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Optimizing the line-up of a sports team in a sallary capped league
Sabo, Adam ; Popela, Pavel (referee) ; Hrabec, Pavel (advisor)
This thesis is focused on the optimization of the lineup of a professional sports team operating under a salary cap condition. In the first part of the thesis, the theoretical foundations necessary for a proper understanding of the issue are introduced. Further, mathematical statistics and optimization methods are explained here and used in data analysis and in the creation of the relevant model. Particular emphasis is put on the methods of principal component analysis and linear programming. In the second part of the thesis, the problem of the optimization task, which takes into account the relevant NHL rules of competition and the salary cap together with performance characteristics of players, is formulated. The formulation was used to develop an optimization model that simulates real conditions in the NHL. This section also presents the application of the model based on historical data. Results obtained from calculations using the Python programming language are presented in the form of graphs, tables, and commentaries, showcasing the optimal team lineups, their characteristics, and respective rankings.
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