Mathematical Modeling of Football Penalties

Michael Ericsson; Jamie Foster

doi:10.59973/emjsr.410

Authors

Michael Ericsson University of Portsmouth, Faculty of Technology, School of Maths and Physics, Portsmouth, PO1 3QL, United Kingdom
Jamie Foster University of Portsmouth, Faculty of Technology, School of Maths and Physics, Portsmouth, PO1 3QL, United Kingdom

DOI:

https://doi.org/10.59973/emjsr.410

Keywords:

Elevation, Azimuth, Angular Velocity, Magnus Force, Vector, Trajectory, Probability

Abstract

This artcile investigates whether there is an optimal strategy when taking a football penalty, using mechanical and statistical modelling. Different techniques such as curved shots and power shots are studied, altering the angles and speed of the strike to show the influence on the ball's path in three-dimensional space, to find optimal values of these initial conditions. The mechanical model shows the trajectory of the ball at different parameter values, with a statistical model also constructed to analyse the likelihood of a goalkeeper saving the penalty. After combining these models, it is found that there are techniques and strategies that yield a significantly greater chance of success from the penalty.

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