Clustering of football players based on performance data and aggregated clustering validity indexes

We analyse football (soccer) player performance data with mixed type variables from the 2014-15 season of eight European major leagues. We cluster these data based on a tailor-made dissimilarity measure. In order to decide between the many available clustering methods and to choose an appropriate number of clusters, we use the approach by Akhanli and Hennig (2020. "Comparing Clusterings and Numbers of Clusters by Aggregation of Calibrated Clustering Validity Indexes." Statistics and Computing 30 (5): 1523-44). This is based on several validation criteria that refer to different desirable characteristics of a clustering. These characteristics are chosen based on the aim of clustering, and this allows to define a suitable validation index as weighted average of calibrated individual indexes measuring the desirable features. We derive two different clusterings. The first one is a partition of the data set into major groups of essentially different players, which can be used for the analysis of a team's composition. The second one divides the data set into many small clusters (with 10 players on average), which can be used for finding players with a very similar profile to a given player. It is discussed in depth what characteristics are desirable for these clusterings. Weighting the criteria for the second clustering is informed by a survey of football experts.