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# Mathematical programming in sports

Mathematical programming in sports refers to the use of mathematical models in making tactical, analytical, performance-based or managerial decisions in training sessions, during the field of play, or in management situations. Programming simply refers to computerizing the planning of activities.

Mathematics is pervasive; it is virtually everywhere – around us, in our day-to-day activities and, of course, in sports. In fact, they become increasingly important in this domain, be it in professional or amateur sport. For example, mathematics programming helps in the improvement of performance, new technologies, technical revolutions, etc. Mathematicians deal with the themes of sport and performance in different ways. Thus, let us discover together and more precisely, how the practice of mathematics has an effect on the sport.

From birth, children discover numbers and geometric shapes, and adults continue to use mathematics in their day to day activities.

Sports and managing high-level athletes is a big business, and thus rely on big business solutions to gain a competitive edge. This is where sports analytics come in. Mathematical equations are a scientific basis that have become essential in all high-level sports. They lay the foundation of work for athletes who do not stop refining their technique to obtain better results.

Breaking records with mathematics

Mathematics can be applied to sporting activities to break records. For instance, Javier Sotomayor has the record of high jump since 1993 and nobody has managed to beat his 2.45 meters until today.

Do you all remember the 2009 World Swimming Championship in Rome? The records were shattered one after another and journalists could not understand this phenomenon. In total, 43 records were broken and set during this period. You have to think that the performance of swimming is measured by the principle of submerged movement, well known in physics, and therefore involves mathematical calculations. Vertical and horizontal forces are exerted and the Archimedes principle also influences it. How is it possible for athletes to continue breaking records? Does the human body have a defined physical limit for performance?

Mathematics helps us with questions concerning how records can be broken and if there is a physical limit to the human body’s performance. A study of September 2012 has shown that the classifications are governed by a mathematical law: the law of power. This law relates two elements: the frequency of an event and its size.

Technology at the service of sport

The advancement of sports equipment is making a big impact on sports science. The combinations of some equipment improve the time spent by swimmers to cross a specific borderline. It’s the same thing that has happened in cycling: the technical improvement of bicycles plays a fundamental role in improving performance. Lighter and more aerodynamic materials help in penetrating the air with minimal resistance.

Mathematics to improve the technical skills of athletes

If mathematics can help you manage your money and calculate percentages in your math courses, then they can also help you with sports. For instance, mathematics allows you to determine the trajectory of the ball. Therefore, it should not surprise us that sport rely heavily on algebra, geometry, multiplication tables, arithmetic, whole numbers, proportions, etc. Athletes no longer go to competitions accompanied only by their coach, their physiotherapist or their nutritionist. As times have changed, now there are other types of professionals who accompany the team. For example, the Australian or the New Zealander team in the J.J.O.O. 2016, had real mathematicians on their team. Their function was to gather data and take into consideration the context to develop statistics to optimize athletic technique in all possible parameters. The goal is clear: to achieve perfection in the discipline and optimize training.

Mathematics in preparing football tournaments

Mathematical analysis is also taken into account in the selections of football teams, since the selectors use it when they have to make the list for a big sports event. The analysis of team performance and the development of mathematical models allow strategic choices based more on logic than on the “instinct of the coach”. It is true that it is something complex, but it can make the difference between a victory and a defeat.