Strategies for Penalty Kicks in Football Games

In the football match, how to score goal has always been the core issue that every team is most concerned about. Penalty kick , one of the most important way to get the score, is worth each football player spends much time analyzing so that they can get score as much as possible. In this text, we solved two questions. One is what initial ball velocities and spins will result in a successful shot to an upper corner from the penalty mark? And another question is what initial ball velocity and spin should the shooting player attempt to create to have the best chance of avoiding the goalkeeper and making the goal? In the first question, we take gravity, air resistance, buoyancy, magnus force into account at the same time. With the help of Python, we successfully calculate out 6618 kinds of footballs with different velocities and spins which are able to get into the goal. We draw the distribution of the six elements of the ball, giving advice to those people who can’t control the velocities and spins of the football exactly how to rise the success rate of shotting to an upper corner from the penalty mark. In the second question, we take four different elements which we think will influence the goalkeeper successfully catching the football , find out the best location the player should aim at. Also we give out the best velocities and spins the football should own in the range we set, which will make the goalkeeper have the lowest possibility to catch the ball.