The set system in archery: the mathematics of who wins

These pages measure a competition rule instead of judging it. The question is not whether the set system is fair, but how often, looking at a handful of arrows, it can tell which of two archers is shooting better, and how much that ability changes compared with the old cumulative score. The model is deliberately spare: an archer is the width of their group, and nothing else. No real archer's score enters the work. The calculation is exact, not simulation-based. When the two aggregation methods are compared at the same number of arrows, cumulative scoring identifies the more precise archer slightly more often than the set system. The maximum gap is 2.32 percentage points: for the worst-case pair, cumulative scoring selects the correct winner 87 times out of 100, compared with 85 for the set system. The loss comes from the rule, not from the match being shorter. Qualification noise is larger than the effect being studied.