Some Aspects of Goalkeeping and Goalscoring in Football

Some aspects of goalkeeping and goalscoring in the game of Football are discussed in this study from physical and mathematical points of view. For goalkeeping, the taller goalkeeper has a reach advantage over the shorter goalkeeper and is therefore better equipped to deal with high balls. However, it is shown from the falling rod problem in physics that the shorter goalkeeper is able to fall a fraction of a second quicker than the taller goalkeeper and is better able to clear low balls. As for goalscoring from a close range, the solid angles subtended by the goal area at the strike location is taken as a measure of effectiveness of a strike.  The solid angles are calculated for ground kicks, aerial side kicks and bicycle kicks and headers from high, low and average heights. The aerial kicks and headers have greater solid angles than the more common ground kicks and are therefore more likely to score from a geometrical point of view. Generally speaking, ground kicks can be executed with greater precision and power, but the goalkeeper also has a better anticipation of their directions. It is more difficult for the goalkeeper to predict the strike location of a header (or an aerial kick) in air (a three-dimensional space) and the subsequent direction of the ball, which makes that strike an even more dangerous one.