## 2 Materials and Methods
### Data Analysis  
The fastest jump smash (greatest post-impact shuttlecock speed) determined using a curve-fitting methodology [4] for each participant where the shuttlecock landed in the designated area was chosen for further analysis. Position data were labelled using Qualisys Track Manager (QTM2018.1: build 4260, Qualisys, Goteburg, Sweden) and gaps within the data were filled using a combination of linear and polynomial interpolation. All body marker position data were filtered within Visual 3D using a 4 th-order, zero-phase, low-pass Butterworth filter with a cut-off frequency of 30 Hz. A 15-segment model in Visual 3D was used to calculate joint moments. Segment inertia parameters were determined using mass distribution ratios [14]. The racket was modelled as two segments (handle and frame) that, when combined, gave typical racket inertia parameters [15]. This allowed some representation of the racket deformation. The racket and hand were linked via a virtual joint that was positioned one-quarter of the way up the grip, allowing transmission of force between the two segments, and this position was assumed constant across all participants. A'resultants moments' inverse dynamics analysis [16] was performed within Visual 3D. For the full equations, readers are referred to the documentation provided by Visual 3D [17]. An iterative algorithm was used to calculate the proximal joint force and then the inertial moment was calculated, which allows the calculation of the joint moments.  
Non-orthogonal joint coordinate systems were created for the elbow and shoulder. The elbow joint coordinate system was calculated based on an X\({}^{\prime}\)Z\" Cardan sequence, corresponding to flexion/extension, adduction/abduction and pronation/supination, where the X and Z\" axes are fixed in the upper arm and forearm coordinate systems, respectively [18]. The shoulder joint coordinate system was calculated based on a Z\({}^{\prime}\)Z\" Cardan sequence, corresponding to the plane of elevation, elevation/depression and internal/external rotation, where the Z and Z\" axes are fixed in the thorax and upper arm coordinate systems [18]. The wrist joint coordinate system was orthogonal and corresponded with the forearm segment, and represented flexion/extension, ulnar/radial deviation and pronation/supination [19].  
To allow a comparison between players, kinematic data were normalised to a swing phase that was defined from the instant where the global anterior-posterior velocity of the racket head centre was above a threshold of 5 m/s (Figure 1a), from which it did not decrease, through to racket-shuttlecock contact (Figure 1c). The instant describing the end of the backswing phase/start of the forward swing phase was calculated at the point where the racket head velocity normal to the stringbed became positive [5]; Figure 1b).  
Pearson product moment correlation analyses were performed for racket head speed at racket-shuttlecock contact with peak moment data at the shoulder, elbow and wrist using SPSS v.20 (IBM Corp., Armonk, NY, USA). Data were tested for normal distribution using the Shapiro-Wilk test, where the assumption of normality was met where \(p>0.05\). Pearson product moment correlations (\(r\)) and their 95% confidence intervals (CI) were interpreted as negligible \(<0.3;0.3\leq\) low \(<0.5;0.5\leq\) moderate \(<0.7;0.7\leq\) high \(<0.9\); very high \(\geq 0.9\)[20].  
For non-normally distributed variables, the Kendall tau-b (\(\tau_{b}\)) correlation was performed, with 95% CI calculated using the 'Fisher's method' [21], and interpreted similarly to Pearson product moment correlations. Combining both effect size and confidence intervals allows interpretation of both the magnitude of the effect and (un)certainty of the parameter estimate [22]. To control for multiple hypothesis testing, the Benjamini-Hochberg correction was used with a false discovery rate of 10%.