Classical ranking methods each rely on a single input: Massey uses point differentials, Colley uses win/loss records, and PageRank uses win proportions. None incorporates the full context of a matchup..
Classical ranking methods each rely on a single input: Massey uses point differentials, Colley uses win/loss records, and PageRank uses win proportions. None incorporates the full context of a matchup. This research develops a general-purpose ranking framework built on graph theory and linear algebra. Competitors are modeled as nodes, and each interaction produces a 10-dimensional feature vector that is mapped to an edge weight via a sigmoid function. The resulting linear system 𝑀 𝑥=−1 is solved to produce ratings with provable mathematical guarantees. The framework is validated on UEFA Champions League 2025–26 data and designed to generalize to student evaluation and recommendation systems.
