Evaluating Soccer Player Movements Using the Attacker-Defender Model

Abstract

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.

Figures (3)

• Figure 1: Expected attacker and defender motions based on the signs of (a) $f_{\mathrm{a}}$ and $\beta_{\mathrm{a}}$, and (b) $f_{\mathrm{d}}$ and $\beta_{\mathrm{d}}$.
• Figure 2: Typical attacker trajectories in regions A1--A4. The red circle and the blue square indicate the starting positions of the attacker and defender, respectively. Dashed and solid lines represent the actual and simulated trajectories, respectively. In all cases, the direction of attack is from left to right.
• Figure 3: Typical defender trajectories in regions D1--D4. The red circle and the blue square indicate the starting positions of the attacker and defender, respectively. Dashed and solid lines represent the actual and simulated trajectories, respectively. In all cases, the direction of attack is from left to right.