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

With no annotations, the description carries the full burden. It does disclose the key computational behavior (Bessel-corrected n-1 denominator) and a rate/quota trait ('5 free trial calls per signed wallet'), which is genuine behavioral context. However it says nothing about input requirements, what happens with n<2, or the shape of the result.

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?

Front-loaded single sentence that leads with the formula, followed by a short quota note. Efficient overall; the emoji and trial-call tail is mild noise but does not bury the core content.

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 one-parameter math utility with no output schema and no annotations, the description covers what is computed but omits input formatting and result shape. It is adequate but leaves the two details an agent most needs in order to invoke it 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?

There is 1 parameter at 0% schema description coverage, and the description only calls it 'an array' while the schema types it as a plain string. The encoding (comma-separated, JSON, whitespace-delimited?) is left completely unspecified, so the agent cannot construct a valid call from the description alone.

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 and resource ('Computes the sample variance of an array') and, critically, names the discriminating formula ('dividing by n minus 1'), which is exactly what separates it from the sibling x402-variance-population. An agent can pick this over the population variant without opening either schema.

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?

The 'sample variance' framing implies when it is appropriate (sample data, n-1 denominator), but there is no explicit when-to-use guidance and no mention of the near-identical siblings x402-variance or x402-variance-sample. Usage is inferable rather than stated.

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