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

No annotations are provided, so the description must disclose behavioral traits. It briefly lists calculations but does not explain side effects, permissions, or behavior when 'r' is omitted (factorial only). The constraints from the schema (n max 170) are not mentioned in the description, leaving the agent unaware of limitations.

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 with two sentences. The first sentence states the core functionality, and the second suggests a related resource. It is front-loaded with key actions, though the 'Returns: {factorial}' part is slightly misleading. Still, it is efficient with no extraneous text.

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 tool's complexity (three calculations from two parameters), the description is not fully complete. It lacks guidance on how to obtain each result (e.g., factorial vs permutation). The existence of an output schema is noted but not described. For a tool in a large set of siblings, more context is needed.

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%, so the baseline is 3. The description adds slight context by linking parameters to functions (e.g., 'r value for P(n,r) and C(n,r)') but does not provide additional meaning beyond the schema. The parameters are already well-documented.

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 calculates factorial, permutations, and combinations. It uses specific verbs and resources, distinguishing it from the many other calculate tools. However, the return value description is incomplete, mentioning only 'factorial' while the tool also returns permutation and combination results.

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 does not explicitly state when to use this tool over alternatives. It mentions 'See list_bundles for related math calculators', which hints at grouping but does not provide clear usage context or exclusions. No direct comparison with other similar tools is given.

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