Three weapons, three regimes of order: per-touch skill transmission and the structural predictability of fencing tournaments

Abstract Background Competitive sport sits between skill and chance, and where a discipline falls depends both on the rules that decide a single contest and on the structure that turns many contests into a ranking. Olympic fencing lets us separate the two: three weapons (épée, foil, sabre) run under one tournament format but score touches differently, so weapon varies the rules of play while competition design stays fixed. Methods We assembled 158,652 pool bouts across 474 FIE Junior World Cup competitions (2015–2026) and measured predictability through three lenses: the rate of intransitive (cyclic) triads within pools; a custom race-to-five per-touch likelihood, fitted by maximum likelihood and as a Bayesian hierarchical model; and a tournament-level concordance built on an artifact-free earned-tier outcome, with the pool-fitted per-touch slope carried into the elimination tableau as a structural out-of-sample test. Results Disorder ranked the weapons épée > sabre > foil (14.5%, 12.4%, and 10.3% cyclic triads, respectively); per-touch skill transmission ran the reverse (marginal slope épée 0.48, sabre 0.80, foil 0.83), with weapon-specific between-tournament heterogeneity largest in foil. Earned-tier concordance (foil 0.684, sabre 0.650, épée 0.638) fell well below artifact-inflated raw-rank values (0.81–0.85). Conclusions We expose and correct a tie-break artifact that inflates conventional fencing predictability and show that the épée prediction gap reflects where the independent-touch reference stops rather than a weapon-specific mechanism: the same departure appears in the priority weapons, where simultaneous touches cannot occur.