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

With no annotations, the description carries the full behavioral burden. It discloses the mathematical definition (divide by n) but nothing about input parsing, output format, or edge cases (n=0, single value, non-numeric entries). The '🆓 5 free trial calls per signed wallet' note is billing context rather than operation behavior.

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, front-loaded with the operation and immediately followed by the defining formula. The trailing emoji/pricing promo is filler but does not obscure the meaning.

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 statistical utility with no annotations and no output schema, the concept is adequately defined, but the untyped string input parameter is a genuine gap that the description does not close. Enough to call the tool in principle, not enough to call it correctly on the first try.

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?

One parameter with 0% schema description coverage, so the description must compensate. Saying 'of an array' hints that 'values' is a numeric collection, but the schema types it as a bare string with no format given (comma-separated, JSON, newline-delimited?). The encoding an agent must actually send is left ambiguous.

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 population standard deviation of an array') and distinguishes the population variant from the sample variant with 'dividing by n'. It does not, however, name or differentiate against identical-looking siblings such as x402-std-dev-population or x402-stddev, so an agent cannot tell which of the aliases to call.

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 formula clause implies a population-vs-sample distinction, but there is no explicit statement of when to use this tool instead of x402-std-dev-sample, x402-sample-variance, or the other stddev aliases. No prerequisites, no exclusion conditions, no alternative named.

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