Fixed points and European soccer leagues: discussing the trajectories of European soccer teams by the density of fixed points - Mourao, P (SPORT TK-EuroAmerican Journal of Sport Sciences, 2018)
All soccer teams visit their final standing ranks before their final journeys. This work analyzes the trajectory of European soccer teams toward their final standing ranks for the seasons between 2004/2005 and 2012/2013. We studied six professional soccer leagues (England, Germany, Italy, the Netherlands, Portugal, and Spain). Referring to the fixed point theorem and to quantile regressions, this article concludes that the Dutch league is the one characterized by the largest value for its fixed point, exhibiting more rank changes than the others with the same percentage of played journeys. The English and Italian leagues were identified as the leagues in which a higher share of teams tended to stabilize at their final standings’ ranks at the earliest journeys.