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 behavioral trait (n-1 sample denominator) and the payment gating ('5 free trial calls per signed wallet'). It says nothing about edge cases such as a single-element or empty array where n-1 yields division by zero, nor about output shape.

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?

One front-loaded sentence stating the computation, followed by the trial-call note; nothing is padded. The only waste is restating the tool name as a 'Std Dev Sample:' prefix.

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?

No output schema and no annotations, so the description must carry everything. It covers the computation and pricing but leaves the input serialization and the return value undetermined, which is a meaningful gap for a tool whose sole parameter is an untyped string.

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 coverage is 0% and the single parameter 'values' is typed as string with no description. The description says 'of an array', but does not explain how the array is encoded into a string (JSON array, comma-separated, etc.), which is exactly the ambiguity the description needed to resolve.

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 ('Returns') and resource ('sample standard deviation of an array') and pins down the algorithm with 'dividing by n minus 1', which implicitly separates it from population std dev. It never names the sibling it is not (x402-population-stddev, x402-stddev, x402-std-dev-population), so differentiation relies on the reader parsing the formula.

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 pick this over the many adjacent stat tools (population std dev, sample variance, variance-sample, standard-error). Nothing states when-not to use it or what input shape is expected, so selection is left entirely to inference from the name.

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