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

Abstract

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.

Spatio-Temporal Analysis of Team Sports

“…When designing a spatial discretization, the number and shape of the induced regions can vary. A common approach is to subdivide the playing area into rectangles of equal size [5,9,17,31,52,60,74], for example see Fig. 4c.…”

“…For example, many papers counted shots made in each region of a subdivision of a basketball court [31,38,56,71,74]. Similarly, Borrie et al [9], Camerino et al [15], Narizuka et al [60], and Cervone et al [17] counted the number of passes made in each region of a subdivision of the playing area.…”

Degree Distribution of Position-Dependent Ball-Passing Networks in Football Games

“…In Fig. 5, we compare the two functions (13) and (14). It is found that the two functions take almost the same values except a high-degree part.…”

“…The solid curves in each panel are the cumulative distribution F (k) of Eq. (13). The values of µ and m for fittings are summarised in Table 3.…”

“…Each node is given the serial numbers, such as "159", "106", and "131", which are determined from the area and player numbers. Further information about the creation of the network is summarised in our previous paper [13].…”