Abstract
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 tau for each player to all locations on the football field. Our main contribution is that two variables tau _{text{of}} and tau _{text{df}} corresponding to the minimum arrival time for offense and defense teams are considered; using tau _{text{of}} and tau _{text{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 shots using real game data are discussed.
Highlights
The field can be calculated based on the equation of motion
Fujimura and Sugihara have investigated the receivable pass variation which quantifies the number of passes a player can r eceive[16] and Ueda et al have examined the relationship between the dominant region and offensive performance of a team[17]
Our space evaluation approach is based on a “minimum arrival time” τ to all locations in the field, which can be calculated based on the physics-based motion model
Summary
The field can be calculated based on the equation of motion. using the equations of motion, the Voronoi regions of players can be suitably modified as per their velocity and acceleration. Fujimura and Sugihara have investigated the receivable pass variation which quantifies the number of passes a player can r eceive[16] and Ueda et al have examined the relationship between the dominant region and offensive performance of a team[17]. Another approach for extension of the definition of a dominant region is a data-driven one wherein individual dominant regions on the field could be estimated using machine learning[18,19]. As applications of our proposed space evaluation method, a new field division approach is discussed and an evaluation of ball passing just before shots for a dataset of football games is presented
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