Non-transitive patterns in long-term football rivalries

The phenomenon of non-transitivity in outcomes, typically observed in non-effort games with predetermined probabilities and immediate clarity, extends to teambased, time-consuming games requiring effort that unfold over a long period of time. This study explores this aspect through an empirical analysis of professional football matches in the Netherlands involving three prominent teams: Feyenoord, Ajax, and PSV. Contrary to conventional expectations, the results reveal a nontransitive pattern over more than three decades, indicating that Feyenoord is more likely to triumph over PSV, PSV over Ajax, and Ajax over Feyenoord than the reverse scenarios.