Background
The concept of Emergence—the phenomena where novel effects, absent in the governing equations, arise from the collective interaction amongst many particles—is a crucial principle in Condensed Matter Physics. Beyond its documentation in this field, Emergence transcends physics and manifests in diverse scenarios like the forming of cells or society. Hence, I posit that Emergence occurs whenever many agents/objects interact under predefined rules and, therefore, identifying quantitative measures for systems with numerous particles exhibiting Emergence using physics tools seems plausible. Soccer, with its simple rules and expansive nature, becomes a suitable subject of study. Drawing inspiration from total football and positional play, I propose that phase transitions, akin to those in matter, also occur in soccer. My project aims to explore soccer's emergent properties by devising quantities reflecting the game's state based on collective player motions. I propose to numerically analyze positional data from professional teams in order to develop a mathematical framework to comprehend transitions in play.