Spatial and Temporal Entropies in the Spanish Football League: A Network Science Perspective

Complexity emerges in measures of the marking dynamics in football games

In this article, we study the dynamics of marking in football matches. To do this, we survey and analyze a database containing the trajectories of players from both teams on the field of play during three professional games. We describe the dynamics through the construction of temporal bipartite networks of proximity. Based on the introduced concept of proximity, the nodes are the players, and the links are defined between opponents that are close enough to each other at a given moment. By studying the evolution of the heterogeneity parameter of the networks during the game, we characterize a scaling law for the average shape of the fluctuations, unveiling the emergence of complexity in the system. Moreover, we propose a simple model to simulate the players' motion in the field from where we obtained the evolution of a synthetic proximity network. We show that the model captures with a remarkable agreement the complexity of the empirical case, hence it proves to be helpful to elucidate the underlying mechanisms responsible for the observed phenomena.

Image registration method using representative feature detection and iterative coherent spatial mapping for infrared medical images with flat regions

In the registration of medical images, nonrigid registration targets, images with large displacement caused by different postures of the human body, and frequent variations in image intensity due to physiological phenomena are substantial problems that make medical images less suitable for intensity-based image registration modes. These problems also greatly increase the difficulty and complexity of feature detection and matching for feature-based image registration modes. This research introduces an automatic image registration algorithm for infrared medical images that offers the following benefits: effective detection of feature points in flat regions (cold patterns) that appear due to changes in the human body’s thermal patterns, improved mismatch removal through coherent spatial mapping for improved feature point matching, and large-displacement optical flow for optimal transformation. This method was compared with various classical gold standard image registration methods to evaluate its performance. The models were compared for the three key steps of the registration process—feature detection, feature point matching, and image transformation—and the results are presented visually and quantitatively. The results demonstrate that the proposed method outperforms existing methods in all tasks, including in terms of the features detected, uniformity of feature points, matching accuracy, and control point sparsity, and achieves optimal image transformation. The performance of the proposed method with four common image types was also evaluated, and the results verify that the proposed method has a high degree of stability and can effectively register medical images under a variety of conditions.

Stochastic model for football's collective dynamics

In this paper, we study collective interaction dynamics emerging in the game of football (soccer). To do so, we surveyed a database containing body-sensor traces measured during three professional football matches, where we observed statistical patterns that we used to propose a stochastic model for the players' motion in the field. The model, which is based on linear interactions, captures to a good approximation the spatiotemporal dynamics of a football team. Our theoretical framework, therefore, can be an effective analytical tool to uncover the underlying cooperative mechanisms behind the complexity of football plays. Moreover, we showed that it can provide handy theoretical support for coaches to evaluate teams' and players' performances in both training sessions and competitive scenarios.

Complexity Evaluation of an Environmental Control and Life-Support System Based on Directed and Undirected Structural Entropy Methods

During manned space missions, an environmental control and life-support system (ECLSS) is employed to meet the life-supporting requirements of astronauts. The ECLSS is a type of hierarchical system, with subsystem—component—single machines, forming a complex structure. Therefore, system-level conceptual designing and performance evaluation of the ECLSS must be conducted. This study reports the top-level scheme of ECLSS, including the subsystems of atmosphere revitalization, water management, and waste management. We propose two schemes based on the design criteria of improving closure and reducing power consumption. In this study, we use the structural entropy method (SEM) to calculate the system order degree to quantitatively evaluate the ECLSS complexity at the top level. The complexity of the system evaluated by directed SEM and undirected SEM presents different rules. The results show that the change in the system structure caused by the replacement of some single technologies will not have great impact on the overall system complexity. The top-level scheme design and complexity evaluation presented in this study may provide technical support for the development of ECLSS in future manned spaceflights.

Mathematical Models to Measure the Variability of Nodes and Networks in Team Sports

Pattern analysis is a widely researched topic in team sports performance analysis, using information theory as a conceptual framework. Bayesian methods are also used in this research field, but the association between these two is being developed. The aim of this paper is to present new mathematical concepts that are based on information and probability theory and can be applied to network analysis in Team Sports. These results are based on the transition matrices of the Markov chain, associated with the adjacency matrices of a network with n nodes and allowing for a more robust analysis of the variability of interactions in team sports. The proposed models refer to individual and collective rates and indexes of total variability between players and teams as well as the overall passing capacity of a network, all of which are demonstrated in the UEFA 2020/2021 Champions League Final.

Entropy of Badminton Strike Positions

The aim of the current study was twofold: (i) to investigate the distribution of the strike positions of badminton players while quantifying the corresponding standard entropy and using an alternative metric (spatial entropy) related to winning and losing points and random positions; and (ii) to evaluate the standard entropy of the receiving positions. With the datasets of 259 badminton matches, we focused on the positions of players’ strokes and the outcome of each point. First, we identified those regions of the court from which hits were most likely to be struck. Second, we computed the standard entropy of stroke positions, and then the spatial entropy, which also considers the order and clustering of the hitting locations in a two-dimensional Euclidean space. Both entropy quantifiers revealed high uncertainty in the striking position; however, specific court locations (i.e., the four corners) are preferred over the rest. When the outcome of each point was taken into account, we observed that the hitting patterns with lower entropy were associated with higher probabilities of winning points. On the contrary, players striking from more random positions were more prone to losing the points.

Dodge and survive: Modeling the predatory nature of dodgeball

The analysis of games and sports as complex systems can give insights into the dynamics of human competition and has been proven useful in soccer, basketball, and other professional sports. In this paper, we present a model for dodgeball, a popular sport in U.S. schools, and analyze it using an ordinary differential equation (ODE) compartmental model and stochastic agent-based game simulations. The ODE model reveals a rich landscape with different game dynamics occurring depending on the strategies used by the teams, which can in some cases be mapped to scenarios in competitive species models. Stochastic agent-based game simulations confirm and complement the predictions of the deterministic ODE models. In some scenarios, game victory can be interpreted as a noise-driven escape from the basin of attraction of a stable fixed point, resulting in extremely long games when the number of players is large. Using the ODE and agent-based models, we construct a strategy to increase the probability of winning.

Node and Network Entropy—A Novel Mathematical Model for Pattern Analysis of Team Sports Behavior

Pattern analysis is a well-established topic in team sports performance analysis, and is usually centered on the analysis of passing sequences. Taking a Bayesian approach to the study of these interactions, this work presents novel entropy mathematical models for Markov chain-based pattern analysis in team sports networks, with Relative Transition Entropy and Network Transition Entropy applied to both passing and reception patterns. To demonstrate their applicability, these mathematical models were used in a case study in football—the 2016/2017 Champions League Final, where both teams were analyzed. The results show that the winning team, Real Madrid, presented greater values for both individual and team transition entropies, which indicate that greater levels of unpredictability may bring teams closer to victory. In conclusion, these metrics may provide information to game analysts, allowing them to provide coaches with accurate and timely information about the key players of the game.

Predicting Wins, Losses and Attributes' Sensitivities in the Soccer World Cup 2018 Using Neural Network Analysis

Predicting the results of soccer competitions and the contributions of match attributes, in particular, has gained popularity in recent years. Big data processing obtained from different sensors, cameras and analysis systems needs modern tools that can provide a deep understanding of the relationship between this huge amount of data produced by sensors and cameras, both linear and non-linear data. Using data mining tools does not appear sufficient to provide a deep understanding of the relationship between the match attributes and results and how to predict or optimize the results based upon performance variables. This study aimed to suggest a different approach to predict wins, losses and attributes' sensitivities which enables the prediction of match results based on the most sensitive attributes that affect it as a second step. A radial basis function neural network model has successfully weighted the effectiveness of all match attributes and classified the team results into the target groups as a win or loss. The neural network model's output demonstrated a correct percentage of win and loss of 83.3% and 72.7% respectively, with a low Root Mean Square training error of 2.9% and testing error of 0.37%. Out of 75 match attributes, 19 were identified as powerful predictors of success. The most powerful respectively were: the Total Team Medium Pass Attempted (MBA) 100%; the Distance Covered Team Average in zone 3 (15-20 km/h; Zone3_TA) 99%; the Team Average ball delivery into the attacking third of the field (TA_DAT) 80.9%; the Total Team Covered Distance without Ball Possession (Not in_Poss_TT) 76.8%; and the Average Distance Covered by Team (Game TA) 75.1%. Therefore, the novel radial based function neural network model can be employed by sports scientists to adapt training, tactics and opposition analysis to improve performance.