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Probabilistic transitivity in sports

Published: 01 December 2019 Publication History

Highlights

Stochastic transitivity can be extended to incorporate ties and home/away asymmetries.
Transitivity quickly narrows down the set of feasible probability matrices.
Given our model, the most popular ranking systems are far away from the best ranking.
2- and 3-point systems perform better than other ranking systems in soccer.
Elo- and the LOP-ranking system perform better in American football and tennis.

Abstract

We seek to find the statistical model that most accurately describes empirically observed results in sports. This model has only two assumptions: a trinomial distribution of outcomes and a transitive relationship between these probabilities. The latter is implemented by imposing constraints on the outcome probabilities. To find the most likely correct ranking, we propose a Branch-and-Bound algorithm and a quicker, heuristic method.
We apply the model to panel data from soccer, American football and tennis. Due to the transitivity assumption, our model has a natural application in comparing ranking systems. Therefore, we use it to evaluate empirically applied ranking schemes.

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Published In

cover image Computers and Operations Research
Computers and Operations Research  Volume 112, Issue C
Dec 2019
271 pages

Publisher

Elsevier Science Ltd.

United Kingdom

Publication History

Published: 01 December 2019

Author Tags

  1. OR in sports
  2. Stochastic transitivity
  3. Trinomial distribution
  4. Ranking
  5. Geometric optimization

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