnig, G.; Kerbl, R.; van Poppel, M. N. M. Reliability, Objectivity, Validity and Reference Levels of the Austrian Balance Check (ABC)-A Novel Balance Field Test for Children, Adolescents and Young Adults to Assess Static Balance. Sports (Basel, Switzerland) 2025, 13 (1). DOI: 10.3390/sports13010005.
Bös, K. Deutscher Motorik-Test 6-18: (DMT 6-18): Manual und internetbasierte Auswertungssoftware, 2. Auflage; Schriften der Deutschen Vereinigung für Sportwissenschaft; Band 186; Feldhaus, Edition Czwalina, 2016.
Cole, T. J.; Lobstein, T. Extended international (IOTF) body mass index cut-offs for thinness, overweight and obesity. Pediatric obesity 2012, 7 (4), 284–294. DOI: 10.1111/j.2047-6310.2012.00064.x.
Cole, T. J.; Green, P. J. Smoothing reference centile curves: the LMS method and penalized likelihood. Statistics in medicine 1992, 11 (10), 1305–1319. DOI: 10.1002/sim.4780111005.
Stemper, T.; Bachmann, C.; Diehlmann, K.; Kemper, B. DüMo Düsseldorfer Modell der Bewegungs-, Sport- und Talentförderung: 2003 - 2018: Konzept, Normwerte, Untersuchungsergebnisse; LIT, 2020.
Gontarev, S.; Kalac, R.; Velickovska, L. A.; Zivkovic, V. Estándares de referencia de aptitud física en niños y adolescentes de Macedonia: el estudio MAKFIT. NUTRICION HOSPITALARIA 2018, 35 (6), 1275–1286. DOI: 10.20960/nh.1881.
Urdan, T. C. Statistics in Plain English, Fifth edition; Routledge, 2022. DOI: 10.4324/9781003006459.
Jarnig, G.; van Poppel, M. N. M.; Kerbl, R. Model Calculation of the Influence of Body Height on Performance in Medicine Ball Throw. Paediatr. Paedolog. Austria 2025. DOI: 10.1007/s00608-025-01329-2.
Bates, D.; Kliegl, R.; Vasishth, S.; Baayen, H. Parsimonious Mixed Models. https://arxiv.org/pdf/1506.04967.
Wickham, H.; Averick, M.; Bryan, J.; Chang, W.; McGowan, L.; François, R.; Grolemund, G.; Hayes, A.; Henry, L.; Hester, J.; Kuhn, M.; Pedersen, T.; Miller, E.; Bache, S.; Müller, K.; Ooms, J.; Robinson, D.; Seidel, D.; Spinu, V.; Takahashi, K.; Vaughan, D.; Wilke, C.; Woo, K.; Yutani, H. Welcome to the Tidyverse. JOSS 2019, 4 (43), 1686. DOI: 10.21105/joss.01686.
Lüdecke, D.; Makowski, D.; Ben-Shachar, M. S.; Patil, I.; Wiernik, B. M.; Bacher, E.; Thériault, R. easystats: Framework for Easy Statistical Modeling, Visualization, and Reporting. CRAN. https://cran.r-project.org/web/packages/easystats/index.html.
R Core Team. R: A Language and Environment for Statistical Computing; R Foundation for Statistical Computing, 2025. https://www.r-project.org/.
Alday, P. M.; Bates, D. MixedModels.jl (v5.1.0); Zenodo, 2025.
Bezanson, J.; Edelman, A.; Karpinski, S.; Shah, V. B. Julia: A Fresh Approach to Numerical Computing. SIAM Review 2017, 59 (1), 65–98. DOI: 10.1137/141000671.
Varela, S.; Diz-Gómez, J. C.; López-Amoedo, D.; Ayán-Pérez, C.; González-Devesa, D. Reliability and validity of the medicine ball throw test in children and adolescents. Kinesiology (Zagreb, Online) 2025, 57 (1), 122–135. DOI: 10.26582/k.57.1.11.
Marques, A.; Henriques-Neto, D.; Peralta, M.; Martins, J.; Gomes, F.; Popovic, S.; Masanovic, B.; Demetriou, Y.; Schlund, A.; Ihle, A. Field-Based Health-Related Physical Fitness Tests in Children and Adolescents: A Systematic Review. Frontiers in Pediatrics 2021, 9, 640028. DOI: 10.3389/fped.2021.640028.
Sacchetti, R.; Ceciliani, A.; Garulli, A.; Masotti, A.; Poletti, G.; Beltrami, P.; Leoni, E. Physical fitness of primary school children in relation to overweight prevalence and physical activity habits. Journal of sports sciences 2012, 30 (7), 633–640. DOI: 10.1080/02640414.2012.661070.
Manzano-Carrasco, S.; Garcia-Unanue, J.; Haapala, E. A.; Felipe, J. L.; Gallardo, L.; Lopez-Fernandez, J. Relationships of BMI, muscle-to-fat ratio, and handgrip strength-to-BMI ratio to physical fitness in Spanish children and adolescents. European Journal of Pediatrics 2023, 182 (5), 2345–2357. DOI: 10.1007/s00431-023-04887-4.
Tomlinson, D. J.; Erskine, R. M.; Morse, C. I.; Winwood, K.; Onambélé-Pearson, G. The impact of obesity on skeletal muscle strength and structure through adolescence to old age. Biogerontology 2016, 17 (3), 467–483. DOI: 10.1007/s10522-015-9626-4.
Nedeljkovic, A.; Mirkov, D. M.; Bozic, P.; Jaric, S. Tests of muscle power output: the role of body size. Int J Sports Med 2009, 30 (2), 100–106. DOI: 10.1055/s-2008-1038886.
Bähr, F.; Wöhrl, T.; Teich, P.; Puta, C.; Kliegl, R. Impact of Height-to-Mass Ratio on Physical Fitness of German Third-Grade Children, 2024. DOI: 10.21203/rs.3.rs-3885133/v1.
Abraham, A.; Lorenzo Jiménez Sáiz, S.; McKeown, S. Planning your coaching: a focus on youth participant development. In: Practical Sports Coaching; Routledge, 2014, pp 44–81. DOI: 10.4324/9780203767566-15.
Harris, B. S.; Blom, L. C.; Visek, A. J. Assessment in Youth Sport: Practical Issues and Best Practice Guidelines. The Sport psychologist 2013, 27 (2), 201–211. DOI: 10.1123/tsp.27.2.201.
Berntzen, I.; Lagestad, P. Effects of coaches' feedback on psychological outcomes in youth football: an intervention study. Frontiers in sports and active living 2025, 7, 1527543. DOI: 10.3389/fspor.2025.1527543.
Baron-Thiene, A.; Alfermann, D. Personal characteristics as predictors for dual career dropout versus continuation – A prospective study of adolescent athletes from German elite sport schools. Psychology of Sport and Exercise 2015, 21, 42–49. DOI: 10.1016/j.psychsport.2015.04.006.
Menting, S. G. P.; Hendry, D. T.; Schiphof-Godart, L.; Elferink-Gemser, M. T.; Hettinga, F. J. Optimal Development of Youth Athletes Toward Elite Athletic Performance: How to Coach Their Motivation, Plan Exercise Training, and Pace the Race. Frontiers in sports and active living 2019, 1, 14. DOI: 10.3389/fspor.2019.00014.

The authors declare no competing interests.

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Enriching Medicine Ball Throw with Anthropometric Information: An Alternative Assessment Method

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Abstract

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Introduction

Methods

Results

Descriptive statistics

Alignment of MBT_A vs. MBT_T with four fitness tasks

Variance components and correlation parameters

Discussion

Traditional and anthropometrically enriched MBT_A

Implications for children’s PF assessment and sports training in general

Limitations

Conclusion

Declarations

References

Additional Declarations

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