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

With no annotations, the description carries the full burden of behavioral disclosure, but it only restates the computation and hints at two input modes ('numbers or values array'). It does not explain whether the result is sample or population standard deviation, how the input string is parsed, what happens with invalid or empty input, or what the output looks like.

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?

The description is short and front-loaded with the core purpose. The second sentence about providing numbers or a values array adds some value, though it is vague. There is no wasted prose, but the opening 'Stddev:' label is unnecessary.

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 tool, the description is not complete enough given the surrounding sibling tools. It fails to distinguish sample versus population standard deviation, does not define the input format, and provides no output expectations, all of which matter for correct invocation in this tool family.

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?

The schema already describes the single `numbers` parameter at 100% coverage, so the baseline is 3. The description adds slight semantic value by mentioning that either numbers or a values array can be provided, but it omits the expected string format and does not clarify whether the array is a JSON array or another representation.

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 clearly states the verb ('Calculate') and the resource ('standard deviation of a set of numbers'), so an agent knows the tool's core function. However, it does not disambiguate between sample and population standard deviation, which matters given siblings like x402-std-dev-sample, x402-std-dev-population, and x402-population-stddev.

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 description gives no explicit guidance on when to choose this tool over alternatives such as get_stats, x402-std-dev-sample, or x402-population-stddev. It only says to provide numbers or a values array, leaving the selection decision to inference.

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