## 2 Materials and Methods
### Instruments  
The players' position data were collected through a LPS (Kinexon Precision Technologies, Munich, Germany), which has been recently validated [10; 12] and used in studies on team sports [11; 14], showing adequate between-device reliability (coefficient of variation around 5%) when compared to well-known systems such as GPS. Firmware versions and application software versions corresponded to the latest releases on the testing date (August 2019). Figure 1 shows the setting of the 9 antennae around the playing field, connected via Ethernet to the main server, and 10 anchor antennae distributed at 3 different levels above the ground in all EURO arenas. UWB (ultra-wideband) LPS can be used as an alternative to professional optical systems and/or global satellite radio communication systems (GPS). In the context of indoor measurement, only camera-based technology can be used since GPS relies on direct paths between receivers carried by each player and a number of satellites. With LPS, the satellite-based measurement principle becomes local anchor-based measures using a local network of antennas, and therefore it can be used for both indoors and outdoors. LPS receivers usually include micro electro mechanical system (MEMs) to complement kinematic data retrieved by local positioning with individual player motion analysis. Typically, sensors include triaxial accelerometers measuring linear acceleration and gyroscopes, measuring angular velocity, all in the three coordinates. Unlike camera-based systems, the inertial sensors attached to each player allow for the precise body linear and angular kinematics to derive accelerations, jumps, impacts, and changes of direction. In each venue, the LPS system were installed, calibrated, and checked for accuracy by a technician who worked for the manufacturer as follows. The exact position of the anchors in reference to the playing field was measured (blue numbered positions in Figure 1). Then, the anchor positions and the playing field position and size were transmitted to the Kinexon application. The location of one sensor at pre-defined positions (corner, penalty line, center point) was checked. In addition, two paths were followed to test the data quality and calculated distance--walking on the sideline and walking on a meander inside the field (black discontinued line in Figure 1). The devices worn by players comprised a sensor (player tag) positioned between the player's shoulder blades using the manufacturer  
Figure 1: Local positioning system (LPS) setting: nine antennae connected to the server in red locations; ten reference antennae (anchors) in blue locations; meander path inside the field followed to check calibration accuracy (black discontinued line). harness. The functionality of the sensors was tested in the venue by randomly walking and checking if signals were received from all units with adequate signal strength. These sensors transmit time signals via radio-technology to the antennae, which send signals via a wide local area network (WLAN) to local static base stations at known locations. A player's momentary position is determined via 20 Hz frequency by calculating the time-of-flight (TOF) of ultra-wide-band radio signals traveling from the transmitter to the base stations, which calculate the actual 2D position of the devices within the playing field. Subsequently, instantaneous speed, i.e., scalar magnitude of velocity, as per the rate of change in horizontal \(\chi\), y positions, and acceleration, as per the rate of change in speed, are derived by calculating the difference between two consecutive positions, i.e., approximating the derivative of the player's position. The raw position and speed data are then filtered and smoothed by means of a Kalman filter for position data and an exponential moving average with a window length of 1 s for speed and position data. The system detects when a player is in possession of the ball, as it tracks both the players and the ball. Thus, it automatically changes offense to defense when appropriate.