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. 2021 Apr 30;16(4):e0250953. doi: 10.1371/journal.pone.0250953

Multidimensional characteristics of young Brazilian volleyball players: A Bayesian multilevel analysis

Felipe G Mendes 1, Ahlan B Lima 1, Marina Christofoletti 1, Ricardo T Quinaud 1, Carine Collet 2, Carlos E Gonçalves 3, Humberto M Carvalho 1,*
Editor: Nili Steinberg4
PMCID: PMC8087100  PMID: 33930069

Abstract

Brazil has been the benchmark for volleyball performance for at least two decades, providing a unique context to examine expertise development. This study examined the variation in body size, functional capacities, motivation for achievement, competitiveness, and deliberate practice of youth volleyball players associated with differences in biological maturity status, chronological age, and accumulated deliberate volleyball practice, adopting a Bayesian multilevel modeling approach. We considered 68 female and 94 male adolescent players (14.2 years, 90% confidence interval: 12.7 to 16.0). Players were grouped by the onset of deliberate volleyball practice as related to biologic maturation milestones [pre-puberty deliberate practice onset (12% of the sample), mid-puberty deliberate practice onset (51% of the sample), and late-puberty deliberate practice onset (37% of the sample). There was substantial variation in body dimensions and functional performance by gender. There was no variation by gender for motivation for deliberate practice and motivation for achievement and competitiveness. The young volleyball players appeared to be highly motivated and committed to deliberate practice, achievement, and competitiveness. Alignment of chronological age, biological maturation, and accumulated training experience allow more in-depth insights into young volleyball players’ development, providing sounder support for coaches´ decisions.

Introduction

The development of young volleyball players into adult sport expertise is likely nonlinear and dependent on many interacting factors to attain optimal physical, technical, tactical, and behavioral characteristics [1]. Hence, the use of multidimensional approaches to understanding young athletes’ development is recommended [24]. A key issue in youth sports lies in interpreting athletes´ performance, which is generally aligned by chronological age. Interpretations based on chronological age per se are incomplete, at best. Often, coaches, researchers, and interested stakeholders infer about players´ growth and maturity status based on chronological age. However, there is wide variability in the development of body size, functions, and behavior during pubertal growth [4, 5]. On the other hand, youth sports programs often assume that sport expertise is positively related to the accumulated number of hours of practice [6, 7]. The variability of accumulated deliberate practice, i.e., accumulated experience in the sport, between players should be considered when interpreting their development.

Movement patterns in volleyball require high-intensity efforts with an intermittent nature, i.e., frequent short bouts of high-intensity exercise followed by periods of low-intensity activity and brief rest periods [8]. The match duration is about 90 minutes. Hence, it requires from players a good fitness level to sustain efforts requiring mainly aerobic and anaerobic alactic energy systems [911]. Considerable demands are also placed on the neuromuscular system during the various sprints and jumps (blocking and spiking) and high-intensity court movement that repeatedly occurs during the match [12]. Overall, volleyball players are expected to express high levels of speed, agility, upper-body and lower-body muscular power [12, 13]. However, relatively little is known about volleyball players’ physical and functional characteristics, particularly during adolescence.

Nowadays, the early onset of deliberate practice has become a mainstream path for talent development. Young athletes are becoming engaged and committed to youth sports programs at early pre-pubertal ages [14, 15]. The engagement in youth sports development programs is probably conditional on a strong orientation towards competitive success, added to a strong will to attain expertise and commitment to high practice volume and intensity [7, 16]. Nevertheless, it remains unclear whether the early onset of deliberate practice positively or negatively affects young athletes’ psychosocial characteristics, particularly achievement and competitiveness motivation and motivation for deliberate practice [1720].

Interpretations of young athletes’ performance or behavior are dependent on individual (e.g., gender, accumulated deliberate practice in the sport, or maturity status) and contextual characteristics (e.g., age-group category or competitive level) [21]. Hence, youth sports observations need to consider cross-classified nesting within and between groups, which often requires coping with an imbalance in sample size and heterogeneity among players. Traditional single-level regression models have been used to deal with the data, especially in settings with a low group-level variation where multiple comparisons are a particular concern [22]. Multilevel models can cope with imbalanced samples and explicitly assume clusters of observations within the data with unique coefficients [23]. The estimates for each cluster take advantage of the full sample information (i.e., shifting estimates toward each other), yielding better estimates [22].

Multilevel models can be fitted within a Bayesian framework [24]. Bayesian methods treat parameters as random variables combining both sample data and prior distribution information to estimate a (posterior) probability distribution that reflects the uncertainty associated with how well they are known, based on the data [25, 26]. Those unfamiliar with Bayesian methods will not see significance tests, but instead, the relative confidence in different models and parameter values is assessed by means, confidence intervals (also referred to as credible intervals), and visual inspection of model predictions [23]. Hence, Bayesian methods allow a direct probabilistic interpretation of confidence intervals and posterior probabilities, relevant in Sport Sciences, where interests often lie in estimating small effects [25].

The Brazil volleyball national teams have been consistently the highest-ranked nation globally at the male adult level and ranging from the highest to the fourth-ranked country at the female level [27]. Hence, youth volleyball programs in Brazil offer a unique context to study expertise development in team sports. This study examined the variation in body size, functional capacities, motivation for achievement, competitiveness, and deliberate practice of youth volleyball players associated with differences in biological maturity status, chronological age, and accumulated deliberate volleyball practice, adopting a Bayesian multilevel modeling approach.

Materials and methods

Study design and participants

The present survey included 162 young volleyball players (female players, n = 68; male players, n = 94). The players were engaged in formal training and competition within under 13 (n = 35), under 15 (n = 71), and under 17 (n = 56) teams from two clubs from Florianópolis, Santa Catarina, and Curitiba, Paraná. The players competed at the state level supervised by the Federação Catarinense de Voleibol and the Federação Paranaense de Voleibol, respectively. The competitive season in Brazil typically runs between February/March until November/December. At the time of the study, all the volleyball players regularly trained (~300–400 min/wk) over a 10-month season (February to November). The Research Ethics Committee approved the study of the Federal University of Santa Catarina. Players and their parents or legal guardians provided written informed consent after giving information about the study’s nature. Participation was voluntary, and the players could withdraw from the study at any time.

Procedures

We calculated chronological age to the nearest 0.1 years by subtracting a birth date from the date of testing. The players were grouped into two-year age categories: under 13 (11.0–12.9), under 15 (13.0–14.9) and under 17 (15.0–16.9) years. Deliberate volleyball practice onset was considered the self-reported age when players started formal training and competition, supervised by a coach within a youth volleyball program registered in the state federation, with no participation in practice and competition in other organized sports.

We used the gender-specific maturity offset protocol [28] to determine payers´ maturity status. The offset equations estimate time before or after peak height velocity (PHV) based on chronological age and stature. We subtracted the offset estimate from chronological age to estimate each player´s age at PHV. Players´ estimated age at PHV was contrasted against a gender-specific reference age at PHV. We derived the references for gender-specific age at PHV based on a meta-analysis of longitudinal growth studies summarized elsewhere [29]. The reference age at PHV was 11.9 (90% confidence interval: 11.8,12.0) years and 13.9 (90% confidence interval; 13.8, 14.0) years for girls and boys, respectively [20]. Then we classified players as follows: early maturers (n = 68), when estimated age at PHV was lower than the gender-specific reference age at PHV by more than six months; average maturers (n = 81) when players´ estimated age at PHV was within plus/minus six months of the gender-specific age at PHV; late maturers (n = 13), when estimated age at PHV was higher than the gender-specific reference age at PHV by more than six months. Nevertheless, we assume the limitations of the maturity offset protocol [4], particularly at the observed age range’s extremes where bias may be more likely [30]. Hence, we allow for the possibility that a player may have been assigned to the wrong maturity status category.

The onset of deliberate volleyball was interpreted relative to pubertal growth milestones, the ages of onset of the pubertal growth spurt, and at PHV [20]. We grouped the players by the onset of deliberate volleyball practice as follows: pre-puberty deliberate volleyball practice onset (n = 17), the players who started practice before the reference age of pubertal growth spurt onset (female: 9.4 years, 90% confidence interval: 9.1 to 9.7; male: 11.1 years, 90% confidence interval: 10.8 to 11.5); mid-puberty deliberate volleyball practice onset (n = 83), the players starting practice between the reference ages of pubertal growth spurt onset age and at PHV; late-puberty deliberate volleyball practice onset (n = 62), the players starting practice after the reference age at PHV.

Stature was measured with a portable stadiometer (Seca model 206, Hanover, MD, USA) to the nearest 0.1 cm. Body mass was measured with a calibrated portable balance (Seca model 770, Hanover, MD, USA) to the nearest 0.1 kg. Wingspan was measured with a standard tape measure to the nearest 0.1 cm, from middle digit to middle digit with both shoulders abducted to 90°. Intra-observer technical errors of measurement were 0.23 (90% confidence interval: 0.17 to 0.42) cm for stature, 0.11 kg (90% confidence interval: 0.07 to 0.27) for body mass and 0.18 cm (90% confidence interval: 0.12 to 0.38) for wingspan.

Considering volleyball-specific effort demands [911], we examined players’ functional capacities by measuring 10-m sprint, vertical jump (countermovement jump), and upper-body muscular power (2-kg medicine ball overhead throw). The players’ running speed was evaluated with a 10-m sprint effort [31] using two photocells (Microgate Polifemo, Bolzano, Italy). The timing gates were positioned at the starting point and 10 m after. Players were instructed to run as quickly as possible the 10-m distance from a standing start. Sprint was measured to the nearest 0.01 s. Intra-observer technical error of measurement was 0.05 s (90% confidence interval: 0.04 to 0.07). Lower-body muscular power was estimated using the vertical jump with countermovement [32]. Vertical jump with countermovement performance was examined using the Optojump photocell system (Microgate, Bolzano, Italy). Players started from an upright standing position and were instructed to begin the jump with a downward movement, which was immediately followed by a concentric upward movement, resulting in a maximal vertical jump. During jumping, hands were held on the hips during all phases of the jumping. Three trials were given with a 30 s rest period, and the best trial was retained for analysis. Intra-observer technical error of measurement was 1.5 cm (90% confidence interval: 1.1 to 2.4). Upper-body muscular power was determined using a 2-kg medicine ball overhead throw. The players were positioned with their knees on the floor, holding the ball with the hands at chest level. They performed an overhead throw for the starting position vigorously as far straight forward as she/he could while maintaining the knees on the floor. The longest distance of three attempts was retained for analysis. Intra-observer technical error of measurement was 0.28 m (90% confidence interval: 0.21 to 0.43).

We used the Deliberate Practice Motivation Questionnaire [33, 34] and the Work and Family Orientation Questionnaire [35]. The Deliberate Practice Motivation Questionnaire, initially designed for chess, comprises 18 items rated on a 5-point Likert scale (1 = completely disagree to 5 = completely agree), considering two dimensions of deliberate practice: will to compete and will to excel. We used the adapted version for team-sports, which was previously translated and validated to Portuguese [7]. The Work and Family Orientation Questionnaire, composed of 19 items and rated on a 5-point Likert scale (1 = completely disagree to 5 = completely agree), assesses four dimensions of achievement: personal unconcern, work, mastery, and competitiveness. This study only used the last three subscales, consistent with previous studies with youth sports samples [4, 20, 36].

Data analysis

Our estimations were based on Bayesian multilevel models considering the variation on body dimensions, functional capacities, and motivation characteristics, adjusting for cross-classified nesting by gender, age group, maturity status, and the onset of deliberate practice among young Brazilian volleyball players. We fitted the models in R [37] using “brms” package [38], which calls Stan [39]. We standardized (z-score) all the outcomes for interpretative convenience and computational efficiency. We used varying-intercept models where each player´s outcome (intercept) was estimated as a function of his/her age group, estimated maturity status, and the onset of deliberate practice. Hence for player i, with indexes a, m, d, and g for age group, maturity status, the onset of deliberate practice, and gender, respectively. The group-level effect terms (also refered to as random effects) and data-level term (also refered as level-1 residuals) were drawn from normal distributions with variances to be estimated from the data:

yi=β0+αa[i]agegroup+αm[i]maturitystatus+αd[i]deliberatepractice+αg[i]gender+ϵi
αa[i]agegroupN(0,σagegroup2),fora=1,2,3.
αm[i]maturitystatusN(0,σmaturitystatus2),form=1,2,3.
αd[i]deliberatepracticeN(0,σdeliberatepractice2),ford=1,2,3.
αg[i]genderN(0,σgender2),forg=1,2.
ϵiN(0,σyi2)

Measurement of young athletes’ performance and behaviors are often noisy, and effects are likely small. Hence, we used weakly informative priors to regularize our estimates, a normal prior (0,5) for the intercept (population-level parameter, also referred to as fixed effect) and group-level parameters. For the data-level residuals (ϵi), we used the “brms” default prior, Student-t (3, 0, 2.5). Given the standardization of the outcomes using a normal (0,1) prior for the parameters, we state that the group-level estimates are unlikely to be greater than one standard deviation of the outcome. We run four chains for 2,000 iterations with a warm-up length of 1,000 iterations in each model. The convergence of Markov chains was inspected with trace plots. We used posterior predictive checks to be confident in our models and estimations [24].

Results

Characteristics of the youth Brazilian volleyball players for the total sample and grouped by gender are shown in Table 1. All but two maturity offset values were positive for the female players, and seventy-one from ninety-four maturity offset values were positive for male players. In general, most of the players in the present sample were beyond the age at PHV. Only 13 players were classified as late maturers. The other players were about evenly distributed as early, and average matures. About 11% of the sample players had pre-puberty onset of deliberate volleyball practice, while about 51% and 38% of the players had mid-puberty and late-puberty deliberate volleyball practice onset, respectively.

Table 1. Posterior estimations and 90% credible intervals of young Brazilian volleyball players by gender.

All sample (n = 162) Female (n = 68) Male (n = 94)
Chronological age, yrs 14.2 (14.0 to 14.5) 14.3 (14.1 to 14.5) 14.2 (14.0 to 14.4)
Maturity offset, yrs 1.58 (1.35 to 1.81) 2.45 (2.24 to 2.67) 0.94 (0.76 to 1.11)
Years of training experience, yrs 1.8 (1.6 to 2.1) 1.9 (1.6 to 2.1) 1.8 (1.6 to 2.0)
Stature, cm 171.2 (169.4 to 172.8) 167.9 (166.2 to 169.6) 173.5 (172.1 to 175.0)
Body mass, kg 63.2 (61.0 to 65.5) 61.5 (59.2 to 63.7) 64.5 (62.6 to 66.4)
Wingspan, cm 175.7 (173.9 to 177.6) 173.0 (171.1 to 174.9) 177.7 (176.1 to 179.3)
Performance
Countermovement jump, cm 25.3 (24.1 to 26.4) 23.5 (22.3 to 24.6) 26.7 (25.6 to 27.5)
2-kg medicine ball throw, m 6.4 (6.1 to 6.6) 6.0 (5.5 to 6.1) 6.8 (6.5 to 7.0)
Sprint 10-m, s 2.12 (2.09 to 2.15) 2.15 (2.12 to 2.18) 2.10 (2.08 to 2.13)
Deliberate practice motivation
Will to excel, 1–5 4.06 (3.92 to 4.20) 3.95 (3.80 to 4.09) 4.15 (4.04 to 4.27)
Will to compete, 1–5 4.49 (4.42 to 4.56) 4.48 (4.40 to 4.54) 4.50 (4.43 to 4.56)
Achievement and competitiveness motivation
Mastery, 1–5 4.30 (4.20 to 4.40) 4.28 (4.19 to 4.37) 4.32 (4.24 to 4.40)
Work, 1–5 4.46 (4.38 to 4.54) 4.46 (4.38 to 4.53) 4.45 (4.39 to 4.52)
Competitiveness, 1–5 3.77 (3.66 to 3.89) 3.64 (3.51 to 3.76) 3.87 (3.77 to 3.97)

Estimations and uncertainty (90% and 67% confidence intervals) of the outcomes are plotted by age group and contrasting with age group by maturity status and the onset of deliberate practice. We separated the plots by gender. Our models accounted for variation associated with age group, maturity status, the onset of deliberate practice, and gender. Hence, we can interpret the effects of target groups, accounting for the other group-effects. Supplementary figures and model codes are available as supplementary material (https://osf.io/ud2ev/).

For body dimensions, variation by gender was substantial (Table 1). As expected, male players were taller and heavier than female players, independent of age and maturity. We plotted players’ body dimensions against the World Health Organization (WHO) growth references for stature [40]. The WHO growth references are available for body mass only until ten years of age [40]. Hence we used the US population growth references for body mass [41]. Overall, the young Brazilian volleyball players compared favorably with the reference samples, mostly above the 75th percentile for stature, with a substantial part of the sample above the 90th percentile of the WHO growth references (Fig 1). As for body mass, the young Brazilian volleyball players showed mostly between the 50th and 75th percentiles for the US population growth references (S1 Fig of S1 File).

Fig 1.

Fig 1

Statures of young female (upper panel) and male (lower panel) volleyball players by chronological age against the World Health Organization (WHO) growth references for stature.

The multilevel regression models estimated parameters are summarized in Table 2. Older female and male players had better functional performance than younger players (Figs 24). After adjusting for age group, maturity status, and the onset of deliberate volleyball practice, estimates varied between female and male players for upper-body muscular power (female estimate = 5.1 m, 90% CI: 1.5 to 8.8; male estimate = 6.8 m, 90% CI: 3.2 to 10.4) and countermovement jump (female estimate = 21.7 cm, 90% CI: 13.3 to 29.0; male estimate = 25.3 cm, 90% CI: 16.8 to 32.6). However, for sprint performance, variation by gender was trivial (female estimate = 2.17 s, 90% CI: 2.07 to 2.29; male estimate = 2.12 cm, 90% CI: 2.03 to 2.24).

Table 2. Multilevel regression models estimates and 90% credible intervals of young Brazilian volleyball players performance and motivation adjusted by age group, maturity status, onset of deliberate practice and gender.

Population-level parameter (β0) Group-level parameters (standard deviation) Data-level residuals (ϵi)
Age group (αa[i]agegroup) Maturity status (αm[i]maturitystatus) onset of deliberate practice αd[i]deliberatepractice Gender (αg[i]gender)
Performance
Countermovement jump, cm -0.28 (-1.79 to 1.21) 1.00 (0.47 to 1.82) 0.25 (0.01 to 0.81) 0.39 (0.04 to 1.07) 0.69 (0.17 to 1.65) 0.78 (0.71 to 0.85)
2-kg medicine ball throw, m -0.22 (-1.74 to 1.29) 1.04 (0.52 to 1.85) 0.49 (0.04 to 1.33) 0.25 (0.01 to 0.85) 0.72 (0.19 to1.64) 0.72 (0.65 to 0.79)
Sprint 10-m, s 0.09 (-1.06 to 1.21) 0.49 (0.10 to 1.21) 0.24 (0.01 to 0.81) 0.36 (0.03 to 1.06) 0.54 (0.05 to 1.46) 0.98 (0.89 to 1.08)
Deliberate practice motivation
Will to excel, 1–5 -0.15 (-1.27 to 0.93) 0.38 (0.04 to 1.06) 0.55 (0.09 to 1.31) 0.27 (0.01 to 0.90) 0.40 (0.02 to1.31) 0.97 (0.88 to 1.07)
Will to compete, 1–5 -0.04 (-0.81 to 0.70) 0.23 (0.01 to 0.74) 0.43 (0.05 to 1.12) 0.26 (0.01 to 0.81) 0.39 (0.02 to 1.24) 1.00 (0.91 to 1.11)
Achievement and competitiveness motivation
Mastery, 1–5 -0.04 (-0.97 to 0.94) 0.24 (0.01 to 0.81) 0.25 (0.01 to 0.80) 0.32 (0.02 to 0.98) 0.42 (0.02 to 1.35) 1.01 (0.92 to 1.11)
Work, 1–5 -0.01–0.68 to 0.67) 0.24 (0.01 to 0.76) 0.25 (0.01 to 0.79) 0.28 (0.01 to 0.85) 0.37 (0.02 to 1.20) 1.01 (0.93 to 1.11)
Competitiveness, 1–5 -0.09 (-1.20 to 1.00) 0.52 (0.11 to 1.28) 0.31 (0.02 to 0.93) 0.38 (0.04 to 1.05) 0.48 (0.03 to 1.36) 0.97 (0.89 to 1.07)

Note: All outcomes were standardized (z-score).

Fig 2.

Fig 2

Posterior estimations and uncertainty (bold lines and thick ones represent 67% and 90% intervals, respectively) for countermovement jump performance by age group and contrasting age group by maturity status (upper plot), and the onset of deliberate practice (lower plot).

Fig 4.

Fig 4

Posterior estimations and uncertainty (bold lines and thick ones represent 67% and 90% intervals, respectively) for 10-m sprint performance by age group and contrasting age group by maturity status (upper plot), and the onset of deliberate practice (lower plot).

Fig 3.

Fig 3

Posterior estimations and uncertainty (bold lines and thick ones represent 67% and 90% intervals, respectively) for 2-kg medicine ball throw performance by age group and contrasting age group by maturity status (upper plot), and the onset of deliberate practice (lower plot).

There was no substantial variation by gender and onset of deliberate volleyball practice for the dimensions of deliberate volleyball practice motivation (Table 2). The scores for both will to excel and will to compete showed small variation by age group, at best. There was variation between players by maturity status in the motivation for will to excel (standardized estimates: early maturers = 0.16, 90% CI -0.31 to 0.56; average maturers = -0.12, 90% CI: -0.54 to 0.27; late maturers = -0.47, 90% CI: -1.07 to 0.13) and will to compete (standardized estimates: early maturers = 0.13, 90% CI -0.25 to 0.51; average maturers = -0.09, 90% CI: -0.45 to 0.24; late maturers = -0.27, 90% CI: -0.83 to 0.23), particularly in the older age groups, i.e., under-15 and under-17 (Fig 5). Only for competitiveness, under 13 players showed lower values for competitiveness than the other age groups (Fig 6). There was no substantial variation between players’ scores by gender, age group, maturity status, and the onset of deliberate practice for achievement and competitiveness motivation (S2–S4 Figs of S1 File).

Fig 5.

Fig 5

Posterior estimations and uncertainty (bold lines and thick ones represent 67% and 90% intervals, respectively) for will to excel (upper plot) and will to compete (lower plot) scores by age group and contrasting age group by maturity status.

Fig 6.

Fig 6

Posterior estimations and uncertainty (bold lines and thick ones represent 67% and 90% intervals, respectively) for competitiveness score by age group and contrasting age group by maturity status (upper plot), and the onset of deliberate practice (lower plot).

Discussion

Studies examining the interacting influence of chronological age, biological maturity status, and accumulated deliberate practice in young athletes´ functional and psychological characteristics are scarce, particularly with female athletes. To our best knowledge, this study is the first to consider age-, maturity-, and deliberate practice-associated variation on growth, functional performance motivation for achievement, competitiveness, and deliberate practice of youth volleyball players. Furthermore, Brazil volleyball national teams have been consistently the reference of the highest adult level for at least the last two decades for both female and male players [27]. Hence, the study of youth volleyball programs in Brazil potentially offers a unique context to understand the expertise development in team sports.

To our best knowledge, available data with youth volleyball characteristics is limited. There was substantial variation in body dimensions and functional performance between young female and male Brazilian volleyball players in the present sample. Young male players were higher, heavier, and with higher performance scores than the young female players. However, there was no variation by gender for motivation for deliberate practice and motivation for achievement and competitiveness. As should be expected, sexual dimorphism needs to be accounted for in the interpretations of young volleyball athletes’ body dimensions and functional capacity [42]. However, the present sample’s young volleyball players appeared to be highly motivated and committed to deliberate practice, achievement, and competitiveness. The present data suggest that the Brazilian youth volleyball training environment also seems to contribute to players being motivated and engaged with deliberate practice, independent of gender. Given the sustained excellence of Brazilian volleyball at the adult level, it may be reasonable to consider that the young Brazilian volleyball players may be oriented towards competitive success and exhibit a strong will to become expert players.

On average, most of the sample young Brazilian volleyball players were above the 75th percentile age- and gender-specific reference of the WHO growth references [40], which include Brazilian data [43]. In many cases, statures were above the 97th percentiles for female and male players (S1 Fig of S1 File). The mean masses of male and female youth Brazilian volleyball players with age and gender-specific were between 50th-90th percentiles of the US population [41]. There is no comparable data available for body mass in the WHO growth references [40]. Available data with young volleyball players is scarce. The young Brazilian volleyball players’ body size was similar to Australian adolescent volleyball players from different competitive levels, i.e., national, state, and novice [12], and the England men’s junior volleyball teams [44]. Body dimensions appear to be highly valued in the selection process of youth volleyball, in particular stature. Interpretation of body dimensions during the pubertal growth period may be problematic, as the variation between individuals is considerable. The transient size advantages of early maturing players may be overvalued with a naïve interpretation.

We used the gender-specific maturity offset equations in the present study, which were recently simplified [28]. The offset equations estimate individuals´ distance to PHV, providing an estimate of their maturity status. The equations give an alternative to having a reference of maturity status when considering cross-sectional observations. However, the equations, the original [45] and simplified version [28], have limited validity [30]. Hence, the protocol may not be a sufficiently sensitive indicator of maturity status requiring a conservative interpretation of the data. In our sample, both female and male volleyball players appeared to be mostly early or average maturers. The present data suggest that early to average maturing and taller girls and boys may be advantaged to be retained within youth volleyball programs. The results may reflect selection or exclusion (self, coach, or some combination), the different success of players advanced in maturation, the changing nature of the game (the increase of the net height in older age groups), or some combination of these factors [46]. A similar trend has been noted in youth sports where body dimensions are determinants of performance [36].

Interestingly, the late-maturing players in our sample, regardless of gender, had a late-onset of deliberate volleyball practice. Furthermore, both female and male players’ functional performance and motivation scores, except competitiveness, did not vary substantially by maturity status, adjusting for age group, and the onset of deliberate practice. Given that late-maturing individuals may have a more significant potential to attain higher adult stature [47], youth volleyball coaches should consider players´ maturity status to help their interpretations about players’ physique, performance, and behavior.

Youth sports programs often are focused on talent development and expertise attainment [48]. Often, coaches and researchers assume the need for early-onset deliberate practice during childhood and extensive accumulation of hours of training through the sports career as imperative to develop expertise in adulthood [49, 50]. Hence, early specialization in many youth sports contexts is the mainstream path for talent development and achievement of professional status in adult sports [14, 15, 51]. However, data in youth soccer [52] and volleyball [53] showed children and adolescents engaged in multi-sports developmental programs and/or with a later onset of deliberate practice attained expertise at adult levels. In volleyball, our data concur with observations of the onset of deliberate practice during the pubertal years or even during late pubertal growth [5355]. Also, the development of expertise in volleyball associated with a later onset of deliberate volleyball practice may benefit from previous multi-sports participation during childhood and early adolescence [53, 54], as postulated in the Developmental Model of Sport Participation framework [56]. However, we did not retain information about players´ previous sports participation and experiences, limiting our interpretation.

Adjusting for age group and maturity status, early accumulation of deliberate volleyball practice does have a substantial contribution to explain variation between players functional capacities, particularly for vertical jump and sprint performance. Given the importance of jump in volleyball, coaches and trainer might need to be cautious interpreting the jump performance at early ages has early advantages, interpreted as a “potential gifted athlete”, probably reflecting differences in accumulated training stimulus. Our results were consistent with observations in young basketball players [20], noting that players with exposure to sport-specific deliberate practice during the pubertal years or late pubertal growth have better overall physiological performance than players with an onset of deliberate practice during childhood. Overall, our data add to the argument that early specialization in sport has not been shown to enhance physiological systems more than diversified participation in physical activity and sport [57]. On the other hand, there was no apparent relation between the early accumulation of deliberate volleyball practice with deliberate practice motivation and achievement and competitiveness motivation. Hence, our data is inconsistent with the claims that early exposure to deliberate single-sport practice decreases motivation for participation [1719, 58], at least in youth volleyball.

Inferences about young athletes´ development based on chronological age, maturity status, or accumulated training experience per se are incomplete, at best. Nevertheless, it remains a common practice of research reporting in youth sports studies. To provide more accurate interpretations, coaches and researchers should align the player’s chronological with its growth pattern and with her or his accumulated sports experience. Hence, researchers should consider modeling approaches that can deal with the different levels and sources of variations (i.e., hierarchical or cross-classified structure), often based on imbalanced samples and noisy measurements. Traditional analytical approaches (e.g., t-tests, least-squares linear regression, analysis of (co)variance, and many others), i.e., single-level fixed effects regressions, are an unsatisfactory default for analysis [22]. Single-level regressions treat the units of analysis as independent observations, and in particular higher-level predictor variables will be the most affected by ignoring grouping [59]. In the alternative, multilevel modeling should be considered as a default approach, as already in several scientific areas [26]. Multilevel models allow and explicitly model the data structure by allowing for residual components at each level in the hierarchy or cluster [59], i.e., the model explicitly variations within and between units (individuals and/or groups). Multilevel models partially pool the information across units to produce better estimates for all units in the data [26]. Nevertheless, multilevel modeling requires more attention to be used properly.

Given the need for transparency and reproducibility in science, we provide the datasets, model codes, and supplementary material supporting this study inference in an open repository (osf.io/ud2ev). Although we discuss and speculate our observations given the currently available knowledge in the literature, we acknowledge that this study represents a single observational study, and interpretations and generalizations need to be conservative. A key feature of Bayesian inference lies in the explicit updating of knowledge based on data accumulated from several observational studies [26], particularly in scientific areas using different sources and data levels such as sport sciences. Hence, this study’s data and its interpretations should be integrated with future studies to provide a more comprehensive understanding of young volleyball players’ development.

Conclusion

Conditional on the data, young Brazilian volleyball players tend to have an onset of deliberate practice during pubertal growth years or late adolescence. Researchers and coaches should consider sexual dimorphism to interpret young volleyball players’ body dimensions and functional capacity. However, motivation characteristics related to deliberate practice, achievement, and competitiveness appear similar in female and male young players. The alignment of chronological age, biological maturation, and accumulated training experience in the sport may allow more in-depth insights into young volleyball players’ development, providing sounder support for coaches´ decisions in youth volleyball. Hence, coaches and others involved with youth volleyball programs need to be familiar with the growth and maturation basic principles.

Supporting information

S1 File

(PDF)

Data Availability

The datasets, model codes and supplementary material supporting the conclusions of this article are available in the OSF repository (osf.io/ud2ev).

Funding Statement

FGM, ABL, MC and RTQ were supported by grants from the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior – Brasil (CAPES) – Finance Code 001. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

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Decision Letter 0

Nili Steinberg

4 Jan 2021

PONE-D-20-27002

Multidimensional characteristics of young Brazilian volleyball players: a Bayesian multilevel analysis

PLOS ONE

Dear Dr. Carvalho,

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Reviewer #2: Yes

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Reviewer #2: Yes

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Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: l118: The abbreviated term, PHV, was observed at first time here, but you did not explain it beforehand. At line 135, I found that the “peak height velocity” was abbreviated to the PHV.

l123,-123, l138-l140, l146-147:

Same information of PHV is duplicated and redundant. Please consider if it should be omitted.

l201:

How did you categorize age groups? In the equation, participants’ age seemed to be divided into four groups.

However, I could not find the descriptions of divided points for age in the Method section.

In figures, age groups were shown as under-17, under-15, and under-13. However, these were three age groups, not four.

l201, l202:

These symbols were mistakes?

for i = 1, 2, 3, 4 -> for a = 1, 2, 3, 4

for s = 1, 2,3 -> for d = 1, 2, 3

l200-l214:

I could not understand well the reason why you applied a multilevel model for this data in which each group included only several categories.

For example, when you inferred the effect of gender on outcomes, it would be enough to estimate the fixed effect of the gender (i.e., slope of the gender on the outcome) using an ordinary regression model. At least, for binary variable (i.e., gender), it seemed to be unnecessary to assume the hierarchical structure of parameters.

In addition, you categorized age into some groups, but the effect of age on outcomes should be inferred using continuous predictive variable. If you pooled continuous age values into some categories, you would lack much information about influence of age on outcome.

Taken together, it seemed that the ordinary regression model would be enough for your analysis. If not so, please explain clearly the purpose of using multilevel model for this study.

l207:

What do “population-level parameter” and “group-level parameters” mean? Is “population-level parameter” equivalent to beta? Is "group-level parameter" equivalent to alpha? If you called sigma "group-level parameter", it would be wrong. Sigma is often called “hyper parameter”. Alpha is often called “random intercept” or “varying intercept”.

What did you set a prior for each sigma?

In addition, in the result section, you should report the results of inferred group-level intercept (i.e., beta) and hyper parameters (i.e., sigma).

Figures, Table, and Figure captions:

Figures and Table do not include enough information. You should also refine them.

In figure 1, what does each color of lines mean?

How did you produce the predicted lines in Figure 1? They seemed to be produced from a nonlinear regression model, but the details of the model were not found. Please explain what “the growth references of the WHO” indicates.

In Figure 2-Figure 6, lines overlapped, and we could not detect each line. Each line should be displayed by shifting each position. In addition, I could not distinguish the 90% and 67% intervals in these Figures.

What does "mat_cat" mean?

l249-l253: I could not figure out which part we should see in each figure in order to understand “there was substantial variation between female and male players”.

Figure 6 is identical with Figure 5?

In Table 1, I could not understand what “1-5”, which was described in “Deliberate practice motivation” and “Achievement and competitiveness motivation”, meant.

Reviewer #2: The authors provide a description of the variation in body size, functional capacities, motivation for achievement and competitiveness, and motivation for deliberate practice of 68F+94M Brazilian adolescent volleyball players. The paper essentially consists of a descriptive statistics (with a Bayesian multilevel modelling for estimates' adjustment), oriented toward the assessment of different levels of motivations. The manuscript is reasonably written, and quite easy to follow also by an audience of non-specialists; from a data science perspective the paper is quite simple and straightforward, with very basic statistical approaches.

Hereafter I list a few points that the authors need to take into account and discuss further:

- aim of the research needs to be better clarified - the descriptive purposes is rather vague and poorly focused

- the use of the Bayesian modelling should be explained in more details, both in terms of motivation and in its mathematical application in the current situation

- the sample size is too small to allow for robust generalisation of the results - in the discussion the conclusions drawn are beyond the support provided by the shown results.

- the term "credible interval" is somehow non-standard; what's the mathematical definition of "credible"? I would suggest using the word "confidence" instead, specifying the statistics used (e.g. 95% bootstrap t-Student)

- the usefulness of the results for volleyball trainers and specialists should be better pointed out, for instance providing some case studies highlighting how decision can be formulated by using the obtained outcomes.

- the use of amateur level player can represent a limiting factor of the study; in the authors' opinion, what are the differences to be expected if pro-level athletes are used instead for the same study?

**********

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Reviewer #2: No

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PLoS One. 2021 Apr 30;16(4):e0250953. doi: 10.1371/journal.pone.0250953.r002

Author response to Decision Letter 0


16 Feb 2021

Dear Prof. Nili Steinberg

We addressed your requests to ensure we followed PLOS ONE's style requirements, including those for file naming, include the table as part of your main manuscript and uploaded as separate "supporting information" the supporting figures. We specifically upload S1 fig wich is referenced in the text.

Hope we appropriatly reply to your requests.

Best regards

Humberto Carvalho

Attachment

Submitted filename: Response to Reviewers.docx

Decision Letter 1

Nili Steinberg

2 Mar 2021

PONE-D-20-27002R1

Multidimensional characteristics of young Brazilian volleyball players: a Bayesian multilevel analysis

PLOS ONE

Dear Dr. Carvalho,

Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.

Please submit your revised manuscript by Apr 16 2021 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosone@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

Please include the following items when submitting your revised manuscript:

  • A rebuttal letter that responds to each point raised by the academic editor and reviewer(s). You should upload this letter as a separate file labeled 'Response to Reviewers'.

  • A marked-up copy of your manuscript that highlights changes made to the original version. You should upload this as a separate file labeled 'Revised Manuscript with Track Changes'.

  • An unmarked version of your revised paper without tracked changes. You should upload this as a separate file labeled 'Manuscript'.

If you would like to make changes to your financial disclosure, please include your updated statement in your cover letter. Guidelines for resubmitting your figure files are available below the reviewer comments at the end of this letter.

If applicable, we recommend that you deposit your laboratory protocols in protocols.io to enhance the reproducibility of your results. Protocols.io assigns your protocol its own identifier (DOI) so that it can be cited independently in the future. For instructions see: http://journals.plos.org/plosone/s/submission-guidelines#loc-laboratory-protocols

We look forward to receiving your revised manuscript.

Kind regards,

Nili Steinberg

Academic Editor

PLOS ONE

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Reviewer #1: (No Response)

Reviewer #2: All comments have been addressed

**********

2. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Partly

Reviewer #2: Yes

**********

3. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: No

Reviewer #2: Yes

**********

4. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: Yes

Reviewer #2: Yes

**********

5. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #1: Yes

Reviewer #2: Yes

**********

6. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: Thank you for your response and revising the manuscript. Some of the concerns I raised earlier have been solved. However, some points which I could not understand well left. Please consider the followings.

>Authors ´ reply: We appreciate the reviewer's comment. Ordinary single-level regression would be innapropriate to deal with the data because:

>(i) the context of observation that presents a cross-classified nesting, as players belong to multiple groups (eg, a late maturing boy from the under 13 age group with an onset of deliberate practice during the pubertal years). Often analysis of covariance is used to interpret the youth sports data, likely overfitting the data, as multiple comparisons are highly problematic using a single-level model, even more in settings with a low group-level variation (Gelman, Hill, & Yajima, 2012);

>(ii) we examined the need to consider multilevel models by looking into null models (the simplest two level model which includes only the group-level parameters (also referred to as random parameters), to measure the proportion of total variance which fell between-groups (i.e., variance partition coefficient also reffered to as intracalss correlation)(Goldstein, 2011). Variance partition correlations higher than 0.05 indicate a substantial variation by the respective group and the need to use multilevel modeling (Goldstein, 2011; Snijders and Bosker, 2012).

>(iii) the key feature of multilevel modelling is shrinkage (partial pooling), by incorporating group- level effects. It allows for more efficient use of the data. These may be understood as a weighted average between the all sample estimate and a group or unit estimate. The specific weights are based on the entire variation of the sample and the group variation (Gelman and Hill, 2007). In particular, the partial pooling will be stronger for smaller units with fewer observations (Buttice and Highton, 2013)

>We agree with the argument to interpret the age effect assuming chronological age in the model. Indeed categorization removes potential variation. We choose to use age groups to echo the ecological context where players are grouped in competitive age groups. Also, following our previous point, partial pooling helps to mitigate the limitations of our choice for group age.

I agree all of advantages of Bayesian analysis you have raised. In addition, I also agree justification of categorizing age into several groups.

However, it is still odd for me that you have assumed the hierarchical structure of effect of gender. I cannot understand well the sense of estimating the variance of the effect between gender, which includes only two groups. Estimating "variance" of normal distribution, which the group including only two categories obeys, seems to be equivalent to estimating the "difference" between the two categories.

For the group including only two categories, in contrast to the regression model using the group as a dummy, the multilevel model seems to contain redundant parameters (i.e., each of individual parameters and standard deviation of normal distribution). The predictive accuracy might not be improved drastically, even if the multilevel model was used. It would not be necessary to consider partial pooling (shrinkage) for gender logically because there are only two groups and unknown groups do not exist.

In order to demonstrate whether there is a variance between male and female (in other words, whether there is a difference between the two), estimating the fixed slope of the gender seems to be enough.

If you do not agree, in your response, please refer to previous works which assumed the multilevel model for groups which include only two groups.

>Authors ´ reply: We used referred to the hyperparameters as population-level effects, which are referred to as fixed effects in frequentist analysis, and group-level effects which are referred to as random effects in frequentist analysis. This is the common designation when using Bayesian analysis. We inserted the comparable frequentist terms in the text to allow the unfamiliar reader with Bayesian analysis to better understand our report. For the residual standard deviation parameter (level-1 standard deviation or referred to as residuals), we adopted the default prior in the brms package. For the group-level effects (i.e., level-2 standard deviations, in this case,,,) we used half-normal priors, as we intend to have a conservative approach on the analysis by stating that the group-level estimates are unlikely to be greater than one standard deviation of the outcome.

I understood that the population-level effects and the group-effects represented the fixed effects (i.e., the intercept of your regression model) and random effects (i.e., sigma_a, sigma_m, sigma_d, and sigma_g), respectively.

You have not report the summary of inferred group-level intercept and group-effects yet, although I suggested earlier. Summary of posterior distributions of estimated parameters (e.g., mean, standard deviation, and 95% CI) may be necessary. As I suggested in the following comment, not only visualization of the results but also numeric information would be needed for objective explanations.

Is the "residual standard deviation parameter (level-1 standard deviation)" equivalent to the standard deviation of the normal distribution which the response variable (i.e., y_{i}) obeys?

In the model, information of the distributions which the response variable obeys is lack. The "level-1 standard deviation" should be shown clearly in the equation of the model.

For instance,

\\hat{y}_{i} = \\beta + \\alpha_{a[i]} + ...

...

y_{i} \\sim Normal(hat_{y}_{i}, \\sigma)

In addition, please explain the "default prior" in brms package concretely (i.e., the name of probability distribution and parameters).

In your response, half-normal priors were set for the group-level effects. However, in the revised manuscript, you described that normal prior (0, 5) was set as prior for group-level parameters. You should clearly describe "half-normal".

>Authors ´reply: We thank the reviewer ´s comment. Hopefully, we provide cleaner and clear Figures now. We dodged the estimates and uncertainty to remove the overlap. The legend titles were corrected in all figures, removing the variable label from the dataset.

For captions in Figure 2-6, you should explain that the bold lines and thick ones represent 67% and 90% intervals, respectively.

The legend of the deliberate practice disappeared in Figure 5, whereas it appeared in other figures. I found that the relationship between the onset of deliberate practice and will to excel (or will to compete) was reported in Figure S2. However, it seemed that S2-S4 Figs were never referred to in the main text.

>Authors ´reply: We apologize for the incorrect upload of the figures, We have corrected appropriately both Figure 5 and Figure 6. The Bayesian inference allows for direct probabilistic comparisons between estimates and uncertainty. Hopefully, with the changes in the Figures, it becomes clear for the reader.

I could not still understand well which of the parts in each figure indicated “substantial variation between female and male players”. Intervals shown in each panel seemed to indicate "variation between players within each gender". The results for each gender were separately shown by divided panels: therefore, it was difficult to compare differences between two genders.

In addition, because the interpretation using only visualized results seemed to be subjective and arbitrary, quantitative reports such as numeric information of intervals of parameters may be necessary. The posterior distributions of each parameter (e.g., group-level parameters such as sigma_gender, or slope of the gender in the regression model) should be reported for the objective interpretations.

>Authors ´reply: It represents the scale used in the questionnaires based on a Likert-like scale. The information about the questionnaires is provided in the methods section. It is a common practice to describe questionnaire scales, but we are open to suggestions to improve our reporting.

Please show the meaning of the number: for example, "(1: disagree, 5: agree)". Similarly, in the method and materials section, it should be described the labels of each number. We could not understand what the greater number meant, if the descriptions were omitted.

Reviewer #2: (No Response)

**********

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PLoS One. 2021 Apr 30;16(4):e0250953. doi: 10.1371/journal.pone.0250953.r004

Author response to Decision Letter 1


23 Mar 2021

Specific reply to reviewer´s comments

Authors´ reply: We appreciate the reviewer´s comments and suggestions. It has been uncommon to have comments to our models that allow us to rethink or correct them and the interpretations. Hopefully, we satisfactorily addressed the reviewer´s concerns.

Reviewer #1: Thank you for your response and revising the manuscript. Some of the concerns I raised earlier have been solved. However, some points which I could not understand well left. Please consider the followings.

>Authors ´ reply: We appreciate the reviewer's comment. Ordinary single-level regression would be inappropriate to deal with the data because:

>(i) the context of observation that presents a cross-classified nesting, as players belong to multiple groups (eg, a late maturing boy from the under 13 age group with an onset of deliberate practice during the pubertal years). Often analysis of covariance is used to interpret the youth sports data, likely overfitting the data, as multiple comparisons are highly problematic using a single-level model, even more in settings with a low group-level variation (Gelman, Hill, & Yajima, 2012);

>(ii) we examined the need to consider multilevel models by looking into null models (the simplest two level model which includes only the group-level parameters (also referred to as random parameters), to measure the proportion of total variance which fell between-groups (i.e., variance partition coefficient also reffered to as intracalss correlation)(Goldstein, 2011). Variance partition correlations higher than 0.05 indicate a substantial variation by the respective group and the need to use multilevel modeling (Goldstein, 2011; Snijders and Bosker, 2012).

>(iii) the key feature of multilevel modelling is shrinkage (partial pooling), by incorporating group- level effects. It allows for more efficient use of the data. These may be understood as a weighted average between the all sample estimate and a group or unit estimate. The specific weights are based on the entire variation of the sample and the group variation (Gelman and Hill, 2007). In particular, the partial pooling will be stronger for smaller units with fewer observations (Buttice and Highton, 2013)

>We agree with the argument to interpret the age effect assuming chronological age in the model. Indeed categorization removes potential variation. We choose to use age groups to echo the ecological context where players are grouped in competitive age groups. Also, following our previous point, partial pooling helps to mitigate the limitations of our choice for group age.

I agree all of advantages of Bayesian analysis you have raised. In addition, I also agree justification of categorizing age into several groups.

However, it is still odd for me that you have assumed the hierarchical structure of effect of gender. I cannot understand well the sense of estimating the variance of the effect between gender, which includes only two groups. Estimating "variance" of normal distribution, which the group including only two categories obeys, seems to be equivalent to estimating the "difference" between the two categories.

For the group including only two categories, in contrast to the regression model using the group as a dummy, the multilevel model seems to contain redundant parameters (i.e., each of individual parameters and standard deviation of normal distribution). The predictive accuracy might not be improved drastically, even if the multilevel model was used. It would not be necessary to consider partial pooling (shrinkage) for gender logically because there are only two groups and unknown groups do not exist.

In order to demonstrate whether there is a variance between male and female (in other words, whether there is a difference between the two), estimating the fixed slope of the gender seems to be enough.

If you do not agree, in your response, please refer to previous works which assumed the multilevel model for groups which include only two groups.

Authors´ reply: We thank the reviewer´s comment and understand the reviewer´s point. There is no substantial gain in the predictive accuracy with our data by include gender and population- or group-level parameters. The first reason we retained varying intercepts by gender was that it makes more sense from a biological perspective to allow for scores to vary by gender, assuming a 2 ×3 ×3 ×3 structure as 54 exchangeable groups. The multilevel approach allows us to estimate the parameters as varying effects, taking advantage of the multilevel structure (cross-classified) of the data. The general approach for multilevel models gives each batch of regression coefficients with greater than two groups an independent normal distribution centered at 0 and with standard deviation estimated from data [1]. Again we recognize that there is limited gain to multilevel modeling for batches with smaller than three groups when prior distributions are noninformative [2], and are often used as population level for computational convenience.

Nevertheless, the inclusion of the variables with two batches as group-level parameters is common, particularly with the increase of computation efficiency [3-7]. However, we do not use noninformative priors, as given the standardization of the outcomes, the priors used for the group-level parameters we expect that the group-level estimates are unlikely to be greater than one standard deviation of the outcome. This choice likely adds a more conservative estimation, while using all available information in the data (and at least to as reflecting better the research context). We hope to have address the reviewer´s comments.

>Authors ´ reply: We used referred to the hyperparameters as population-level effects, which are referred to as fixed effects in frequentist analysis, and group-level effects which are referred to as random effects in frequentist analysis. This is the common designation when using Bayesian analysis. We inserted the comparable frequentist terms in the text to allow the unfamiliar reader with Bayesian analysis to better understand our report. For the residual standard deviation parameter (level-1 standard deviation or referred to as residuals), we adopted the default prior in the brms package. For the group-level effects (i.e., level-2 standard deviations, in this case,,,) we used half-normal priors, as we intend to have a conservative approach on the analysis by stating that the group-level estimates are unlikely to be greater than one standard deviation of the outcome.

I understood that the population-level effects and the group-effects represented the fixed effects (i.e., the intercept of your regression model) and random effects (i.e., sigma_a, sigma_m, sigma_d, and sigma_g), respectively.

You have not report the summary of inferred group-level intercept and group-effects yet, although I suggested earlier. Summary of posterior distributions of estimated parameters (e.g., mean, standard deviation, and 95% CI) may be necessary. As I suggested in the following comment, not only visualization of the results but also numeric information would be needed for objective explanations.

Is the "residual standard deviation parameter (level-1 standard deviation)" equivalent to the standard deviation of the normal distribution which the response variable (i.e., y_{i}) obeys?

In the model, information of the distributions which the response variable obeys is lack. The "level-1 standard deviation" should be shown clearly in the equation of the model.

For instance,

\\hat{y}_{i} = \\beta + \\alpha_{a[i]} + ...

...

y_{i} \\sim Normal(hat_{y}_{i}, \\sigma)

In addition, please explain the "default prior" in brms package concretely (i.e., the name of probability distribution and parameters).

Authors´ reply:

We agree with the reviewer´s point. The multilevel equation was incomplete without the level-1 residual parameter. We added the level 1 residual. We also added in the text the “brms” default prior used, Student-t (3, 0, 2.5). We added a summary of the posterior distributions as a table, as suggested.

In your response, half-normal priors were set for the group-level effects. However, in the revised manuscript, you described that normal prior (0, 5) was set as prior for group-level parameters. You should clearly describe "half-normal".

Authors´ reply: We apologize if we were incorrect in our response. We used a normal prior (0,1) for the group parameters. It was correctly stated in the manuscript. By default “brms” sets their left boundary to zero, to keep the HMC algorithm from exploring negative variance values. But formally, we state the definition of a normal prior in the equation and in “brms” code. Hopefully, our reply is now clear.

>Authors ´reply: We thank the reviewer ´s comment. Hopefully, we provide cleaner and clear Figures now. We dodged the estimates and uncertainty to remove the overlap. The legend titles were corrected in all figures, removing the variable label from the dataset.

For captions in Figure 2-6, you should explain that the bold lines and thick ones represent 67% and 90% intervals, respectively.

The legend of the deliberate practice disappeared in Figure 5, whereas it appeared in other figures. I found that the relationship between the onset of deliberate practice and will to excel (or will to compete) was reported in Figure S2. However, it seemed that S2-S4 Figs were never referred to in the main text.

Authors´ reply: We added the information about the uncertainty intervals in the figure caption. In figure 5, contrasts are presented by age group and maturity status. Hence we represented only the legend for maturity status, and give the information in the figure caption. We also added S5 Fig that was missing. We added information in the results section to refer to the supplementary material.

>Authors ´reply: We apologize for the incorrect upload of the figures, We have corrected appropriately both Figure 5 and Figure 6. The Bayesian inference allows for direct probabilistic comparisons between estimates and uncertainty. Hopefully, with the changes in the Figures, it becomes clear for the reader.

I could not still understand well which of the parts in each figure indicated “substantial variation between female and male players”. Intervals shown in each panel seemed to indicate "variation between players within each gender". The results for each gender were separately shown by divided panels: therefore, it was difficult to compare differences between two genders.

In addition, because the interpretation using only visualized results seemed to be subjective and arbitrary, quantitative reports such as numeric information of intervals of parameters may be necessary. The posterior distributions of each parameter (e.g., group-level parameters such as sigma_gender, or slope of the gender in the regression model) should be reported for the objective interpretations.

Authors´ reply: As suggested, we added estimates in the text to allow for direct comparisons, also with the models estimates in Table 2. We also were conservative in the qualification of variation between groups, and interpret mainly comparing the 90% intervals. As we report the figures in the questionnaire scales for the questionnaires, we reported in the text the standardized estimate to allow a complete interpretation of the results to the reader.

>Authors ´reply: It represents the scale used in the questionnaires based on a Likert-like scale. The information about the questionnaires is provided in the methods section. It is a common practice to describe questionnaire scales, but we are open to suggestions to improve our reporting.

Please show the meaning of the number: for example, "(1: disagree, 5: agree)". Similarly, in the method and materials section, it should be described the labels of each number. We could not understand what the greater number meant, if the descriptions were omitted.

Authors´ reply: We agree. We added both in the methods section and in the figures scale about the meaning of the likert-like scale (1 = completely disagree to 5 = completely agree). We also re-scaled the estimates to the original scale to allow a direct interpretation to the reader.

References:

1. Park DK, Gelman A, Bafumi J (2004) Bayesian Multilevel Estimation with Poststratification: State-Level Estimates from National Polls. Political Analysis 12: 375-385.

2. Gelman A (2006) Prior distributions for variance parameters in hierarchical models (comment on article by Browne and Draper). 515-534.

3. Warshaw C, Rodden J (2012) How Should We Measure District-Level Public Opinion on Individual Issues? The Journal of Politics 74: 203-219.

4. Leemann L, Wasserfallen F (2020) Measuring Attitudes – Multilevel Modeling with Post-Stratification (MrP). In: Curini L, Franzese R, editors. The SAGE Handbook of Research Methods in Political Science and International Relations. 1st ed. Los Angeles, CA: SAGE. pp. 371-384.

5. Claassen C, Traunmüller R (2020) Improving and Validating Survey Estimates of Religious Demography Using Bayesian Multilevel Models and Poststratification. Sociological Methods & Research 49: 603-636.

6. Loux T, Nelson EJ, Arnold LD, Shacham E, Schootman M (2019) Using multilevel regression with poststratification to obtain regional health estimates from a Facebook-recruited sample. Annals of Epidemiology 39: 15-20.e15.

7. Kiewiet de Jonge CP, Langer G, Sinozich S (2018) Predicting State Presidential Election Results Using National Tracking Polls and Multilevel Regression with Poststratification (MRP). Public Opinion Quarterly 82: 419-446.

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Decision Letter 2

Nili Steinberg

19 Apr 2021

Multidimensional characteristics of young Brazilian volleyball players: a Bayesian multilevel analysis

PONE-D-20-27002R2

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Reviewer #1: All comments have been addressed

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Reviewer #1: Yes

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Reviewer #1: Yes

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Reviewer #1: Thank you for sending the revised manuscript. All concerns I have raised are solved and readability has also been improved .

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Acceptance letter

Nili Steinberg

21 Apr 2021

PONE-D-20-27002R2

Multidimensional characteristics of young Brazilian volleyball players: a Bayesian multilevel analysis

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