Tokenometrica: Trace-Grounded Accounting and Scaling Laws for Agentic Token Demand

LLM agents are metered and billed in tokens, yet a token total says neither where the tokens went nor how they will grow as tasks get longer. We introduce Tokenometrica, a framework that treats every agent run as an observable metered trace and partitions each model call, through an exact accounting identity, into new prompt, replayed context, completion, reasoning, tool-schema, tool-argument, and tool-observation tokens. Token-demand functions over families of traces are stated with ordinary $O/\Theta$ in named scale variables under an explicit quality floor. We prove a replay law: under full-history replay, a $K$-round loop costs $\Theta (K^2)$ tokens, with a closed-form depth beyond which replay dominates. Under random termination, expected token demand is finite if and only if $\mathbb{E}[M^2]<\infty$, and the bill inherits half the tail index of the interaction count. We also give an exact log-mean Divisia identity that attributes an empirical scaling exponent to mechanisms. We apply Tokenometrica to 26,437 public trajectories from $\tau$-bench, ${\tau }^2$-bench, and SWE-agent, covering nine LLMs including a reasoning model; the reconstructed meters match provider-reported usage within 0.6% median error. Replayed context and repeatedly exposed tool schemas account for 89–96% of tokens in every system. Model-generated tokens are under 3% for non-reasoning agents, and reasoning adds only 5.3% for o4-mini because it is never replayed. On SWE-agent the token elasticity in rounds rises from 1.06 to 1.69 as runs lengthen, and replay explains 93% of it. Replay-aware forecasts cut the error of interaction-count extrapolation by about half. Live $\tau$-bench runs confirm the architectural saving that counterfactual accounting predicts, but expose a behavioral cost: with less in context an agent takes more calls, which replay makes expensive, so masking keeps half its predicted saving and every tool-loading variant raised the bill. A 15-round circuit breaker makes each resolved SWE-agent issue $3.2\times$ cheaper.