Application of the Hungarian Algorithm in Baseball Team Selection

Application of the Hungarian Algorithm in Baseball Team Selection and Assignment S.S. Britz and M.J. von Maltitz Keywords: Hungarian algorithm, Kuhn-Munkres algorithm, team selection, position assignment, baseball team University of the Free State Department Mathematical Statistics and Actuarial Science 1 Abstract Measuring and comparing the performance of athletes in all forms of team sports require more than a modest amount of data reflecting the athletes’ abilities. When investigating the skill of baseball players in South Africa, however, one has to

make do with a combination of personal opinion, gut feeling and a few descriptive statistics. This research is aimed at developing a system with which to assess the abilities of baseball players in all practical aspects of the sport and compose a team in which all the players are assigned to positions such that the collective team skill is maximised for a specific goal. The system itself is of such a nature that any group of baseball players can apply it, with some help from a statistician. The optimisation process that selects the team is carried out using the Hungarian algorithm, a mathematical method of optimally assigning a set of persons to a set of jobs. 2 Table of Contents 1 Introduction .............................................................................................................................. 5 2 Literature Review ...................................................................................................................... 9 2.1 Team Selection Strategies ................................................................................................................. 7 2.2 The Development of the Hungarian Algorithm ................................................................................ 9 3 Methodology .......................................................................................................................... 13 3.1 The Baseball Aptitude Tests ............................................................................................................ 11 3.1.1 Hitting Test ............................................................................................................................... 12 3.1.2 Speed Test ................................................................................................................................ 12 3.1.3 Pitching Test ............................................................................................................................. 12 3.1.4 Throwing Tests ......................................................................................................................... 13 3.1.5 Fielding Tests ............................................................................................................................ 13 3.1.6 Reach Test ................................................................................................................................ 14 3.1.7 Reaction Test ............................................................................................................................ 14 3.2 Data Transformation Procedures .................................................................................................... 15 3.2.1 Success Percentages ................................................................................................................ 15 3.2.2 Less is More.............................................................................................................................. 16 3.2.3 The Reach Test and Hitting Test .............................................................................................. 17 3.2.4 Relative Scores ......................................................................................................................... 18 3.3 Dimension of the Data .................................................................................................................... 19 3.4 Introducing Weights ........................................................................................................................ 20 3.5 How the Hungarian Algorithm Works ............................................................................................. 22 4 Application ............................................................................................................................. 27 4.1 Testing for Multidimensional Data ................................................................................................. 27 4.2 The Optimal Baseball Team ............................................................................................................ 29 4.2.1 Optimal Defence ...................................................................................................................... 30 4.2.2 Medium Offence ...................................................................................................................... 34 4.2.3 Strong Offence ......................................................................................................................... 38 4.2.4 Maximum Aggression .............................................................................................................. 39 4.3 Introducing Relief Pitchers .............................................................................................................. 42 4.4 An Overview of the Team Selections .............................................................................................. 45 5 Conclusion .............................................................................................................................. 49 5.1 Further Research ............................................................................................................................. 47 3 Chapter 1 - Introduction The sport of baseball, also referred to as ‘the great American pastime’ (Bergan, 1982), has been steadily growing in popularity worldwide for the past few decades. The Olympic Games first recognized baseball as an official sport at the 1992 Summer Olympics. The sport was played at seven previous Olympic Games stretching as far back as 1912, but only as a demonstration sport. Rising interest and newly participating nations have led to the creation of the World Baseball Classic, equivalent to the World Cup in other sports. The establishment of this tournament in 2006...

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