Applying graphs and complex networks to football metric interpretation.

This work presents a methodology for analysing the interactions between players in a football team, from the point of view of graph theory and complex networks. We model the complex network of passing interactions between players of a same team in 32 official matches of the Liga de Fútbol Profesional (Spain), using a passing/reception graph. This methodology allows us to understand the play structure of the team, by analysing the offensive phases of game-play. We utilise two different strategies for characterising the contribution of the players to the team: the clustering coefficient, and centrality metrics (closeness and betweenness). We show the application of this methodology by analyzing the performance of a professional Spanish team according to these metrics and the distribution of passing/reception in the field. Keeping in mind the dynamic nature of collective sports, in the future we will incorporate metrics which allows us to analyse the performance of the team also according to the circumstances of game-play and to different contextual variables such as, the utilisation of the field space, the time, and the ball, according to specific tactical situations.

Análisis y evaluación del lanzamiento de esquina (córner) en el fútbol de alto nivel / Analysis and evaluation of the corner kick in soccer at the highest level

Objetivo. Analizar cuál es la trascendencia del córner durante un partido de fútbol y conocer cuáles son las acciones principales que tienen lugar durante un saque de esquina en el fútbol profesional masculino de alto nivel. Métodos. Se analizaron 333 lanzamientos de esquina ejecutados en 35 partidos correspondientes a cinco competiciones internacionales de selecciones nacionales. Para su análisis se establecieron 370 posibles soluciones potenciales que fueron categorizadas a partir de cuatro niveles: lado de lanzamiento; profundidad del saque de esquina; posición del campo a la que se lanza el balón y acciones de segunda jugada. Resultados. El número de córneres por partido fue de 9,54 ± 1,02 (varianza: 11,79; rango: 5 - 18). Su número se comporta como una distribución de Poisson. Las características dominantes son los lanzamientos del lado derecho (52,4%) frente al izquierdo (47,6%); los saques largos (82,8%) sobre los cortos (17,2%); los lanzamientos al centro (53,7%) sobre los que se envían al primer poste (28,2%) o el segundo poste (28,2%). En la finalización de la jugada, los despejes (182 - 58,9%) y los contraataques (31 - 10,0%) superaron a los saques de esquina que terminan en remates a portería (53 - 17,2%) o se convierten en goles (5 - 1,6%). Conclusiones. El córner es una acción frecuentemente utilizada en un partido de fútbol, pero con un bajo nivel de efectividad (1,6/partido). Entendemos que, dado el bajo número de goles que suelen marcarse en un partido, la máxima optimización de estas acciones tácticas alcanza un valor relevante en el fútbol moderno(AU)

Objective. To analyze the corner significance during a soccer game and to know which are the main actions that occur during a corner kick in senior male professional soccer. Methods. We analyzed 333 corner kicks executed in 35 games, corresponding to five national team international competitions. For its analysis, 370 possible solutions were categorized based on four levels: Kick side, corner kick deepness; field position at which the ball is thrown and second play actions. Results. The number of corners per game was 9.54 ± 1.02 (variance: 11.79; range: 5 - 18). Its behavior follows the Poisson distribution. The key features are the right side kicks (52.4%) vs. left side (47.6%); the long kicks (82.8%) over the short ones (17.2%); the center kicks (53.7%) over the ones sent to the first post (28.2%) or the second post (28.2%). At the end of the play, the number of clearances (182 - 58.9%) and counterattacks (31 - 10.0%) outperformed the number of corner kicks ending in shots on goals (53 - 17.2%) or becoming in goals (5 - 1.6%). Conclusion. The corner is a common action used during a soccer match but with a low effectiveness level (1.6/match). We understand that, given the low number of goals scored during a game, the maximum optimization of these tactical actions reaches a relevant value in modern soccer(AU)

The limitations of scaling laws in the prediction of performance in endurance events.

In the twentieth century, scientists have examined running speed over various distances, analyzing world records and studying the ability of an athlete to sustain a given speed. Assuming that running speed expresses the response of a non-linear multisystemic behavior, the relationship between these two variables (distance vs. velocity) can therefore be evaluated by applying scaling laws that fulfill the key principles of specificity and individuality of each athlete, yet responding to bioenergetic and functional patterns that are well-known to sports physiology. Since speed loss as distance increases exhibits fractal behavior, with small changes in the speed-reduction curve due to the effect of fatigue, it must be recognized that no universal scaling law can account, with acceptable precision, for the effect exerted by fatigue on potential speed at any given moment in a race. Power laws using a range of scaling exponents provide technical staff and athletes with a reliable, non-invasive tool for planning of training schedules, predicting athletes' performances over various distances and comparing the performance of specialists in different track events. The equations for the scaling laws for the distances investigated here were: V1500=15.00 × D⁻°·¹° (R²=0.99); V3000=12.76 × D⁻°·°8 (R²=0.99); V5000=11.55 × D⁻°·°7 (R²=0.99); V10,000=11.59 × D⁻°·°7 (R²=0.99); V21,095=10.78 × D⁻°·°6 (R²=0.97); V42,175=10.27 × D⁻°·°57 (R²=0.99).

Male powerlifting performance described from the viewpoint of complex systems.

This paper reflects on the factors that condition performance in powerlifting and proposes that the result-generating process is inadequately described by the allometric equations commonly used. We analysed the scores of 1812 lifters belonging to all body mass categories, and analysed the changes in the results achieved in each weight category and by each competitor. Current performance-predicting methods take into account biological variables, paying no heed to other competition features. Performance in male powerlifting (as in other strength sports) behaves as a self-organised system with non-linear interactions between its components. Thus, multiple internal and external elements must condition changes in a competitor's score, the most important being body mass, body size, the number of practitioners, and the concurrency of favourable factors in one individual. It was observed that each behaved in a specific form in the high level, according to the individuals' circumstances, which make up the main elements of the competitive system in every category. In powerlifting, official weight categories are generally organised in three different groups: light (<52.0 to <60 kg), medium (<67.5 to <90.0 kg) and heavy (<100 to >125 kg) lifter categories, each one of them with specific allometric exponents. The exponent should be revised periodically, especially with regard to the internal dynamics of the category, and adjusted according to possible changes affecting competition.

Locating Pollicott-Ruelle resonances in chaotic dynamical systems: a class of numerical schemes.

A class of numerical methods to determine Pollicott-Ruelle resonances in chaotic dynamical systems is proposed. This is achieved by relating some existing procedures that make use of the Padé approximants, and interpolating exponentials to both the memory function techniques used in the theory of relaxation and the filter diagonalization method used in the harmonic inversion of time correlation functions. This relationship leads to a theoretical framework in which all these methods become equivalent and which allows for new and improved numerical schemes.