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

No annotations are supplied, so the description carries the full behavioral burden. It discloses the pricing/auth context (5 free trial calls per signed wallet), which is genuinely useful, but says nothing about the underlying formula (sample vs population), how errors or non-numeric input are handled, 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?

The definition is short and the computational purpose is front-loaded. The leading 'Stddev:' duplicates the tool name, and the trial-call sentence is promotional rather than operational, so a portion of the limited text does not help invocation.

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 two-parameter numeric calculator with no annotations and no output schema, the description should at minimum pin down the input format and which standard deviation is computed. It leaves both unresolved while spending a sentence on pricing, so an agent could easily call the wrong sibling or pass malformed input.

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 description coverage is 0%, so the description must compensate for the two undocumented string parameters. It only says 'Provide numbers or values array', which reveals that the two fields are interchangeable but not the expected format (comma-separated, JSON array, whitespace-delimited), whether they are mutually exclusive, or what happens if both or neither are supplied.

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: 'Calculate the standard deviation of a set of numbers.' An agent knows exactly what computation happens. However, it fails to distinguish itself from sibling tools such as x402-std-dev-sample, x402-std-dev-population, x402-population-stddev, and x402-moving-std, so the agent cannot tell which stddev variant this is.

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?

'Provide numbers or values array' tells the agent how to supply input, not when to prefer this tool over the many stddev alternatives. There is no guidance on sample vs population, minimum input size, or the sibling tools it replaces, leaving selection entirely to inference.

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