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Goals are results of pin-point shots and it is a pivotal decision in soccer when, how and where to shoot. The main contribution of this study is two-fold. At first, after showing that there exists high spatial correlation in the data of…

Applications · Statistics 2021-04-08 Soudeep Deb , Debangan Dey

Technology offers new ways to measure the locations of the players and of the ball in sports. This translates to the trajectories the ball takes on the field as a result of the tactics the team applies. The challenge professionals in soccer…

Computer Vision and Pattern Recognition · Computer Science 2015-08-11 Laszlo Gyarmati , Xavier Anguera

In sports analytics, home field advantage is a robust phenomenon where the home team wins more games than the away team. However, discovering the causal factors behind home field advantage presents unique challenges due to the…

Applications · Statistics 2025-06-16 Minhao Qi , Hengrui Cai , Guanyu Hu , Weining Shen

We investigated the temporal distribution of goals in soccer using event-level data from 3,433 matches across 21 leagues and competitions. Contrary to the prevailing notion of randomness, we found that the probability of a goal being scored…

Voronoi diagrams appear in many areas in science and technology and have numerous applications. They have been the subject of extensive investigation during the last decades. Roughly speaking, they are a certain decomposition of a given…

Computational Geometry · Computer Science 2015-03-19 Daniel Reem

In fluid team sports such as soccer and basketball, analyzing team formation is one of the most intuitive ways to understand tactics from domain participants' point of view. However, existing approaches either assume that team formation is…

Applications · Statistics 2023-06-13 Hyunsung Kim , Bit Kim , Dongwook Chung , Jinsung Yoon , Sang-Ki Ko

In-game win probability models, which provide a sports team's likelihood of winning at each point in a game based on historical observations, are becoming increasingly popular. In baseball, basketball and American football, they have become…

Machine Learning · Computer Science 2021-08-16 Pieter Robberechts , Jan Van Haaren , Jesse Davis

The non-scientific event of a soccer match is analysed on a strictly scientific level. The analysis is based on the recently introduced concept of a team fitness (Eur. Phys. J. B 67, 445, 2009) and requires the use of finite-size scaling. A…

Data Analysis, Statistics and Probability · Physics 2010-03-03 Andreas Heuer , Christian Mueller , Oliver Rubner

In this note we introduce a hierarchy of phase spaces for static friction, which give a graphical way to systematically quantify the directional dependence in static friction via subregions of the phase spaces. We experimentally plot these…

Soft Condensed Matter · Physics 2017-09-13 Shankar Ghosh , A. P. Merin , Nitin Nitsure

Ultimate is a sport in which teams of seven players compete for points by passing a disc into the end zone. A distinctive aspect of Ultimate is that the player holding the disc is unable to move, underscoring the significance of creating…

Computer Vision and Pattern Recognition · Computer Science 2024-09-24 Shunsuke Iwashita , Atom Scott , Rikuhei Umemoto , Ning Ding , Keisuke Fujii

Traditional approaches to measuring visual exploratory behavior in soccer rely on counting visual exploratory actions (VEAs) based on rapid head movements exceeding 125{\deg}/s, but this method suffer from player position bias (i.e., a…

Machine Learning · Computer Science 2026-02-24 Joris Bekkers

Experiments on the motion of a particle on an inclined rough plane have yielded some surprising results. For example, it was found that the frictional force acting on the ball is viscous, {\it i.e.} proportional to the velocity rather than…

Condensed Matter · Physics 2009-10-28 G. G. Batrouni , S. Dippel , L. Samson

Motion prediction in soccer involves capturing complex dynamics from player and ball interactions. We present FootBots, an encoder-decoder transformer-based architecture addressing motion prediction and conditioned motion prediction through…

Computer Vision and Pattern Recognition · Computer Science 2024-07-01 Guillem Capellera , Luis Ferraz , Antonio Rubio , Antonio Agudo , Francesc Moreno-Noguer

Change of direction is a key element of player movement in American football, yet there remains a lack of objective approaches for in-game performance evaluation of this athletic trait. Using tracking data, we propose a Bayesian…

Applications · Statistics 2025-07-09 Quang Nguyen , Ronald Yurko

When immersed into a fluid of active Brownian particles, passive bodies might start to undergo linear or angular directed motion depending on their shape. Here we exploit the divergence theorem to relate the forces responsible for this…

Soft Condensed Matter · Physics 2021-04-14 Thomas Speck , Ashreya Jayaram

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…

Artificial Intelligence · Computer Science 2025-05-23 Rikuhei Umemoto , Keisuke Fujii

In this article, we study the dynamics of marking in football matches. To do this, we surveyed and analyzed a database containing the trajectories of players from both teams on the field of play during three professional games. We describe…

Data Analysis, Statistics and Probability · Physics 2022-11-09 A. Chacoma , M. N. Kuperman , O. V. Billoni

We present a novel approach for studying the global dynamics of a vibro-impact pair, that is, a ball moving in a harmonically forced capsule. Motivated by a specific context of vibro-impact energy harvesting, we develop the method with…

Dynamical Systems · Mathematics 2024-12-06 Lanjing Bao , Rachel Kuske , Daniil Yurchenko , Igor Belykh

Focusing on motion of two interacting players in football games, two velocity vectors for the pair of one player and the nearest opponent player exhibit strong alignment. Especially, we find that there exists a characteristic interpersonal…

Physics and Society · Physics 2018-02-20 Takuma Narizuka , Yoshihiro Yamazaki

Vortices play an unique role in heat and momentum transports in astro- and geo-physics, and it is also the origin of the Earth's dynamo. A question existing for a long time is whether the movement of vortices can be predicted or understood…