Braking and Defender Interchangeability in Three-Duty Futsal Cover Arrival Time, Body Allocation and Simultaneous Clearance

Abstract

To determine when four defenders can maintain pressure, interception and goal-side cover after one defender becomes unavailable. A theoretical calculation on a 40-by-20-m court combines rest-to-rest translation, heading adjustment and continuous-time separation checks. Defenders accelerate at 3.00 m s⁻², brake at 4.00 m s⁻² and occupy three 0.20-m-radius duty regions by 1.80 s. Hall’s matching condition identifies the number of complete defender losses compatible with cover. Two starting arrangements each generate six capability links and four complete assignments. Concentrated overlap requires defenders A and B for pressure and interception; distributed overlap permits cover after any single loss. The minimum neighbourhood surpluses are consequently zero and one. Minimum centre separations are 0.572659 and 0.662607 m against a 0.50-m requirement. Under independent defender availability of q = 0.80, complete-cover probabilities are 0.61440 and 0.81920. Central actions become eligible at 1.655625 s. At a 1.80-s deadline, their braking requirement is 2.807631 m s⁻². A ±0.05-s timing interval leaves the distributed arrangement’s surplus between −1 and 1 at 1.70 s, but fixes it at 1 at 1.80 s. Defender interchangeability depends on the distinct bodies available to each group of simultaneous duties. An additional capability increases loss tolerance only when it adds a body to every duty group attaining the minimum surplus. The numerical values follow from the stated movement assumptions; they are not measurements of athletes.