Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/103923
Authors: 
Tiwisina, Johannes
Külpmann, Philipp
Year of Publication: 
2014
Series/Report no.: 
Working Papers, Center for Mathematical Economics 520
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.
Subjects: 
stochastic transitivity
trinomial
geometric optimization
ranking
branch and bound
linear ordering problem
ELO
tabu search
football
soccer
tennis
bundesliga
NFL
ATP
JEL: 
L83
C61
C63
C81
Persistent Identifier of the first edition: 
Document Type: 
Working Paper

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