arXiv subjects

Takuma Narizuka

Publications and source records attributed to Takuma Narizuka.

12 recordsLinked to original sources

arXiv2026

Evaluating Soccer Player Movements Using the Attacker-Defender Model

The present study investigates the attacker-defender (AD) model proposed by Brink et al. (2023), a motion model that describes the interactions between a ball carrier (attacker) and the nearest defender during ball possession. The model is based on the equations of motion for both players, incorporating resistance, goal-oriented force, and opponent-oriented force. It generates trajectories based on physically interpretable parameters. Although the AD model reproduces real dribbling trajectories well, previous studies have explored only a limited range of parameter values and relied on relatively small datasets. This study aims to (1) enhance parameter optimization by solving the AD model for one player with the opponent's actual trajectory fixed, (2) validate the model's applicability to a large dataset from 306 J1 League matches, and (3) demonstrate distinct playing styles of attackers and defenders based on the full range of optimized parameters.

physics.soc-ph↗

arXiv2026

Quantifying defensive pressure on the ball carrier in soccer based on minimum arrival time

Defensive pressure on the ball carrier is a fundamental component of soccer tactics. Existing pressure measures often involve additional modeling assumptions, which may reduce interpretability. In this study, we quantify defensive pressure as the opponent minimum arrival time to the ball-carrier location, computed from a physics-based motion model. Using synchronized event and tracking data from all 306 matches in the top division of the Japan Professional Football League during the 2023 season, we analyze the statistical characteristics and temporal evolution of this quantity during ball-possession intervals. The results show that the opponent minimum arrival time tends to decrease during possession and to increase again at the start of the next possession after ball release. We also find that possessions starting under stronger defensive pressure tend to yield smaller ball progression, and that, for intentional open-play passes, possessions ending under stronger pressure are more likely to be lost. These findings indicate that minimum arrival time provides an interpretable and physically grounded measure of immediate defensive pressure on the ball carrier. The proposed framework provides a simple and interpretable baseline for quantifying pressing dynamics from tracking data.

physics.soc-ph↗

arXiv2026

A behavioral principle underlying attacker-defender interactions in soccer

Soccer is widely popular for its simple rules and complex yet coordinated play that unfolds on the pitch. Nevertheless, the fundamental mechanisms governing such play are not well understood: what shapes player interactions on the pitch? What short-term goals guide players' decisions about their movements over the next few seconds? We address these questions by focusing on one-on-one settings in open play, in which the attacker, in possession of the ball and typically dribbling, faces a defender aiming to stop or delay the attacker's actions over a short period. Here we develop a mathematical model of attacker-defender interactions and analyze 306 professional soccer games. Synthesizing the large-scale dataset with an analysis of the model reveals a simple behavioral principle that may underlie these interactions: the defender seeks to minimize their future relative speed to the attacker, whereas the attacker initiates their movements to preempt the defender's objective. This principle, relative-speed minimization, provides a consistent and unified account of the empirical data. Since our framework depends little on soccer-specific details, this principle may govern diverse pursuit-evasion scenarios as well as other invasion team sports.

physics.soc-ph↗

arXiv2023

Theory and data analysis of player and team ball possession time in football

In this study, the stochastic properties of player and team ball possession times in professional football matches are examined. Data analysis shows that player possession time follows a gamma distribution and the player count of a team possession event follows a mixture of two geometric distributions. We propose a formula for expressing team possession time in terms of player possession time and player count in a team's possession, verifying its validity through data analysis. Furthermore, we calculate an approximate form of the distribution of team possession time, and study its asymptotic property.

physics.soc-ph↗

arXiv2023

Validation of a motion model for soccer players' sprint by means of tracking data

In soccer game analysis, the widespread availability of play-by-play and tracking data has made it possible to test mathematical models that have been discussed mainly theoretically. One of the essential models in soccer game analysis is a motion model that predicts the arrival point of a player in $ t $ s. Although many space evaluation and pass prediction methods rely on motion models, the validity of each has not been fully clarified. This study focuses on the motion model proposed by Fujimura and Sugihara (Fujimura-Sugihara model) under sprint conditions based on the equation of motion. A previous study indicated that the Fujimura-Sugihara model is ineffective for soccer games because it generates a circular arrival region. This study aims to examine the validity of the Fujimura-Sugihara model using soccer tracking data. Specifically, we quantitatively compare the arrival regions of players between the model and real data. We show that the boundary of the player's arrival region is circular rather than elliptical, which is consistent with the model. We also show that the initial speed dependence of the arrival region satisfies the solution of the model. Furthermore, we propose a method for estimating valid kinetic parameters in the model directly from tracking data and discuss the limitations of the model for soccer games based on the estimated parameters.

physics.soc-ph↗

arXiv2020

Space evaluation in football games via field weighting based on tracking data

In football game analysis, space evaluation is an important issue because it is directly related to the quality of ball passing or player formations. Previous studies have primarily focused on a field division approach wherein a field is divided into dominant regions in which a certain player can arrive prior to any other players. However, the field division approach is oversimplified because all locations within a region are regarded as uniform herein. The objective of the current study is to propose a fundamental framework for space evaluation based on field weighting. In particular, we employed the motion model and calculated a minimum arrival time $ τ$ for each player to all locations on the football field. Our main contribution is that two variables $ τ_{\textrm{of}} $ and $ τ_{\textrm{df}} $ corresponding to the minimum arrival time for offense and defense teams are considered; using $ τ_{\textrm{of}} $ and $ τ_{\textrm{df}} $, new orthogonal variables $ z_{1} $ and $ z_{2} $ are defined. In particular, based on real datasets comprising of data from 45 football games of the J1 League in 2018, we provide a detailed characterization of $ z_{1} $ and $ z_{2} $ in terms of ball passing. By using our method, we found that $ z_{1}(\vec{x}, t) $ and $ z_{2}(\vec{x}, t) $ represent the degree of safety for a pass made to $ \vec{x} $ at $ t $ and degree of sparsity of $ \vec{x} $ at $ t $, respectively; the success probability of passes could be well-fitted using a sigmoid function. Moreover, a new type of field division approach and evaluation of ball passing just before shoots using real game data are discussed.

physics.soc-ph↗

arXiv2019

Lifetime distributions for adjacency relationships in a Vicsek model

We investigate the statistical properties of adjacency relationships in a two-dimensional Vicsek model. We define adjacent edges for all particles at every time step by (a) Delaunay triangulation and (b) Euclidean distance, and obtain cumulative distributions $ P(τ) $ of lifetime $ τ$ of the edges. We find that the shape of $ P(τ) $ changes from an exponential to a power law depending on the interaction radius, which is a parameter of the Vicsek model. We discuss the emergence of the power-law distribution from the viewpoint of first passage time problem for a fractional Brownian motion.

physics.soc-ph↗

arXiv2019

Clustering algorithm for formations in football games

This paper develops a clustering algorithm for formations in team sports, with a focus on football games. Our method first clusters formations into several average formations: `442,' `4141,' `433,' `541,' and `343.' Then, each average formation is further divided into more specific patterns in which the configurations of players are slightly different. The latter step is based on hierarchical clustering and the Delaunay method, which defines the formation of a team as an adjacency matrix of Delaunay triangulation. A formation clustered using our method is expressed in a form such as `442-C1'.

physics.soc-ph↗

arXiv2018

Characterization of the formation structure in team sports

We propose a method to identify the formation structure in team sports based on Delaunay triangulation. The adjacency matrix obtained from the Delaunay triangulation for each player is regarded as the formation pattern. Our method allows time-series analysis and a quantitative comparison of formations. A classification algorithm of formations is also proposed by combining our method with hierarchical clustering.

physics.soc-ph↗

arXiv2018

Statistical properties for directional alignment and chasing of players in football games

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 distance $ r\simeq 500 $ cm below which the circular variance for their alignment decreases rapidly. By introducing the order parameter $ ϕ(t) $ in order to measure degree of alignment of players' velocity vectors, we also find that the angle distribution between the nearest players' velocity vectors becomes wrapped Cauchy ($ ϕ\lesssim 0.7 $) and the mixture of von Mises and wrapped Cauchy distributions ($ ϕ\gtrsim 0.7 $), respectively. To understand these findings, we construct a simple model for the motion of the two interacting players with the following rules: chasing between the players and the reset of the chasing. We numerically show that our model successfully reproduce the results obtained from the actual data. Moreover, from the numerical study, we find that there is another characteristic distance $ r\simeq 1000 $ cm below which player's chasing starts.

physics.soc-ph↗

arXiv2015

Degree distribution of position-dependent ball-passing networks in football games

We propose a simple stochastic model describing the position-dependent ball-passing network in football games. In this network, a player on a certain area in the divided fields is a node, and a pass between two nodes corresponds to an edge. Our model is characterized by the consecutive choice of a node dependent on its intrinsic fitness. We derive the explicit expression of the degree distribution, and find that the derived distribution reproduces the real data quit well.

physics.soc-ph↗

arXiv2014

Statistical properties of position-dependent ball-passing networks in football games

Statistical properties of position-dependent ball-passing networks in real football games are examined. We find that the networks have the small-world property, and their degree distributions are fitted well by a truncated gamma distribution function. In order to reproduce these properties of networks, a model based on a Markov chain is proposed.

physics.data-an↗