For agent loops and tool calling, the frontier model is not automatically the right call: if a challenger sits ~3% below on benchmarks at ~5× cheaper input, high-volume pipelines usually take the deal — until multi-step error compounding says otherwise. All models below are hypothetical and every number is illustrative, plotted as benchmark score × input price (log) × latency. Drag to orbit, hover a point to inspect.
An agent that succeeds on each step with probability p finishes an n-step chain with probability:
Small per-step gaps explode over long chains: 0.9930 ≈ 74%, but 0.9630 ≈ 29%. So the cheap model wins when chains are short, verifiable, or retryable — and loses when a single silent failure poisons a 40-step run. (Per-step p here is an illustrative mapping from benchmark score, not a measured value.)
Volume amplifies price. At 1B input tokens/month, the gap between $3.0/M and $0.6/M is $2.4M vs $0.6M-scale spend per year — a 3-point benchmark delta rarely justifies that unless it changes task success materially.
Retries change the math. If failures are detectable (tests, schemas, tool errors), a cheap model with one retry often beats an expensive one-shot: effective success 1−(1−p)² at ~2× the cheap price is still far below premium price.
Route, don't choose. Mature stacks send routine steps to the cheap model and escalate hard or high-stakes steps — the frontier point on this chart becomes a router policy, not a single pick.