This thesis aims to construct a ranking system measuring the latent variable football ability with random utility methodologies. We consider discriminal processes that are based on gamma distributions. We model football match outcomes as normal, logistic and Laplace Thurstone processes and relate these to Luce´s choice axiom. Numerical optimization of the likelihoods computed through a general linear model produces parameter estimates. Thurstone´s Case V model, the normal model, is closest to the real ranking based on ranking correlation measured by Kendall´s tau. Dawkins´ model, the Laplace model, has the highest value for goodness of fit, measured by the Akaike Information Criterion, due to its ability to model fat tails and a sharp peak simultaneously. Luce’s model, the logistic distribution, overestimates the thickness of the tails and is too flat at the peak. Thurstone´s Case V model cannot cope with the excess kurtosis.

Koning, A.J.
hdl.handle.net/2105/37437
Econometrie
Erasmus School of Economics

Raghoenath, Y.S. (Yugesh). (2017, March 30). Fitting Gamma Ranking Models to Soccer Data: Luce’s Choice Axiom and Thurstone’s Law in Practice. Econometrie. Retrieved from http://hdl.handle.net/2105/37437