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 covered. The description adds one useful behavioral note beyond that — the multiplicative implementation avoids factorial overflow for large n — but says nothing about precision, return type, or limits on n.

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?

A single front-loaded sentence with zero filler; the operation is stated first and the implementation note follows. Nothing in it is redundant or wasteful.

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 two-parameter pure-math calculator with full schema coverage and annotations covering safety, the description is nearly complete. The only omission is the return value (a single count), which is trivial to infer, though there is no output schema to state it.

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% ('Total items, at least 1' and 'Items chosen, between 0 and n'), so the schema already carries parameter meaning. The description's 'n choose r' phrasing restates the parameter relationship without adding constraints or format details beyond the schema.

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 a specific verb and resource ('Compute the number of distinct combinations, n choose r'), which is unambiguous against a sibling list of unrelated calculators. It does not explicitly differentiate itself from any sibling, but no close alternative (e.g. permutations) exists to confuse it with.

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?

Usage is only implied: an agent can infer this is the tool for choosing unordered subsets, but the description gives no when-to-use framing, no comparison to alternatives such as permutations, and no guidance on edge cases like r = 0 or r = n.

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