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

No annotations are provided, so the description carries the full burden. It does add one genuinely useful behavioral fact — the sign convention of the result (positive = right tail, negative = left) — which helps interpretation. It says nothing about input encoding, minimum sample size, or behavior on degenerate inputs, so it is only partially complete.

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?

A tight single sentence with the purpose front-loaded and no filler; the interpretation hint is appended efficiently. Slightly dense but nothing is wasted.

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?

With no output schema, the description is the only source of return-value semantics, and it only gestures at the sign meaning without stating the return type or scale. It also omits how the values string should be formatted. Adequate for a trivial calculator, but not thorough.

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 100% with a single parameter, so the baseline is 3. The description does say 'Provide values array', which reinforces the single input, but it also calls it an 'array' while the schema types it as a string, adding a mild ambiguity rather than resolving one.

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 skewness of a distribution') and clarifies what the metric measures, so an agent knows exactly what computation this performs. However, it never distinguishes itself from the sibling x402-skewness-sample, and population versus sample skewness is precisely the distinction an agent would need; that omission keeps it below a 5.

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 statement of when to use this tool versus alternatives such as x402-skewness-sample, x402-kurtosis-sample, or x402-stats. Usage is only implied by the metric name, and no preconditions (e.g. minimum number of values) are given.

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