An Application of Stochastic Dominances in Sports Analytics

  1. Fernández Ponce, José María
  2. Rodríguez Griñolo, Rosario
  3. Troncoso Molina, Miguel Angel
Revista:
Estudios de economía aplicada

ISSN: 1133-3197 1697-5731

Año de publicación: 2022

Título del ejemplar: Sports Analytics within Sports Economics and Management

Volumen: 40

Número: 1

Tipo: Artículo

DOI: 10.25115/EEA.V40I1.7002 DIALNET GOOGLE SCHOLAR lock_openAcceso abierto editor

Otras publicaciones en: Estudios de economía aplicada

Resumen

Stochastic orders or stochastic dominance as they are known in Economics have been widely studied and applied in a variety of scientific fields, from Biology to Systems Engineering. However, to the best of our knowledge there is an application gap in the field of Sports Analytics or Sports Sciences. In this paper, we attempt a first approach to a possible application of stochastic orders to a dataset of LaLiga (Spain) football matches. Our aim is simply to show how a comparison can be extended beyond a simple metric comparison. In particular, we will focus on the first and second dominance stochastic orders as they are the most intuitive and simple to interpret and are also the most widely used in Economics.

Referencias bibliográficas

  • Damodaran, U. "Stohcastic dominance and analysis of od batting performance: the Indian ricket team, 1989-2005". Journal of Sports Science and Medicine, (2006), Vol. 5, 503-508.
  • Denuit, M.; Dhane, J.; Goovaerts, M. and Kaas, R. "Actuarial Theory for Dependent Risks. Measures, Orders and Models". John Wiley and Sons, Ltd. 2005.
  • Ensum, J.; Pollard, R. and Taylor, S. "Applications of logistic regression to shots at goal in association football: calculation of shot probabilities, quantification of factors and player/team". Journal of Sports Sciences ,(2004), 22 (6), 504.
  • Ghojogh, B.; Ghojogh, A.; Crowley, M. and Karray, F. "Fitting a mixture distribution to data: tutorial.". arXiv:1901.06708v2 [stat.OT].
  • Hadar, J. and Russell, WR. "Stochastic dominance and diversification". Journal fo Economic Theory 3, (1971), 3, 288-305.
  • Hahn, ED. "Mixture densities for project management activity times: A robust approach to PERT". European Journal of Operational Research, (2008), vol 188(2), 450-459.
  • Kopa,M.; Kabašinskas, A and Šutiené, K. "A stochastic dominance approach to pension-fun selection." IMA Journal of Management Mathematics 33, (2022), 1, 139-160.
  • Macdonald, B. "An Expected Goals Model for Evaluating NHL Teams and Players". MIT Sloan Sports Analytics Conference 2012, Boston, USA.
  • Pollard, R.; Ensum, J. and Taylor, S. "Estimating the probability of a shot resulting in a goal: The effects of distance, angle and space". International Journal of Soccer and Science, (2004), (1), 50-55.
  • Schröeder, C. and Rahmann, S. "A hybrid parameter estimation algortihm for beta mixtures and applications to methylation state classification". Algorithms for Molecular Biology, (2017), -21.
  • Shaked, M. and Shanthikumar, G. " Stochastic Orders and Their Applications". Academic Press, Boston. 1994.
  • Singh, K. "Introducing Expected Threat (xT)". 2019. https://karun.in/blog/expected-threat.html.
  • Spearman, W. "Beyond Expected Goals". MIT Sloan Sports Analytics Conference 2018, Boston, MA.
  • Tippett, J. "The Expected Goals Philosophy: A Game-Changing Way of Analysing Football". (Independently published).
  • Zhanyu Ma and Leijon, A. "Bayesian Estimation of Beta Mixture Models with Variational Inference". IEEE Transactions on Pattern Analysis and Machine Intelligence, (2011), vol. 33,