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

With no annotations provided, the description carries the full behavioral burden. It discloses the core computation and the non-negative input constraint, which is useful. However, it omits behavioral details such as the schema's string-typed inputs, behavior when k > n, return format, or overflow/precision limitations. For a pure calculation tool this is adequate but not thorough.

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 two efficient sentences, front-loading the formula and adding a concise constraint. Every word contributes meaning, with no fluff or repetition.

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 deterministic tool, the description explains what is computed and the input constraint. Yet it lacks explicit mention of the return value, the string-vs-number input type mismatch, and edge-case behavior such as n < k. Given there is no output schema and no annotations, these omissions leave an agent to guess about important invocation details.

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?

The schema descriptions are vague ('K to process', 'N to process'), and the tool description adds meaningful semantics by explaining n and k's roles in the formula and requiring both to be >= 0. However, there is a notable inconsistency: the schema declares both parameters as strings, while the description implies numeric values ('both >=0') without clarifying whether the API expects string representations of numbers. Since schema coverage is 100%, the baseline is 3, and the description only partially compensates for the conceptual gap.

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 operation: 'Calculate the binomial coefficient C(n,k)' along with the mathematical interpretation 'number of ways to choose k items from n'. This precise verb+resource pairing easily distinguishes it from even similarly named siblings like x402-binomial-coefficient or x402-combination-count.

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 says 'Provide n and k', which is a minimal usage directive, but it gives no guidance on when to choose this tool versus the many closely related siblings such as x402-binomial-coefficient, x402-combination-count, x402-permutations, or x402-multinomial. It also does not state any exclusions or alternative selection criteria.

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