Three Weapons, Three Regimes of Order: Per-Touch Skill Transmission and the Structural Predictability of Fencing Tournaments

In the world of competitive sport, there is a constant tension between two forces: the skill of the athlete and the luck of the draw. A tournament is not just a collection of matches; it is a machine designed to turn individual contests into a final ranking. The rules of a single match decide who wins that moment, but the structure of the tournament decides how that moment counts toward the final standing. If the rules are too chaotic, the better player might lose simply because of a fluke. If the structure is too rigid, it might hide the true talent of an underdog. Scientists who study performance want to know exactly where a sport falls on this spectrum. They ask: how often does the better competitor actually win? And does the answer change depending on the specific rules of the game?

Fencing offers a unique laboratory to answer these questions. It is a sport where three different weapons—épée, foil, and sabre—compete under the exact same tournament format. The athletes move through the same pool of preliminary matches and the same knockout bracket. The only thing that changes is how a point is scored. In one weapon, a fencer can score even if they are hit at the same time as their opponent. In the others, a referee must decide who had the right to attack first, awarding the point to only one person. Because the tournament structure stays fixed while the scoring rules shift, researchers can isolate exactly how those rules change the balance between skill and chance. This is not just about fencing; it is about understanding how the design of a competition shapes the story of who is truly the best.

A team of researchers set out to measure this balance using a massive amount of data. They gathered the results of over 158,000 preliminary matches from nearly 500 international junior tournaments held between 2015 and 2026. This collection included every match from the three weapons, allowing them to compare the weapons directly. Their goal was to see which weapon produced the most predictable results and which was the most chaotic. To do this, they looked at the matches in three different ways. First, they checked for "rock-paper-scissors" loops, where fencer A beats fencer B, fencer B beats fencer C, but fencer C beats fencer A. These loops are a sign of disorder; in a perfectly skill-based system, the strongest fencer should always rise to the top without such contradictions. Second, they analyzed how much a single point in a match told them about the fencers' relative skill. Finally, they looked at the final tournament rankings to see if the best seeds actually won, but they had to be careful about how they measured "winning."

The researchers discovered a hidden flaw in how fencing tournaments are usually judged. In the final rankings, if two fencers lose in the same round, the system breaks the tie by looking at their starting seed. This means the final list is partly a reflection of the starting list, not just what happened on the strip. When the researchers corrected for this, the apparent predictability of the sport dropped significantly. The raw numbers had made the tournaments look more orderly than they really were. Once this artificial boost was removed, a clear pattern emerged. The foil weapon was the most orderly, followed by sabre, with épée being the most chaotic. In the foil matches, the better-seeded fencer won more often, and there were fewer confusing loops where the results contradicted each other. In épée, the results were much more random, with the best seeds winning less frequently and more cycles of upsets occurring.

To understand why this happened, the team looked at the mechanics of the scoring itself. They treated every match as a race to five points and calculated how much a fencer's starting advantage translated into a higher chance of scoring the next point. They found that in foil, a small advantage in skill or seeding translated very strongly into a higher chance of scoring a point. In épée, that same advantage translated much more weakly. This explains the chaos: in épée, the rules allow both fencers to score at the same time if they hit simultaneously. This creates "non-discriminating" moments where the score goes up, but it doesn't clearly show who was better in that exchange. In foil and sabre, the rules force a decision on every point, making each touch a clearer signal of who is superior.

The study also revealed that the chaos in épée is not just about the double-touch rule. The researchers found that even in the other two weapons, where double touches are impossible, the matches were still more predictable than a simple model of independent points would suggest. This means that fencers are not just firing off random shots; they are reacting to the flow of the match, building momentum, and adjusting their tactics. The model they used assumed every point was independent, like flipping a coin, but real fencing is a chain of connected events. The fact that épée was even more chaotic than the others suggests that the double-touch rule adds a layer of randomness on top of this natural flow, but it is not the only source of the disorder.

One of the most significant findings was about how much the results varied from one tournament to the next. The researchers found that the predictability of foil matches changed the most depending on which tournament was being held. This suggests that the human element of refereeing plays a huge role. In foil and sabre, a referee must decide who had the right of way, a judgment call that can vary from one official to another. In épée, an electronic machine decides if a touch landed, removing the human element. The data showed that the weapon relying on human judgment had the most variation in how skill translated to results, while the weapon relying on the machine was the most consistent, even though it was the most chaotic overall.

The implications of these findings reach beyond the fencing strip. For tournament organizers, the results suggest that using the same format for all three weapons might not be fair. Because épée matches carry less information about who is truly better, a single match is a noisier signal. This means that in épée, the current tournament structure might allow more upsets and less protection for the best seeds than in foil. The researchers propose that if the goal is to ensure the best fencer wins, the format for épée might need to be adjusted, perhaps with larger pools or different seeding rules, to compensate for the extra randomness built into its scoring.

For coaches and selectors, the data offers a new way to evaluate talent. Because a single épée match is less reliable at showing the true skill gap, selection committees should perhaps rely more on a fencer's performance over a whole season rather than a single tournament result. In foil, a single match tells you more about who is better, so it might be a fairer basis for immediate selection. The study also provides a tool for referees. By measuring how much the results vary from one event to another, federations could track whether their referees are making consistent calls, using the data to improve training and certification.

Ultimately, this research shows that the rules of a game do more than just decide who gets a point; they shape the entire story of the competition. The same athletes, competing in the same structure, produce different levels of order and chaos simply because of how a point is awarded. The study corrects a long-standing illusion in how fencing rankings are read, revealing that the apparent order was partly a trick of the scoring system. By peeling back that layer, the researchers showed that while skill always matters, the path from talent to victory is paved by the specific rules of the weapon being used. The most orderly weapon is the one where every point demands a clear winner, and the most chaotic is the one where two fencers can win at the same time.