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.

A spatial Markovian framework for estimating regional and local dynamics of annual plants with dormancy.

Many species have a dormant stage in their life cycle, including seeds for plants. The dormancy stage influences the species dynamics but is often undetectable. One way to include dormancy is to model it as a hidden dynamical state within a Markovian framework. Models within this framework have already been proposed but with different limitations: only presence/absence observations are modelled, the dormancy stage is limited to one year, or colonisation from neighbouring patches is not taken into account. We propose a hidden Markov model that describes the local and regional dynamics of a species that can undergo dormancy with a potentially infinite dormancy time. Populations are modelled with abundance classes. Our model considers the colonisation process as the indistinguishable influence of neighbour non-dormant population states on a dormant population state in a patch. It would be expected that parameter estimation, hidden state estimation and prediction of the next non-dormant populations would have an exponential computational time in terms of the number of patches. However, we demonstrate that estimation, hidden state estimation and prediction are all achievable in a linear computational time. Numerical experiments on simulated data show that the state of dormant populations can easily be retrieved, as well as the state of future non-dormant populations. Our framework provides a simple and efficient tool that could be further used to analyse and compare annual plants dynamics like weed species survival strategies in crop fields.