What does this equation mean?

Anthropic’s own engineering documentation gives concrete magnitudes for what n$\bar{s}$ looks like in a realistic deployment. A worked example lists five connected MCP servers — GitHub with 35 tools consuming roughly 26,000 tokens, Slack with 11 tools at roughly 21,000, Sentry with 5 tools at roughly 3,000, Grafana with 5 tools at roughly 3,000, and Splunk with 2 tools at roughly 2,000 — for a total the documentation states plainly: “That’s 58 tools consuming approximately 55K tokens before the conversation even starts” [ 5 ] . A separate figure from the same source is larger still: “At Anthropic, we’ve seen tool definitions consume 134K tokens before optimization” [ 5 ] . Dividing the first figure through gives a rough sense of scale — roughly 950 tokens of schema per tool on average across that particular set of five servers, an estimate this article derives from Anthropic’s published numbers rather than one the documentation states directly, and one that will vary considerably by tool. A single connected productivity suite can therefore spend more tokens describing what it could do than most single-turn prompts spend on the task itself.