What does this equation mean?

A simple linear model makes the assumption underneath that spread explicit. If a system prompt costs $T_0$ tokens before any tools are added, and each of n tools costs on average $\bar{t}$ tokens to describe, total schema overhead is approximately $T(n) \approx T_0 + n\,\bar{t}$. Under a fixed context budget B , the largest catalogue that fits is roughly $n_{\max}$ $\approx$ (B - $T_0$)/$\bar{t}$ . The model is a reasonable first approximation, and it is also the assumption a tenfold per-tool variance directly undermines: $\bar t$ is not a constant of the tool, it is a property of how verbosely that tool’s schema and description happen to be written, which is an editorial choice rather than a physical fact about the function. A recent controlled study of exactly this trade-off tested fourteen models from 1.5B to 32B parameters plus one frontier API model across 6,566 controlled tool calls at three context budgets, and found that at an 8K-token budget uncompressed JSON schemas produced a near-zero 2.6% average exact-match accuracy, while a compression technique recovering 44 to 50% of the schema tokens lifted that same accuracy by an average of 20.5 percentage points across all eight models tested at that budget, with the gap narrowing to a point or less once the budget widened to 32K tokens [ 12 ] . The same paper estimated that frontier models could accommodate roughly 494 tools described as ordinary JSON schema before overflowing context, versus over 800 with compression applied [ 12 ] — a second confirmation that “how many tools can this system hold” is a joint function of budget and schema verbosity, not a fixed number attributable to the model alone.