Maximizing performance with an eye on the finances: a chance-constrained model for football transfer market decisions
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Maximizing performance with an eye on the finances: a chance‑constrained model for football transfer market decisions G. Pantuso1 · L. M. Hvattum2 Received: 17 January 2020 / Accepted: 9 October 2020 © Sociedad de Estadística e Investigación Operativa 2020
Abstract Composing a team of professional players is among the most crucial decisions in association football. Nevertheless, transfer market decisions are often based on myopic objectives and are questionable from a financial point of view. This paper introduces a chance-constrained model to provide analytic support to club managers during transfer windows. The model seeks a top-performing team while adapting to different budgets and financial-risk profiles. In addition, it provides a new rating system that is able to numerically reflect the on-field performance of football players and thus contribute to an objective assessment of football players. The model and rating system are tested on a case study based on real market data. The data from the case study are available online for the benefit of future research. Keywords Association football · Team composition · Sport · Sports management · Stochastic programming · Integer programming Mathematics Subject Classification 90C15 · 90C10 · 90C90
1 Introduction Composing a team of players is among the most crucial decisions a football club’s manager is required to make. In fact, the main component of a football club’s costs is expenditure on players, through both wages and transfer fees (Dobson and Goddard * G. Pantuso [email protected] L. M. Hvattum [email protected] 1
Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
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Faculty of Logistics, Molde University College, Britvegen 2, 6410 Molde, Norway
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2001). However, the analysis performed by Kuper and Szymanski (2018) illustrates that transfer decisions are often based on myopic objectives and impulsive reactions, and are overly influenced by factors such as recent performances (Lewis 2004), particularly in big tournaments, nationality, and even hair color. With few exceptions, football clubs are in general bad businesses, rarely making profits and most often accumulating considerable debts. The authors explain that poor management of football clubs is tolerated, because, unlike in most industries, clubs in practice never go bankrupt. History shows that creditors rarely claim their credits to the extent of causing the default of the club. In other words: “no bank manager or tax collector wants to say: The century-old local club is closing. I am turning off the lights” (Kuper and Szymanski 2018). In practice, clubs eventually find someone who bails them out, change management, narrow the budget, and force them to restart by competing at lower standards (e.g., being relegated). According to UEFA, this dramatic scenario is changing for the better. In their Club Licensing Benchmarking Report for the financial year 2016 (UEFA 2018), UEFA reports that the
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