## 2 Materials and Methods
### Experimental Design
#### 2.2.4 Measurement of External Load Variables  
The assessment of the external load during MF and SMP was conducted using inertial measurement units (IMU, WIMU PRO(tm), RealTrack Systems, Almeria, Spain), which have been employed in previous studies with badminton players [6; 19]. These devices include different sensors (accelerometer, gyroscope, magnetometer) to record time-motion data (outdoor: Global Navigation Satellite System, GNSS; indoor: Ultra-Wideband, UWB), as well as metrics related to specific actions and skills. Each unit features an internal microprocessor, 2 GB of flash memory, and a high-speed USB interface to record, store, and upload data. They were powered by an internal battery with a 4 h lifespan, had dimensions of 81 mm \(\times\) 45 mm \(\times\) 16 mm, and a total mass of 70 g. The sensors operated at a sampling frequency of 18 Hz for UWB and 1000 Hz for the accelerometer, magnetometer, and gyroscope [19; 20; 21]. Before data collection during MF and SMP drills, a Local Positioning System (LPS) was established using eight ultra-wideband antennas, placed according to the manufacturer's guidelines and previous studies [6; 19]. The antennas were arranged in a rectangle, spaced from 10 to 16 m apart, and mounted on tripods at a height of 3 m. Calibration of the UWB system was performed following established protocols [6; 19; 21], and the intra-unit and inter-unit reliability have previously been reported for WIMU PRO(tm) in indoor conditions [20]. Briefly, the antennas were switched on sequentially, with the master antenna activated last. A 5 min auto-calibration protocol synchronized all antennas to a common clock. Afterward, at each position update (18 Hz), the master antenna sent a time synchronization signal. Then, the tracking devices were turned on, undergoing a 1 min recognition and communication process with the antennas. The accuracy of the system was tested, yielding a mean absolute error for the x-position of 5.2 \(\pm\) 3.1 cm and for the y-position of 5.8 \(\pm\) 2.3 cm [20]. Similarly, accelerometer calibration was conducted according to the methodology outlined in prior research [19], which also reported intra- and inter-unit reliability (CV values of 0.5-1.05 and 1.1-1.2%, respectively) with near-perfect inter-device correlations (r = 0.99-1.00), and very low day-to-day variability (r = 0.84-0.97). The IMU device was secured to the interscapular level (i.e., at approximately the level of the 2 nd thoracic vertebra) of the players five minutes prior to the warm-up [19] using a specially designed neoprene vest provided by the manufacturer. This ensured a secure fit without restricting typical badminton movements. To avoid inter-unit error, participants wore the same device for all observations [22].  
All data obtained from the devices were linked and extracted after matches for analyses using the specific manufacturer's software (SPRO(tm), RealTrack Systems, Almeria, Spain).  
Based on previous research [6], suggesting that the following variables were the most representative during an international badminton tournament, and in order to reduce the number of variables included in the study, we included the following in the analysis: (1) relative distance, RD (m/min): total distance covered related to total playing time; (2) maximum acceleration, AccMAX (m/s\({}^{2}\)): maximum acceleration reached during the different situations (training/match); (3) AccRel (n/min): number of accelerations related to total playing time; (4) SpeedMAX (km/h): maximum speed performed throughout the situation; (5) average HR, HRAVG (bpm); (6) relative jumps, RJumps (n/min): number of jumps performed related to playing time; (7) average takeoff force; TakeOffAVG; (8) force average measured at all takeoffs during the different situations; (9) average landing force, LandingAVG; (10) force average measured at all landings during the different situations.