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

With no annotations, the description must carry the full behavioral burden. It does disclose the computation formula and a payment/usage constraint ('5 free trial calls per signed wallet'), which is genuinely useful context, but says nothing about edge cases (e.g. mean of zero producing an undefined result) or what the response contains.

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 gives the operation and formula with no padding. The trailing emoji/promo clause is minor noise for tool selection but does convey a real usage constraint.

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?

With no output schema and no annotations, the description should ideally cover input format and return shape. It adequately conveys what is computed but leaves the only parameter's format and the result structure unspecified, which is a meaningful gap for a computation tool.

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, so the description must compensate — and it does not. An agent cannot tell from either source whether 'values' is a comma-separated string, a JSON array literal, or a space-delimited list, which is essential for correct invocation.

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 verb ('Computes') and the exact statistic, plus the formula ('population standard deviation divided by mean'), which disambiguates it from a sample-based coefficient of variation. It does not, however, distinguish itself from the near-identical sibling x402-coeff-variation, which an agent could equally well 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?

There is no statement of when to use this tool versus alternatives, no prerequisites, and no mention of the obvious duplicate sibling x402-coeff-variation. The only context given is a promotional note about free trial calls.

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