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Data analytics in sports is crucial to evaluate the performance of single players and the whole team. The literature proposes a number of tools for both offence and defence scenarios. Data coming from tracking location of players, in this…
We consider a broad class of stochastic imitation dynamics over networks, encompassing several well known learning models such as the replicator dynamics. In the considered models, players have no global information about the game…
Soccer is a globally renowned sport with significant applications in video games and VR/AR. However, generating realistic soccer motions remains challenging due to the intricate interactions between the human player and the ball. In this…
Understanding football tactics is crucial for managers and analysts. Previous research has proposed models based on spatial and kinematic equations, but these are computationally expensive. Also, Reinforcement learning approaches use player…
This paper explores the concept of "momentum" in sports competitions through the use of the TOPSIS model and 0-1 logistic regression model. First, the TOPSIS model is employed to evaluate the performance of two tennis players, with…
This paper presents a new framework for player valuation in European football, by fusing principles from financial mathematics and network theory. The valuation model leverages a "passing matrix" to encapsulate player interactions on the…
A knowledgeable observer of a game of football (soccer) can make a subjective evaluation of the quality of passes made between players during the game. We investigate the problem of producing an automated system to make the same evaluation…
We develop two statistical models for space-time abundance data based on a stochastic underlying continuous individual movement. In contrast to current models for abundance in statistical ecology, our models exploit the explicit connection…
Many intelligent user interfaces employ application and user models to determine the user's preferences, goals and likely future actions. Such models require application analysis, adaptation and expansion. Building and maintaining such…
Basketball games evolve continuously in space and time as players constantly interact with their teammates, the opposing team, and the ball. However, current analyses of basketball outcomes rely on discretized summaries of the game that…
Understanding trajectories in multi-agent scenarios requires addressing various tasks, including predicting future movements, imputing missing observations, inferring the status of unseen agents, and classifying different global states.…
We propose a new mathematical model for the decision-making of players in football (soccer) and the efficiency of the game style. Our approach is based on $4$-networks, which is a mathematical concept that we introduce. The decision of…
Analysis of invasive sports such as soccer is challenging because the game situation changes continuously in time and space, and multiple agents individually recognize the game situation and make decisions. Previous studies using deep…
Soccer is undeniably the most popular sport world-wide and everyone from general managers and coaching staff to fans and media are interested in evaluating players' performance. Metrics applied successfully in other sports, such as the…
In this work we introduce an approach for modeling and analyzing collective behavior of a group of agents using moments. We represent the group of agents via their distribution and derive a method to estimate the dynamics of the moments. We…
In soccer, contextual player performance metrics are invaluable to coaches. For example, the ability to perform under pressure during matches distinguishes the elite from the average. Appropriate pressure metric enables teams to assess…
A mathematical model for behavioral changes by pair interactions (i.e. due to direct contact) of individuals is developed. Three kinds of pair interactions can be distinguished: Imitative processes, avoidance processes, and compromising…
We propose a foundation model for soccer, which is able to predict subsequent actions in a soccer match from a given input sequence of actions. As a proof of concept, we train a transformer architecture on three seasons of data from a…
In many real-world complex systems, the behavior can be observed as a collection of discrete events generated by multiple interacting agents. Analyzing the dynamics of these multi-agent systems, especially team sports, often relies on…
We present a modeling framework for dynamical and bursty contact networks made of agents in social interaction. We consider agents' behavior at short time scales, in which the contact network is formed by disconnected cliques of different…