*2.1. Subjects*

A total of 23 male basketball players from the top-ranked Slovenian basketball club were included in the study (Table 1). All subjects reported their right arm as the preferred shooting arm. Subjects with previous upper limb injuries (past 6 months), neurological disorders, low back pain, or recent general illness were excluded from the study. The inclusion criteria were regular basketball training in past 3 years at least 4 times per week. The subjects and their parents/guardians were informed about the testing procedures and provided written informed consent prior to commencing the study. The experiment was approved by the Slovenian Medical Ethics Committee (approval no. 0120-99/2018/5) according to the Declaration of Helsinki.


**Table 1.** Characteristics of Subjects.

N—the number of participants; BMI—Body mass index.

#### *2.2. Study Design and Testing Procedures*

For each subject, we captured measurements of (i) kRTD-SF, TMVC, and RTDPEAK for EE and VF of the self-reported preferred arm and (ii) shooting performance at two di fferent distances from the basket in two separate visits. On the first measurement day, the subjects performed isometric strength tests for EE and VF (random order) preceded by a 10 min warm-up consisting of 5 min of light running, 4 min of dynamic stretching, and 1 min of activation exercises (10 repetitions of squats, push-ups, and V-ups). The isometric strength tests were performed before their regular training in the laboratory setting. The next day, on the second measurement day, the subjects performed 10 throws at two di fferent distances (random order) from the basket after the standardized warm-up protocol described before. The shooting performance was assessed in the gym basketball gym before their regular training. The flowchart of the study is outlined on the Figure 1.

**Figure 1.** The flowchart of the measurement protocols. MVC—maximal voluntary isometric contraction.

Following the warm-up, the subject was positioned in a custom-made dynamometer (S2P, Science to Practice, ltd., Ljubljana, Slovenia) which was used for TMVC and RTDPEAK and kRTD-SF assessment. Participants position during elbow extension or volar flexion TMVC, RTDPEAK, and kRTD-SF assessment is presented and described in Figure 2. In all cases, the lever arm (i.e., the linear distance from the axis of the joint and the centre of the distal force-detecting support) was measured and considered in the torque calculation. The signals from force transducers during elbow extension (Bending beam load cell 1-Z6FC3/200kg, HBM, Darmstadt, Germany) and volar flexion (Tension compression load cell FL25-50 kg, Forsentek, Shenzhen, China) were amplified (Isotel, Logatec, Slovenia) and converted from analogue to digital signal (NI USB-6211, National Instruments, Austin, TX, USA). Signals were sampled at 1000 Hz by a custom-made LabView 2015 software (National Instruments Corp., Augustin, TX, USA). In case of TMVC and RTDPEAK, the raw signals were smoothed (moving average filter, 5 ms time-window). In RTD-SF analyses the signals were filtered using a lowpass Butterworth filter with cut-off frequency at 5 Hz, while corresponding RTD of each contraction was calculated as a peak value of derivate of the torque curve [4]. All measurements were processed by a single investigator.

**Figure 2.** Measurement set-up: (**a**) Subject in the custom-built elbow extensor dynamometer. Subjects were seated (knee and hip in 90◦ position, trunk in upright position) on a bench with back support, while their shoulder and elbow were flexed at 90◦ in sagittal plane (forearm was in neutral position). The trunk and the shoulder of the performing arm were fixed to the back support, while the elbow was fixated to the lower support of the dynamometer. The force sensor was at the upper support, where the subject placed the wrist, which was fixated using elastic bands (to provide tension and proper contact between wrist and dynamometer support). (**b**) Subject in the custom-built volar flexor dynamometer. Subjects were seated on a chair. The subject's shoulder and elbow were both flexed at 90◦, while their forearm (pronated position) was placed in a custom-made dynamometer which allows full forearm fixation. Wrist was in neutral position. 1—force sensor, 2—joint fixations, 3—monitor for visual feedback, 4—elastic band

#### *2.3. Testing TMVC and RTDPEAK*

In TMVC testing subjects were instructed to gradually increase the force and push as hard as possible against the elbow (Figure 2a) and wrist dynamometer's support (Figure 2b). Contractions were sustained for at least 3 s; meanwhile, verbal encouragemen<sup>t</sup> was given to the subject. TMVC for each muscle group was calculated (Nm/kg) as the maximal mean value ona1s time interval. Each participant performed three repetitions for each muscle group. The greatest TMVC was used for statistical analysis.

Three isometric MVCs for each muscle group (EE and VF) with a 60 s rest between trials were repeated, while in this case subjects were instructed to push as hard and explosive as possible to calculate their RTDPEAK (maximum of the toque-time derivative). Greatest RTDPEAK (Nm/kg s) was used for statistical analysis.

#### *2.4. Testing RTD-SF*

The RTD-SF relationship for each muscle group was computed from sets of 20–25 explosive isometric contractions at four different submaximal intensities (20%, 40%, 60%, and 80% of TMVC) (Figure 3a,c) in a random order, as previously described [1]. Subjects rested for 60 s between different contraction intensities and 3 min between each task, i.e., muscle group. The target torque was displayed as a horizontal line on a graph on a computer screen placed at the subject's eye level (Figure 2). The subjects were instructed to contract and relax as fast as possible.

**Figure 3.** Sample recording of rapid torque pulses of (**a**) elbow extensors and (**c**) volar flexors to a variety of amplitudes. Rate of torque development scaling factor (RTD-SF) plot of (**b**) elbow extensors (**b**) and (**d**) volar flexors with data points taken from the peaks of the preferred arm.

The regression parameters kRTD-SF (/s) and r2RTD-SF were obtained from the relationship between the peak torque and the corresponding peak RTD.

#### *2.5. Testing Shooting Performance*

During the second visit, the subjects performed 10 throws at two different distances, orientated frontally towards the basket. Shooting distances were selected in random order for each subject. Shooting performance from short distance was performed from half the distance between the basket and free throw line (2.3 m), while shooting form the longer distance was performed from 8.9 m (three-point line + distance between free throw and three-point line). From each subject shooting performance from each distance was assessed (n/10).

#### *2.6. Statistical Analysis*

Descriptive data of the dependent variables are presented as means and standard deviations. The Shapiro–Wilk test was used to assess data normality. Fisher's z-transformation was used to transform r2RTD-SF in case of RTD-SF to obtain normal distribution. The di fferences in kRTD-SF, TMVC, and RTDPEAK between groups were evaluated with a two-tailed independent sample t-test and Cohen's d e ffect size (ES). The ES was interpreted as negligible (<0.2), small (0.2–0.5), moderate (0.5–0.8), and large (≥0.8) [17]. Pearson correlation coe fficients were used to determine the relationship between kRTD-SF, TMVC, and RTDPEAK of EE and VF and shooting performance from short and long distance. The correlation coe fficient was interpreted in as (0.00–0.19 trivial; 0.10–0.29 small; 0.30–0.49 moderate; 0.50–0.69 large; 0.70–0.89 very large; 0.90–0.99 nearly perfect; and 1.00 perfect) [18]. Moreover, we assessed the reliability of kRTD-SF, TMVC, and RTDPEAK by calculating two-way random model intra-class correlation coe fficients (ICC) for single measures and standard error of measurement, expressed as the coe fficient of variation (CV). For TMVC and RTDPEAK, we conducted inter-repetition reliability, while for the RFD-SF, we split the data from each intensity into two halves, and compared kRTD-SF r2RTD-SF obtained from both subsets of the data. The level of statistical significance was set at *p* < 0.05. Statistical analyses were performed using the SPSS (IBM SPSS version 26.0, Chicago, IL, USA) software package.
