How Much Uncorrected Refractive Error Can Ready-Made Spectacles Actually Fix? A Coverage Bound as a Function of Astigmatism and Anisometropia

Ready-made spherical spectacles are distributed at scale wherever custom refraction is scarce, but they carry no cylinder correction, use one equal power for both eyes, and come in coarse steps over a limited range. In a stated population of 182,445 modelled adults whose visual impairment is solely refractive and fully correctable, generated from parametric distributions fitted to published refraction-survey summaries (Holden et al. 2016; Hashemi et al. 2018; Vitale et al. 2008), ready-made spectacles in 0.50 D steps over -6.00 D to +4.00 D bring the better eye to 6/12 or better for 95.2% under optimistic best matching, against 100% for full custom correction, but only 59.8% when both eyes must reach 6/12 with the same equal power. Step size is nearly irrelevant (0.25 D steps: 95.4% better-eye, 62.3% both-eyes); uncorrected cylinder fails the 6/12 target above 1.61 D, coverage is 0.0% when the least astigmatic eye carries 2.00 D or more of cylinder, and both-eyes coverage is 0.17% at 1.50-2.00 D of anisometropia and 0.0% above it. A minimum stock of three powers (+1.50, -1.50, -3.50 D) covers 77.1% on the better-eye criterion. Of those left behind, 79.2% have 1.50 D or more of cylinder in the better eye and high myopes (-6.00 D or less) are covered at only 60.0%. SIMULATED, NOT MEASURED: all numbers are reproducible from the deposited compute.py.