Frontier large language models (LLMs) deliver the strongest response quality but carry per-token prices often more than an order of magnitude above those of smaller, task-adequate models. Smart model routing addresses this mismatch by assigning each query to the cheapest model expected to answer it adequately, rather than sending every request to the most capable, most expensive endpoint. This paper develops a formal cost-quality optimization framework for routing -- including a derived optimal threshold-policy structure, a calibration-versus-discrimination distinction, a cascade breakeven condition, and a sensitivity analysis over price ratio and traffic skew -- situates that framework against the principal routing architectures and the signals used to estimate query difficulty, and works through a numerical example showing how a calibrated router can reduce blended inference cost by roughly an order of magnitude relative to an always-frontier deployment under specific, stated pricing and traffic assumptions, reporting both the gross reduction from routing policy alone and the net figure with the router's own overhead priced in. We situate this figure against the range reported by published routing systems (roughly 2x to frontier-level accuracy at one-fifth the cost), and close with the practical risks -- under- and over-routing, aggregate quality constraints masking segment-level harm, calibration without discrimination, calibration drift, prompt injection into routing signals, and operational failures such as tier outages and multi-provider price variation -- that determine whether the savings materialize in production. The analysis is primarily analytical, complemented by a GSM8K evaluation of the cascade framework (Section 5), validated (Section 5.2); extending the evaluation across tasks and model families is future work.

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