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

With no annotations, the description carries the full burden, and it does disclose a useful edge case (returns null when the mean is zero) plus a free-trial quota. It does not disclose input format, error behavior for malformed values, or whether the result is a ratio/percent, so it is only partially transparent for a computation tool.

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?

A single front-loaded sentence that defines the formula precisely, with the free-trial note appended. Minor waste in the 'Coeff Variation:' prefix that merely restates the name, but overall tight and well-ordered.

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?

For a simple one-parameter math tool with no output schema, the description covers the computation and the zero-mean edge case, which is the core of what an agent needs. The missing input format for 'values' and lack of sibling differentiation are the main gaps.

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?

The single 'values' parameter has 0% schema description coverage, and the description only alludes to 'mean of values' without specifying how the input is supplied (comma-separated string, JSON array, etc.). With a documented parameter and a string type, the description should compensate but does not.

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?

States a specific computation (population standard deviation divided by the mean) with an explicit verb and resource, which is more than the name alone conveys. However, it does not distinguish itself from the near-identical sibling x402-coefficient-of-variation, leaving the agent unable to tell which CV tool to pick.

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?

No when-to-use guidance, no prerequisites, and no mention of alternatives or the near-duplicate x402-coefficient-of-variation sibling. The agent is left to infer usage entirely from the formula.

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