Even though having more possession does not necessarily lead to winning, teams like Manchester City, Liverpool, and Leeds United notably have tried to recover the ball quickly after they lost it over the past few years. Nowadays, some of the top managers in the world apply high-pressing styles, and concepts such as the five-second rule, usually credited to Guardiola, have been spreading out [9][10], becoming a fundamental part of how lots of teams have played over the recent years. Expressions like "don't let them breathe" and "get the ball back as soon as possible" are often heard in the media [4][5][6], but what are the actions that most lead to a change in possession? What is the influence of a team's positioning on the ball recovery? Which are the players that more often collapse when under pressure? Can we evaluate the defensive dynamics of teams that do not necessarily press the player in possession as intensely as those mentioned above? We try to answer those and other questions in this paper by creating a Generalized Action based Ball Recovery model (GABR) using Statsbomb 360$^\circ$ data.

With the development of measurement technology, data on the movements of actual games in various sports are available and are expected to be used for planning and evaluating the tactics and strategy. In particular, defense in team sports is generally difficult to be evaluated because of the lack of statistical data. Conventional evaluation methods based on predictions of scores are considered unreliable and predict rare events throughout the entire game, and it is difficult to evaluate various plays leading up to a score. On the other hand, evaluation methods based on certain plays that lead to scoring and dominant regions are sometimes unsuitable to evaluate the performance (e.g., goals scored) of players and teams. In this study, we propose a method to evaluate team defense from a comprehensive perspective related to team performance based on the prediction of ball recovery and being attacked, which occur more frequently than goals, using player actions and positional data of all players and the ball. Using data from 45 soccer matches, we examined the relationship between the proposed index and team performance in actual matches and throughout a season. Results show that the proposed classifiers more accurately predicted the true events than the existing classifiers which were based on rare events (i.e., goals). Also, the proposed index had a moderate correlation with the long-term outcomes of the season. These results suggest that the proposed index might be a more reliable indicator rather than winning or losing with the inclusion of accidental factors.

For a certain class of distributions, we prove that the linear programming relaxation of $k$-medoids clustering---a variant of $k$-means clustering where means are replaced by exemplars from within the dataset---distinguishes points drawn from nonoverlapping balls with high probability once the number of points drawn and the separation distance between any two balls are sufficiently large. Our results hold in the nontrivial regime where the separation distance is small enough that points drawn from different balls may be closer to each other than points drawn from the same ball; in this case, clustering by thresholding pairwise distances between points can fail. We also exhibit numerical evidence of high-probability recovery in a substantially more permissive regime.