Context-size / cache-efficiency is not a first-class metric

[willwashburn]

Problem

Burn has no metric for how much context is being paid for per unit of output. The number that actually defined a recent spend incident — a 382:1 context-to-output token ratio — isn't surfaced anywhere in summary, hotspots, or findings. Nothing would have flagged that session as anomalous on cache/context-efficiency grounds even though it was the clearest signal available.

Evidence (2026-07-30 fleet spend forensics)

• The incident session's defining characteristic was a 382:1 ratio of context tokens read to output tokens produced — i.e. enormous prompt re-processing for very little generated output.
• Existing findings/hotspots rank by dollar cost (see Pricing table missing current-generation models — unpriced turns bury real hotspots #503) or raw token totals, neither of which isolates this shape of waste. A session can be cheap in absolute tokens and still be pathologically inefficient in context-to-output ratio, or vice versa.

Proposal

1. Add context-tokens-per-output-token as a headline/summary metric, computed per turn and rolled up per session.
2. Surface a per-session context-size distribution (e.g. p50/p95/max of context tokens per inference) so outlier sessions are visible without hand-computing the ratio.
3. Consider a findings rule that flags sessions above a configurable context:output ratio threshold, independent of dollar cost.