  In this article, I argue that the concept of the standard Voronoi diagram is
incorrect for the calculation of dominance area in soccer. The correct region
that should replace the polygonal Voronoi region controlled by a player emerges
naturally by studying the motion of the players. It turns out that the
widely-used standard Voronoi diagram is true only when all 22 players have the
same speed (with vanishing speed being a special case) and it should be
replaced by other diagrams whose regions have more complicated boundaries. The
unfortunate error happened when the mathematical concept of the Voronoi diagram
that has an implicit vanishing speed for its points was transferred to soccer
without looking at the kinematical issues involved in the game of soccer. For
this reason, as a byproduct of this work, I argue for the promotion of
"soccerdynamics", model building for soccer by looking at the underlying
mechanisms and not just adopting mathematical ideas only for their appeal and
beauty.
