The Successive Controlled Collapse of Strategic Attractors: A Non-Invasive Population Profiling of Skill-Luck Dynamics in High-Variance Systems

This research proposes a non-linear dynamical framework to enhance the predictive accuracy of Michael Mauboussin’s Success Equation (2012) in high-stakes competitive environments, specifically professional sports. By integrating the Successive Controlled Collapse (SCC) protocol with the Shopping Mall Dilemma (Hala, 2026), we shift from static "IndividualProfiling" (season-long track records) to "Blind State-Space Profiling." We hypothesize that in systems where skill levels are nearly identical, the outcome is governed by Exponential Forgetting of initial conditions. Through computational simulations, we demonstrate that as a game progresses, the identities of Team A (Skill) and Team B (Luck) are erased, converging toward an invariant measure within symbolic basins of attraction. Our results indicate that predicting the "Successive Collapse" of a system’s internal coupling provides a superior utility for forecasting extreme outcomes than traditional linear metrics.