The main purpose of this study was to describe the most demanding scenarios of match play in basketball through a number of physical demand measures (high-intensity accelerations and decelerations, relative distance covered, and relative distance covered in established speed zones) for four different rolling average time epochs (30, 60, 180, and 300 s) during an official international tournament. A secondary purpose was to identify whether there were significant differences in physical demand measures among playing positions (centers, guards, and forwards) and levels (two best classified teams in the tournament and remaining teams), match scoring (winning, losing, and drawing), and playing periods (match quarter) at the moment of the most demanding scenarios. Data were collected from 94 male under 18 (U18) elite basketball players (age: 17.4 ± 0.7 years; stature: 199.0 ± 11.9 cm; body mass: 87.1 ± 13.1 kg) competing in a Euroleague Basketball Tournament. Measures were compared via a Bayesian inference analysis. The results revealed the presence of position-related differences [Bayesian factor (BF) > 10 (at least strong evidence) and standardized effect size (δ) > 0.6 (at least moderate)] so that centers covered a lower relative distance at speed zone 1 and had lower high-intensity accelerations and decelerations than guards. However, the Bayesian analysis did not demonstrate the existence of significant differences in any physical demand measure in relation to the playing level, match scoring, and playing periods at the moment of the most demanding scenarios. Therefore, this study provides coaches and strength and conditioning specialists with a most demanding scenario reference on physical demands that can be used as an upper limit threshold in the training and rehabilitation monitoring processes.