Error Budgets For and Against the Shadow: Which Input Buys the Next Factor of Two

Every shadow comparison is a sum of variances, and the terms differ so much between the two sources that a single strategy for improving 'the shadow test' cannot serve both. For M87* the total budget is 13.8 per cent, with the mass term contributing 61 per cent of the variance; halving the mass error brings the total to 10.1 per cent, while halving the diameter error brings it only to 12.3. For Sagittarius A* the total is 14.5 per cent and the ring-to-shadow conversion contributes 99 per cent of the variance; halving the conversion error yields 7.3 per cent, while halving the already small mass and distance terms yields nothing measurable. The next factor of two for each source is therefore bought in a different shop: a dynamical mass campaign for M87*, and a simulation-calibration campaign for Sagittarius A*. Funding or telescope time allocated the other way round is, on these numbers, spent on terms that do not move the total. Computed from published uncertainties; simulated, not measured.