Singular value decomposition entropy of the standing matrix for quantifying competitiveness of soccer leagues

Competitiveness is a key characteristic of professional sports. Its quantification is of prime importance as it is one of the main indicators that allow fans, investors and betting agencies to determine their position in the market. This work studied the competitiveness of ten professional European men’s soccer leagues for the seasons from 2010/11 to 2021/22. The approach considered the matrix of standings for a given season and the computing of the corresponding SVD entropy as an index of randomness. The higher the entropy, the more uncertain the evolution of the standing, and hence the more unpredictable the distribution of points achieved by clubs. The results showed that the soccer leagues are not perfectly competitive since the SVD entropy is not consistent with a random matrix. The degree of competitiveness varied with time, with the Italian Serie A and the French Ligue 1 showing the highest competitiveness in the early 2010s seasons. The English Premier League increased its competitiveness in recent past seasons, while Ligue 1 exhibited a marked decrease. Overall, the results showed that the approach proposed in the present work provides valuable insights into the evolution of the competitiveness of soccer leagues and stands as a suitable framework for inter-league comparison.