Monte Carlo simulations of the failure of unidirectional fiber composites in a plane transverse to the fiber direction are performed on much larger patches than in previous works, assuming a realistic load redistribution scheme from broken to intact fibers. Computational effort involved in these simulations is substantially reduced using an algorithm based on the quadtree data structure. The empirical strength distribution obtained from the simulations has a weak-link character, regardless of the variability in fiber strengths. The empirical strength distribution is well captured by a probabilistic model based on the growth of a tight cluster of fiber breaks. It is also well captured by regarding composite patch failure as the failure of the weakest equal load-sharing bundle of a certain size, following Curtin [Phys. Rev. Lett. 80, 1445 (1998)PRLTAO0031-900710.1103/PhysRevLett.80.1445]. The approximate coincidence of these two predictions identifies the dominant failure mechanism underlying Curtin's empirical scaling relationship. © 2017 American Physical Society.