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

With no annotations at all, the description carries the full behavioral burden, yet it says nothing about which estimator is used (sample vs population), input format (comma-separated? JSON array?), accepted value types, or the shape of the result. For a statistics tool sitting beside several near-identical stddev variants, that omission is material.

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?

Two short sentences, front-loaded with the purpose and then the input hint, with no filler. It is efficient, though 'Stddev:' as a prefix is slightly redundant with the tool name.

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 calculation tool with no annotations and no output schema, the description should at minimum pin down sample-vs-population and the input string format; it does neither, leaving an agent unable to choose between this and the several other stddev-suffixed siblings.

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 reported at 100%, so the baseline is 3, and the sentence 'Provide numbers or values array' does sketch that one of the two params carries the data. It does not explain whether 'numbers' and 'values' are aliases, mutually exclusive, or whether the string should be comma-separated, so it adds little beyond the schema's own tautological descriptions.

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 gives a specific verb and resource ('Calculate the standard deviation of a set of numbers'), which is unambiguous on its own. However, it does nothing to distinguish this tool from the many closely related siblings (x402-std-dev-population, x402-std-dev-sample, x402-population-stddev, x402-variance-sample, x402-trimmed-std), so an agent cannot tell which standard-deviation 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?

There is no guidance on when to use this tool versus the alternative stddev/variance siblings, and no statement of whether it computes a sample or population statistic. The only usage-like instruction ('Provide numbers or values array') describes input, not selection criteria.

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