The fact that several fundamental physical constants — the cosmological constant, the Higgs mass, the strength of the electromagnetic and the strong nuclear couplings, the protonelectron mass ratio, the deuteron binding energy — appear to lie within narrow ranges of parameter space within which complex chemistry and the formation of long-lived stars and galaxies become possible has, since the 1970s, generated one of the most contested explanatory disputes in the foundations of physics. The two principal proposed explanations are causally and epistemically inequivalent. The first is the design hypothesis, on which the values of the constants reflect intentional fine-tuning by some agent. The second is the multiverse-with-anthropicselection hypothesis, on which the constants take varying values across a vast ensemble of physically realised universes, and observers necessarily find themselves in the subset of universes whose parameter values permit observer formation. Between 2016 and 2022, a substantial philosophical literature has clarified the structure of the multiverse-with-anthropic-selection argument, identified several long-standing objections (the inverse gambler's fallacy, the typicality problem, the measure problem, and the problem of specifying an independent probability distribution over the multiverse), and produced a new generation of formal Bayesian and decision-theoretic analyses of the argument. The dialectical situation in mid-2022 was that the multiverse-anthropic explanation is taken seriously by a non-trivial portion of the physics and philosophy of physics communities but is not regarded as decisive, and that a clear metric for the explanatory strength of competing multiverse-anthropic accounts has not been formulated. In this article I propose, as the original contribution, the Anthropic Explanation Strength Index (AESI), a single normalised composite metric — bounded on [0,1] — that integrates five performance dimensions (independent multiverse evidence, probability-measure specificity, inverse-gambler's-fallacy resistance, typicality-prediction generation, and Standard-Model parameter compatibility) and returns a quantitative ranking of competing multiverse-anthropic explanations. Applied to four canonical multiverse frameworks (eternal inflation plus string landscape, Tegmark Level IV mathematical universe, Everettian quantum branching with parameter variation, and bubble-nucleation cosmology), AESI returns values in the 0.30-0.55 range, indicating that none of the canonical frameworks currently meets the threshold of decisive explanatory power and that the anthropic explanation should be regarded as a working hypothesis rather than as a settled solution to the fine-tuning problem.