A mathematics-based new penalty area in football: tackling diving

A novel penalty area (PA) for football (soccer) is proposed; it is based on considering mathematically the actual scoring possibility on the 2 dimensions near the goal. It is shown that the 150-year-old rectangular area is mathematically disproportionate; this can be causing too much diving or simulation by players around the goal and also too many matches that are decided unfairly. The goal or objective is to reduce these problems–and others–with a new PA based on the proposed scoring potential measure which is in turn based on the angle towards the goal line (between posts) and the distance to the centre of this line.