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

Annotations already declare readOnlyHint, idempotentHint, and openWorldHint=false, so the safety profile is covered. The description adds genuinely non-structured behavior: the pricing model ($0.05 per successful call over x402 USDC on Base), ddof semantics distinguishing sample vs population forms, and the reproducibility guarantee for percentile interpolation. It omits output format/pagination details, but for a deterministic pure-computation tool this is rich context.

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 single dense but well-ordered sentence front-loads the core purpose and the computed statistics, then layers ddof behavior, interpolation, and pricing. It is long but every clause carries information; minor density could be improved by splitting the parenthetical ddof explanation.

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?

There is no output schema, so the description carries the burden of enumerating returned fields, which it does comprehensively (including the *_population variants and quartiles). Combined with ddof, method, limits, and pricing, an agent has everything needed to call it 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 description coverage is 100%, so the schema already documents ddof, method, values, and percentiles; baseline is 3. The description reinforces ddof's default sample form and the always-population fields, and emphasizes the named interpolation method's purpose, but adds no syntax or format detail the schema lacks.

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+resource ('Descriptive statistics for a supplied numeric array') and enumerates exactly what is computed (count, mean, median, mode, variance, stddev, quartiles, IQR, skewness, kurtosis, percentiles). It is unambiguous against numeric siblings like num_radix or num_allocate, which serve entirely different purposes.

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?

The phrase 'in one call' implies the tool consolidates statistics that would otherwise require multiple computations, giving implied context. However, no sibling tool performs statistics, so there is no alternative to route to, and the description states no when-not-to-use conditions or input constraints (e.g. minimum array length).

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