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

Annotations already declare readOnlyHint=true, destructiveHint=false, and openWorldHint=false, so the safety profile is fully covered and the description adds nothing on top of it. It does not mention behavior on edge cases (single-element sample data, division by zero) or anything beyond the schema's own default. No contradiction with annotations, but very thin added value.

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 short fragments, front-loaded with the purpose and followed by the key parameter. No waste, though the telegraphic style leaves it slightly under-specified rather than tight.

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 two-parameter, single-purpose tool with a full schema and an output schema, this is minimally sufficient to call correctly. The gap is the lack of any guidance on choosing population vs sample, which matters for numerical correctness.

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 description coverage is 100% and both parameters carry descriptions and examples, so the baseline of 3 applies. The description only echoes the variance_type enum and its default, which the schema already states, adding no new semantics.

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 names the exact statistical quantity (variance) and both supported variants, which is enough to tell it apart from neighbors such as calculator_std, calculator_mean, and calculator_range. It stops short of an explicit verb, but the resource is unambiguous.

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?

There is no statement of when to use this over calculator_std or calculator_range, nor when to prefer population versus sample variance. The default is restated, but no selection criteria are given, so the agent must infer from statistical convention alone.

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