variance

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

Annotations already indicate readOnlyHint, destructiveHint, idempotentHint. The description adds the formula distinction (n-1 vs n) but no additional behavioral context like error handling or large data behavior.

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, very concise, front-loaded with main purpose. No wasted words.

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 mathematical tool with two parameters and no output schema, it covers the key distinction. Lacks explanation of return value, but that is acceptable.

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 has 0% coverage. The description explains the 'population' parameter but not the 'numbers' parameter, which is required. Partial compensation.

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 it calculates variance and distinguishes between sample (n-1) and population (n) based on the 'population' parameter. It is specific and differentiates from sibling tools like std_dev.

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 tells the user when to set 'population: true' for population variance, implying default is sample. Does not explicitly mention alternatives or when not to use, but context is clear.

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