Probabilistic Transitivity in Sports

Johannes Tiwisina and Philipp Külpmann
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Johannes Tiwisina: Center for Mathematical Economics, Bielefeld University
Philipp Külpmann: Center for Mathematical Economics, Bielefeld University
Authors registered in the RePEc Author Service: Philipp Külpmann

No 520, Center for Mathematical Economics Working Papers from Center for Mathematical Economics, Bielefeld University

Abstract: We seek to find the statistical model that most accurately describes empirically observed results in sports. The idea of a transitive relation concerning the team strengths is implemented by imposing a set of constraints on the outcome probabilities. We theoretically investigate the resulting optimization problem and draw comparisons to similar problems from the existing literature including the linear ordering problem and the isotonic regression problem. Our optimization problem turns out to be very complicated to solve. We propose a branch and bound algorithm for an exact solution and for larger sets of teams a heuristic method for quickly finding a „good“ solution. Finally we apply the described methods to panel data from soccer, American football and tennis and also use our framework to compare the performance of empirically applied ranking schemes.

Keywords: stochastic transitivity; trinomial; geometric optimization; ranking; branch and bound; linear ordering problem; elo; tabu search; football; soccer; tennis; bundesliga; nfl; atp (search for similar items in EconPapers)
Pages: 28
Date: 2016-03-15
New Economics Papers: this item is included in nep-cmp, nep-ore and nep-spo
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https://pub.uni-bielefeld.de/download/2901643/2902675 First Version, 2014 (application/x-download)

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Persistent link: https://EconPapers.repec.org/RePEc:bie:wpaper:520

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