A competing risk survival analysis of the impacts of team formation on goals in professional football.

Introduction: This study investigated the influence of team formation on goal-scoring efficiency through analysing the time required for a goal to be scored in elite football matches. Method: The analysis was conducted using a comprehensive open access dataset encompassing eight major football competitions, including prestigious events such as the World Cup and the UEFA Champions League. It notably focused on the competing risks framework and employed the Fine and Gray model to account for the interplay between two competing events: team A scoring and team B scoring. Results: Through analysis of Team A's goal occurrences, we assessed the offensive capabilities of its formation and the defensive effectiveness of Team B's composition in relation to the time it took for Team A to score a goal. Findings revealed that teams employing the 4-3-3 and 4-2-3-1 formations outperformed other formations (3-4-3, 3-5-2, 4-4-2, 4-5-1, 5-3-2, 5-4-1) regarding goal-scoring efficiency. Discussion: By shedding light on the impact of team formation on goal scoring, this research contributes to a deeper understanding of some of the successful strategic aspects of elite football.

Growth charts for small sample sizes using unsupervised clustering: Application to canine early growth.

Breed-specific growth curves (GCs) are needed for neonatal puppies, but breed-specific data may be insufficient. We investigated an unsupervised clustering methodology for modeling GCs by augmenting breed-specific data with data from breeds having similar growth profiles. Puppy breeds were grouped by median growth profiles (bodyweights between birth and Day 20) using hierarchical clustering on principal components. Median bodyweights for breeds in a cluster were centered to that cluster's median and used to model cluster GCs by Generalized Additive Models for Location, Shape and Scale. These were centered back to breed growth profiles to produce cluster-scale breed GCs. The accuracy of breed-scale GCs modeled with breed-specific data only and cluster-scale breed GCs were compared when modeled from diminishing sample sizes. A complete dataset of Labrador Retriever bodyweights (birth to Day 20) was split into training (410 puppies) and test (460 puppies) datasets. Cluster-scale breed and breed-scale GCs were modelled from defined sample sizes from the training dataset. Quality criteria were the percentages of observed data in the test dataset outside the target growth centiles of simulations. Accuracy of cluster-scale breed GCs remained consistently high down to sampling sizes of three. They slightly overestimated breed variability, but centile curves were smooth and consistent with breed-scale GCs modeled from the complete Labrador Retriever dataset. At sampling sizes ≤ 20, the quality of breed-scale GCs reduced notably. In conclusion, GCs for neonatal puppies generated using a breed-cluster hybrid methodology can be more satisfactory than GCs at purely the breed level when sample sizes are small.