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

Takuma Narizuka, Yoshihiro Yamazaki

    Research output: Contribution to journalArticle

    1 Citation (Scopus)

    Abstract

    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 ≃ 500 cm below which the circular variance for their alignment decreases rapidly. By introducing the order parameter φ(t) in order to measure the degree of alignment of the players velocity vectors, we also find that the angle distribution between the nearest players velocity vectors becomes of wrapped Cauchy type (φ ≳ 0.7) and the mixture of von Mises and wrapped Cauchy distributions (φ ≳ 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 reproduces the results obtained from the actual data. Moreover, from the numerical study, we find that there is another characteristic distance r ≃ 1000 cm below which players chasing starts.

    Original languageEnglish
    Article number68001
    JournalEPL
    Volume116
    Issue number6
    DOIs
    Publication statusPublished - 2016 Dec 1

    Fingerprint

    games
    alignment

    ASJC Scopus subject areas

    • Physics and Astronomy(all)

    Cite this

    Statistical properties for directional alignment and chasing of players in football games. / Narizuka, Takuma; Yamazaki, Yoshihiro.

    In: EPL, Vol. 116, No. 6, 68001, 01.12.2016.

    Research output: Contribution to journalArticle

    @article{921e7dec984b4a4b857a9ae3801094ce,
    title = "Statistical properties for directional alignment and chasing of players in football games",
    abstract = "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 ≃ 500 cm below which the circular variance for their alignment decreases rapidly. By introducing the order parameter φ(t) in order to measure the degree of alignment of the players velocity vectors, we also find that the angle distribution between the nearest players velocity vectors becomes of wrapped Cauchy type (φ ≳ 0.7) and the mixture of von Mises and wrapped Cauchy distributions (φ ≳ 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 reproduces the results obtained from the actual data. Moreover, from the numerical study, we find that there is another characteristic distance r ≃ 1000 cm below which players chasing starts.",
    author = "Takuma Narizuka and Yoshihiro Yamazaki",
    year = "2016",
    month = "12",
    day = "1",
    doi = "10.1209/0295-5075/116/68001",
    language = "English",
    volume = "116",
    journal = "EPL",
    issn = "0295-5075",
    publisher = "IOP Publishing Ltd.",
    number = "6",

    }

    TY - JOUR

    T1 - Statistical properties for directional alignment and chasing of players in football games

    AU - Narizuka, Takuma

    AU - Yamazaki, Yoshihiro

    PY - 2016/12/1

    Y1 - 2016/12/1

    N2 - 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 ≃ 500 cm below which the circular variance for their alignment decreases rapidly. By introducing the order parameter φ(t) in order to measure the degree of alignment of the players velocity vectors, we also find that the angle distribution between the nearest players velocity vectors becomes of wrapped Cauchy type (φ ≳ 0.7) and the mixture of von Mises and wrapped Cauchy distributions (φ ≳ 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 reproduces the results obtained from the actual data. Moreover, from the numerical study, we find that there is another characteristic distance r ≃ 1000 cm below which players chasing starts.

    AB - 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 ≃ 500 cm below which the circular variance for their alignment decreases rapidly. By introducing the order parameter φ(t) in order to measure the degree of alignment of the players velocity vectors, we also find that the angle distribution between the nearest players velocity vectors becomes of wrapped Cauchy type (φ ≳ 0.7) and the mixture of von Mises and wrapped Cauchy distributions (φ ≳ 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 reproduces the results obtained from the actual data. Moreover, from the numerical study, we find that there is another characteristic distance r ≃ 1000 cm below which players chasing starts.

    UR - http://www.scopus.com/inward/record.url?scp=85014028769&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=85014028769&partnerID=8YFLogxK

    U2 - 10.1209/0295-5075/116/68001

    DO - 10.1209/0295-5075/116/68001

    M3 - Article

    AN - SCOPUS:85014028769

    VL - 116

    JO - EPL

    JF - EPL

    SN - 0295-5075

    IS - 6

    M1 - 68001

    ER -