The Poisson model limits in NBA basketball: Complexity in team sports

• We proved that basketball scoring does not follow a unique distribution.
• Poisson model fails in some game times, where Power Laws show up.
• The result of the competed basketball games depends on the last minute of the game.
• Events likelihood with dt=1 s is the highest in last minute; free throws mainly.
• Teams play in order to reach last minute. Basketball behaves as Red Queen Hypothesis.

Team sports are frequently studied by researchers. There is presumption that scoring in basketball is a random process and that can be described using the Poisson Model. Basketball is a collaboration-opposition sport, where the non-linear local interactions among players are reflected in the evolution of the score that ultimately determines the winner. In the NBA, the outcomes of close games are often decided in the last minute, where fouls play a main role. We examined 6130 NBA games in order to analyze the time intervals between baskets and scoring dynamics. Most numbers of baskets (nn) over a time interval (ΔTΔT) follow a Poisson distribution, but some (e.g., ΔT=10ΔT=10 s, n>3n>3) behave as a Power Law. The Poisson distribution includes most baskets in any game, in most game situations, but in close games in the last minute, the numbers of events are distributed following a Power Law. The number of events can be adjusted by a mixture of two distributions. In close games, both teams try to maintain their advantage solely in order to reach the last minute: a completely different game. For this reason, we propose to use the Poisson model as a reference. The complex dynamics will emerge from the limits of this model.