Large Language Models increasingly rely on structured data for inference and function calling. However, standard formats like JSON introduce significant verbosity that inflates token usage and inference costs. This analysis presents a formal mathematical comparison between TOON and JSON to evaluate whether TOON achieves quantifiable efficiency gains by eliminating structural redundancy.

Under the assumptions described below (compact JSON, canonical TOON, ASCII keys and punctuation, shallow to moderate nesting, and mostly unquoted TOON strings), TOON's structural overhead is lower than compact JSON for the structure families analyzed here, except arrays of arrays.