Extracting insights from the shape of EuroLeague data using statistics and topology

Abstract

[en] Mapper is a tool for topological data analysis (TDA) which was designed in 2007 in order to study shape features of high-dimensional data sets, allowing to visualize them in a more comprehensive way. Our work is mainly practical but it also provides a theoretical background that sustains the methods used and the results obtained. We combine statistical techniques with topological data analysis to discern the structure of our data. We performed a principal component analysis, computed persistent homology, and applied Mapper to the EuroLeague data from the 2019–2020 season without taking into account the playoff matches. Our goal was to determine the underlying distribution of types of players and compare our results with those of a previous study based on data from the NBA.