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

No annotations and no behavioral disclosure whatsoever. Nothing about input format (the single param is a string, presumably a list), numeric domain constraints, negative/zero handling, or output shape. The no-annotation burden is entirely unmet.

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?

It is short, but that brevity reflects under-specification rather than efficiency. The only content is a restatement of the name, so nothing meaningful is front-loaded.

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?

A single-parameter computation tool with no annotations, no output schema, and an ambiguous string input demands far more description than this. The definition does not supply the minimum needed to call the tool 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 100% but the one description present ('Values to process') is itself vague. The tool description adds no meaning about how values should be formatted (comma-separated? array?) even though the param being a string makes format knowledge essential.

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 "Geometric Mean: Mean of geometric" restates the tool name and gives a near-tautological gloss. It does not state a verb+resource operation or distinguish this from the many sibling mean/statistics tools such as x402-mean-of, x402-harmonic-mean, x402-weighted-mean.

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?

No when-to-use guidance, no exclusions, no named alternatives. In a toolset containing harmonic mean, weighted mean, geometric series, and geometric pmf siblings, the agent receives zero routing information.

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