New model for the decision-making and the game style in football

Abstract

We propose a new mathematical model for the decision-making of players in football (soccer) and the efficiency of the game style. Our approach is based on $4$-networks, which is a mathematical concept that we introduce. The decision of players is expressed by a mathematical function depending on the game style chosen by the coach. Moreover, we measure the efficiency of the game style by a sequence of 4-networks.

Figures (2)

• Figure 1: Example of a situation where two players with different probability of goal-scoring
• Figure 2: A $4$-network of the player $t_8$

Theorems & Definitions (1)

• Definition 3.1