Yves de Saá Guerra

BASKETBALL SCORING IN NBA GAMES: AN EXAMPLE OF COMPLEXITY

Scoring in a basketball game is a process highly dynamic and non-linear type. The level of NBA teams improve each season. They incorporate to their rosters the best players in the world. These and other mechanisms, make the scoring in the NBA basketball games be something exciting, where, on rare occasions, we really know what will be the result at the end of the game. We analyzed all the games of the 2005-06, 2006-07, 2007-08, 2008-09, 2009-10 NBA regular seasons (6150 games). We have studied the evolution of the scoring and the time intervals between points. These do not behave uniformly, but present more predictable areas. In turn, we have analyzed the scoring in the games regarding the differences in points. Exists different areas of behavior related with the scorea and each zone has a different nature. There are point that we can consider as tipping points. The presence of these critical points suggests that there are phase transitions where the dynamic scoring of the games varies significantly.Abstract Scoring in a basketball game is a highly dynamic, non-linear process. NBA teams try to be more and more competitive each season. For instance, they incorporate into their rosters the best players in the world. This and other mechanisms concur to make the scoring process in NBA games exciting and rarely predictable. This paper is to study the behavior of timing and scoring in basketball games. The authors analyze all the games in five NBA regular seasons (2005–06, 2006–07, 2007–08, 2008–09, 2009–10), for a total of 6150 games. Scoring does not behave uniformly; therefore, the authors also analyze the distributions of the differences in points in the basketball games. To further analyze the behavior of the tail of the distribution, the authors also carry out a semilog-plot and a log-log plot to verify whether this trend approaches a Poisson distribution or a PL. This paper reveals different areas of behavior related to the score, with specific instances of time that could be considered tipping points of the game. The presence of these critical points suggests that there are phase transitions where the dynamic scoring of the games varies significantly.

Design and flow in basketball

Basketball game flow and its design can be described as in many others natural systems. The structure, shape and functionality evolve in time and are closely related to performance in several sports. Basketball is a collaboration-opposition sport, thus games present critical points. Non-linear local interactions among players are reflected in the score evolution, the order parameter. Some researchers often presume that scoring in basketball is a random process, meaning memoryless, described using Poisson Model. Scoring cannot be described by a unique distribution. We examined 6130 NBA games and analyzed time intervals between points and scoring dynamic. In the NBA, the most competed games are decided in the last minute, where fouls play a main role (94.02%). Both teams try to keep their advantage solely in order to reach the last minute, where a different game will be played, which can be considered as an example of Red Queen Hypothesis. We also measured the game flow through players real interactions: passes, screens and space creations. Data follow a homogeneous distribution up to a certain value, suggesting that teams resolve the situation with a few steps (diffuse flow). But, if the situation becomes more critical, the dynamics turn into a Power Law Distribution, they modify the game flow spontaneously into a Scale-Free flow (hierarchical flow). These processes take place simultaneously and continuously during game time. Therefore teams would be considered as self-organizing systems.