Related papers: Statistics of football dynamics
The human society is a very complex system; still, there are several non-trivial, general features. One type of them is the presence of power-law distributed quantities in temporal statistics. In this Letter, we focus on the origin of…
The characterization of record events is considered for a discrete-time random walk model with long-term memory arising from correlations between successive steps. An important feature is that the correlations are strong enough to give rise…
Professional team sports provide an excellent domain for studying the dynamics of social competitions. These games are constructed with simple, well-defined rules and payoffs that admit a high-dimensional set of possible actions and…
In soccer, game context can result in skewing offensive statistics in ways that might misrepresent how well a team has played. For instance, in England's 1-2 loss to France in the 2022 FIFA World Cup quarterfinal, England attempted…
Player tracking data have provided great opportunities to generate novel insights into understudied areas of American football, such as pre-snap motion. Using a Bayesian multilevel model with heterogeneous variances, we provide an…
In the so-called "microscopic" models of vehicular traffic, attention is paid explicitly to each individual vehicle each of which is represented by a "particle"; the nature of the "interactions" among these particles is determined by the…
A mass ejection model in a time-dependent random environment with both temporal and spatial correlations is introduced. When the environment has a finite correlation length, individual particle trajectories are found to diffuse at large…
In the pursuit of natural language understanding, there has been a long standing interest in tracking state changes throughout narratives. Impressive progress has been made in modeling the state of transaction-centric dialogues and…
Besides of complexities concerning to football championships, it is identified some regularities in them. These regularities refer to goal distributions by goal-players and by games. In particular, the goal distribution by goal-players it…
The increasing availability of spatio-temporal tracking data has created new opportunities for analysing tactical behaviour in football. However, many existing approaches evaluate passes primarily through outcome-based metrics such as…
Moves in chess games are usually analyzed on a case-by-case basis by professional players, but thanks to the availability of large game databases, we can envision another approach of the game. Here, we indeed adopt a very different point of…
Symmetric random walks in $R^d$ and $Z^d$ are considered. It is assumed that the jump distribution density has moderate tails, i.e., several density moments are finite, including the second one. The global (for all $x$ and $t$) asymptotic…
Scoring goals in a soccer match can be interpreted as a stochastic process. In the most simple description of a soccer match one assumes that scoring goals can be described by a constant goal rate for each team, implying simple Poissonian…
Several populational networks present complex topologies when implemented in evolutionary algorithms. A common feature of these topologies is the emergence of a power law. Power law behavior with different scaling factors can also be…
The dynamics of many social, technological and economic phenomena are driven by individual human actions, turning the quantitative understanding of human behavior into a central question of modern science. Current models of human dynamics,…
We propose a bottom-up approach to the study of possession and its outcomes for association football, based on probabilistic finite state automata with transition probabilities described by a Markov process. We show how even a very simple…
We consider nonequilibrium systems with complex dynamics in stationary states with large fluctuations of intensive quantities (e.g. the temperature, chemical potential, or energy dissipation) on long time scales. Depending on the…
The horizontal dynamics of a bouncing ball interacting with an irregular surface is investigated and is found to demonstrate behavior analogous to a random walk. Its stochastic character is substantiated by the calculation of a permutation…
These notes cover one of the topics of the class given in the Les Houches Summer School ``Mathematical statistical physics'' in July 2005. The lectures tried to give a summary of the recent mathematical results about the long-time behaviour…
Many complex phenomena, from the selection of traits in biological systems to hierarchy formation in social and economic entities, show signs of competition and heterogeneous performance in the temporal evolution of their components, which…