Geometric simplification of a new penalty area for football

Abstract

A geometric simplification of a recent proposal for a new geometry of the penalty area for football (soccer) is presented. A simplified line is necessary because the fully mathematical curve previously proposed can be difficult to implement in the real world of football, which has thousands of tournaments at all -economic and generational- levels of the sport. The idea behind the proposal is that the game and its fairness can be improved if the penalty area is drawn according to mathematics or a measure of actual scoring chance.