2604.00601 A Hidden Invariant in International Football: Spectral Gap Stability of the Win–Draw–Loss Markov Chain (1902–2026)
We model sequences of international football match outcomes (win, draw, loss) as a first-order Markov chain and study the evolution of its spectral properties over 120 years of data. Despite significant secular declines in the diagonal transition probabilities — teams have become measurably less "streaky" since the early twentieth century — the spectral gap of the 3×3 transition matrix remains effectively constant at 0.