covariance

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

No annotations are provided, so the description carries the full burden of behavioral disclosure. It only states what the tool does ('calculate covariance') without detailing behavioral traits such as input validation (e.g., handling non-numeric strings in arrays), error handling, computational complexity, or output format. For a statistical calculation tool with no annotation coverage, this is a significant gap in transparency.

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 concise and front-loaded, stating the core purpose in the first phrase. The additional context in parentheses ('measures how variables change together') and domain/category tags add value without unnecessary verbosity. However, the domain/category tags might be slightly redundant if the server context already implies statistical tools, but they do not detract significantly from clarity.

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?

Given the complexity of a statistical calculation with 3 parameters (2 required), no annotations, no output schema, and 0% schema description coverage, the description is incomplete. It lacks essential details such as parameter explanations, behavioral context, and output expectations. For a tool that performs a non-trivial mathematical operation, this description does not provide enough information for reliable agent invocation.

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 input schema has 0% description coverage, and the tool description does not explain the parameters at all. It mentions 'two datasets' but does not clarify the meaning of 'xs', 'ys', or 'population'. Without any parameter semantics in the description, the agent must rely solely on the schema's property names, which is insufficient for understanding how to use the tool correctly.

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 tool's purpose: 'Calculate the covariance between two datasets' with a brief explanation ('measures how variables change together'). It specifies the verb ('calculate') and resource ('covariance between two datasets'), making the function unambiguous. However, it does not differentiate from sibling tools like 'correlation', which is a related statistical measure, leaving room for improvement in sibling distinction.

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 provides no guidance on when to use this tool versus alternatives. It mentions the domain ('statistics') and category ('general'), but this is too vague to help an agent decide between this and sibling tools like 'correlation' or 'variance'. There are no explicit when/when-not instructions or named alternatives, limiting its utility in tool selection.

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