Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

Annotations already declare readOnly and idempotent, and the description adds valuable behavioral context: 'Pure text computation, no simulation, no RNG — deterministic output,' the educational intent ('TEACH'), and a key limitation ('complexity factors... the M/M/c model can't see'). This goes beyond annotations and is consistent with them.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Is the description appropriately sized, front-loaded, and free of redundancy?

Three sentences, each serving a distinct purpose: what the tool returns, when to use it, and its deterministic/limitation nature. No redundancy or filler; information is front-loaded and efficiently structured.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

Without an output schema, the description fully enumerates the output components ('where you sit on the utilization curve, what ρ means, what one more/fewer server would do, and complexity factors'). It also covers optional parameter behavior and determinism, making it complete for an agent to select and invoke correctly.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema coverage is 100%, so baseline is 3, but the description adds meaning by linking arrivalRate, serviceRate, and servers to ρ computation and by explaining the optional parameter's behavior: 'If omitted, the tool computes ρ from the inputs and gives a parameter-only interpretation.' This clarifies how parameters influence the output beyond what the schema states.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Does the description clearly state what the tool does and how it differs from similar tools?

The description clearly states the tool 'returns a queueing-theory framed interpretation' for an M/M/c configuration, listing specific output components like utilization curve position and plain-language ρ meaning. It distinguishes itself from siblings by explicitly contrasting with simulation ('no simulation, no RNG') and framing its role as teaching context around a number, not just returning the number.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Does the description explain when to use this tool, when not to, or what alternatives exist?

Provides explicit when-to-use guidance: 'Use this to TEACH while answering — when the user wants context around a number, not just the number itself.' It implies alternatives (simulation tools, theoretical explanations) but does not name specific sibling tools or give explicit when-not-to-use conditions, stopping short of a 5.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.