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.