Multi-agent systems (MAS) tackle complex tasks by distributing expertise, though this often comes at the cost of heavy coordination overhead, context fragmentation, and brittle phase ordering. Distilling a MAS into a single-agent skill can bypass these costs, but this conversion lacks a principled answer for when and what to distill. Instead, the empirical outcome is surprisingly inconsistent: skill lift ranges from a 28% improvement to a 2% degradation across metrics of the exact same task. In this work, we reveal that skill utility is governed not by the task, but by the evaluation metric. We introduce Metric Freedom (F), the first a priori predictor of skill utility. F measures the topological rigidity of a metric's scoring landscape by quantifying how output diversity couples with score variance via a Mantel test. Guided by F, we propose AdaSkill, a two-stage adaptive distillation framework. Stage 1 acts as a selective extraction mechanism, extracting tools and knowledge while discarding restrictive structures on "free" metrics to preserve exploration. Stage 2 applies iterative refinement selectively on free metrics, exploiting their forgiving scoring landscape to safely maximize remaining headroom. Evaluating across 4 tasks, 11 datasets, and 6 metrics, F strongly predicts skill utility (r=-0.85, p<0.0001). Strikingly, identical agent trajectories yield diametrically opposite skill lifts under rigid versus free metrics, demonstrating that skill utility is fundamentally a metric-level property. Driven by this signal, AdaSkill matches or exceeds the original MAS while reducing cost up to 8x and latency by up to 15x.