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. It explains the sign interpretation of the result, which is useful, but it does not disclose data requirements (e.g., minimum number of observations), behavior on degenerate inputs, or the return shape. Critically, the instruction "Provide values array" conflicts with the empty input schema, which is a behavioral mismatch an agent will hit at invocation time.

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 sentences with the verb and resource front-loaded, and the interpretive note about tail direction earns its place. The "Skewness:" prefix is mildly redundant with the tool name but not harmful. The values instruction is vague, but the text is appropriately sized.

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 statistical tool with no annotations, no output schema, and an empty input schema, the description is insufficient for reliable invocation. It fails to specify the form of the values input, the minimum array size, whether this is population skewness (given the skewness-sample sibling), or what the tool returns. An agent would likely guess incorrectly on the population/sample distinction and the parameter contract.

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 description names the key conceptual input ("values array") and explains what it represents, which is beyond what the empty schema provides. However, the schema defines zero properties, so an agent cannot map that instruction to an actual parameter to populate. The 0-param baseline of 4 is pulled down by the instruction referencing a parameter that does not exist in the schema.

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?

"Calculate the skewness of a distribution" is a specific verb+resource statement, and the parenthetical clarifies the interpretation of the result (positive=right tail, negative=left). However, it does not distinguish this tool from the direct sibling x402-skewness-sample, so an agent cannot tell whether this is the population or sample variant without external knowledge.

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 guidance is given on when to use this tool versus alternatives. The sibling x402-skewness-sample is nearly identical in name, yet the description never explains the population-vs-sample tradeoff that should select one over the other, nor does it say when skewness is the right statistic versus get_stats or other distribution tools.

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