calculate_z_score

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

With no annotations provided, the description carries the full burden. It describes the computation, inputs, and return values (z, percentile, p-value), which is transparent. It does not detail edge cases or assumptions, but these are minimal given the simple mathematical operation.

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?

Three sentences, front-loaded with the core purpose, efficiently covering inputs, uses, and outputs. Every sentence adds value with no redundancy.

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 with full schema coverage and an output schema, the description is complete: it explains what the tool computes, its uses, and what it returns. No critical information is missing.

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% with clear descriptions for each parameter. The description adds no additional semantic meaning beyond restating the inputs, so it does not compensate beyond the baseline.

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 that the tool computes z-score and percentile from three specified inputs, with explicit use cases for statistics and outlier detection. It distinguishes itself from numerous sibling calculate_* tools by naming its specific function and output.

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?

It explicitly says to use for statistics and outlier detection, and references list_bundles for related math calculators, implying when to explore alternatives. However, it does not explicitly state when not to use this tool over specific siblings.

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