Original research A log-linear analysis of efficiency in elite basketball applied to observational methodology Roberto Alsasua 1 , Daniel Lapresa 2 , Javier Arana 2 and M Teresa Anguera 3 Abstract Although the full potential of observational methodology is realized through diachronic analyses, synchronic analyses can be used to investigate associations between categorical variables. Log-linear modeling is an appropriate method for investigating associations between three or more dimensions using multidimensional contingency tables. We provide a practical example of how we used log-linear analysis to study efficiency in a men’s basketball competition played by Spain’s top teams using a model containing three dimensions (and their respective categories): position of last pass before a shot, position of shot, and result of shot. The best-fit and most parsimonious model (i.e., the model that provided the best explanation of the observed frequencies in the contingency table and that contained the fewest effects) was a conditional independence model in which last pass position and shot position were associated independently of the categories in the shot result dimension and the interaction between shot position and shot result was not affected by the categories in the last pass dimension. Estimation and subsequent interpretation of the significant parameters in the selected model showed how log-linear modeling can provide basketball coaches with practical insights within an observational methodology study. Keywords Basketball, efficiency, last pass position, shot position, log-linear Introduction This study has a twofold objective. Our first aim is methodological in nature and consists of illustrating the potential of log-linear analysis applied to observa- tional methodology 1 by providing a simple, practical example of how this synchronic technique can be used to study efficiency in sport. Our second aim, which is substantive in nature, is to shed light on successful and unsuccessful play in elite men’s basketball by studying associations between the position of the last pass before a shot (last pass position), the area of the court from where the shot was taken (shot position), and the outcome (favorable vs. unfavorable) of the shot (shot result). Efficiency in basketball has been analyzed by study- ing the impact of different game-related variables on shot outcomes (e.g., basket, missed basket, foul). 2–5 In studies of this type, it is essential to know the exact position of the shot, not only to analyze bio- mechanical factors, which have an obvious impact on scoring success, 6–8 but also to study tactics related to timing and positioning. 9,10 Shooting success has also been analyzed from the perspective of where the actions leading up to a shot occur, 11–13 with particular empha- sis on the position of the last pass. 14–16 To satisfy the methodological aim of this study and present a conceptually simple application of log-linear analysis, we included just three dimensions in our model, as the more dimensions there are, the more complicated it is to interpret results. The specific aim was to investigate synchronic associations between last pass position, shot position, and shot result. Reviewer: Bill Gerrard (Leeds University Business School). Arne Gu ¨llich (Kaiserslautern University of Technology). 1 Department of Educational Sciences, University of La Rioja, La Rioja (UNIR), Spain 2 Department of Education, International University of La Rioja, La Rioja, Spain 3 Faculty of Psychology, Institute of Neurosciences, University of Barcelona, Barcelona, Spain Corresponding author: Daniel Lapresa, Department of Educational Sciences, University of La Rioja, Edificio Vives, C/ Luis de Ulloa, s/n. 26004 Logron ˜o, La Rioja, Spain. Email: daniel.lapresa@unirioja.es International Journal of Sports Science & Coaching 0(0) 1–9 ! The Author(s) 2019 Article reuse guidelines: sagepub.com/journals-permissions DOI: 10.1177/1747954119837819 journals.sagepub.com/home/spo