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

With no annotations, the description carries the full burden. It usefully discloses the payment/trial model, which is real behavioral context, but says nothing about expected input format, whether the groups must be equal or unequal size, the numeric type of the output, or error behavior. For a stats tool with zero annotation coverage this is a substantial gap.

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 clauses with the operation front-loaded and no filler; the only slight detour is the promotional trial-call note appended at the end.

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 annotations, no output schema, and 0% parameter documentation, yet the description supplies only a one-line definition. For a four-parameter statistics tool with ambiguous parameter naming, this is not complete enough to call 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?

Schema coverage is 0% across four string parameters (a, b, group1, group2) and the description only says 'two sample groups'. It never explains which pair of parameters actually represents the groups, nor whether inputs are comma-separated strings, JSON arrays, or something else, so the agent cannot reliably construct a call.

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 pooled standard deviation') and names the input domain ('two sample groups'), so an agent knows exactly what operation it performs. It does not, however, distinguish itself from the very close siblings x402-pooled-variance, x402-std-dev-sample, or x402-stddev, leaving the agent to infer the difference.

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 choose pooled standard deviation over the sample/population stddev or pooled-variance siblings, and no prerequisites or exclusion conditions. The only contextual sentence concerns billing ('5 free trial calls per signed wallet'), not usage.

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