Scorecard-Driven Dynamic Model Routing in Multi-Agent Pipelines: A Bayesian Risk Analytics Framework for Cost-Aware LLM Orchestration

Abstract The deployment of Large Language Models (LLMs) across multi-agent pipelines introduces an acute multi-objective resource allocation problem under operational, financial, and safety uncertainties. While commercial and open-source gateways predominantly rely on static list pricing ($/1M$/1M tokens) and black-box neural classification heuristics, empirical evidence demonstrates that real-world completion cost diverges from nominal list prices by over 25×25× due to token-burn variance across reasoning models. Drawing upon two decades of banking credit-risk modeling, we propose the Scorecard Router: an interpretable, auditable, and mathematically grounded framework that transposes Internal Ratings-Based (IRB) and Low Default Portfolio (LDP) methodologies into dynamic LLM orchestration. We establish two operational regimes: (1) an Empirical Scorecard Framework (ESF) applying Multi-Criteria Decision Making (AHP/SAW) for data-rich production tasks, and (2) an LDP-Based Bayesian Framework (LDP-BF) utilizing Beta-Binomial conjugacy, Pluto--Tasche conservative upper-bound failure estimators, and vertical data-borrowing when execution history is sparse (N<30N<30). Crucially, the architecture categorizes multi-agent workloads into three distinct operational governance domains: (i) Productivity Use Cases (low risk, light governance, maximizing cost-efficiency and throughput), (ii) Decision Support Use Cases (medium risk, mandatory Human-in-the-Loop validation, optimizing factual consistency), and (iii) Agentic Decision-Making Use Cases (high financial/legal risk, strict deterministic safety guardrails, immutable audit trails, prioritizing safety over cost/latency). We formulate pipeline routing as a repeated game optimizing the Cost Per Successful Run (CPSR=E[Cost]/P(Success)) while providing both rigorous mathematical proofs and intuitive conceptual explanations accessible to enterprise practitioners. Evaluated across 10,000 multi-agent benchmark iterations, the Scorecard Router achieves a 64–78%64–78% reduction in aggregate token expenditures while guaranteeing 100%100% compliance with deterministic safety and latency SLAs.