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

Annotations already declare readOnly/idempotent/non-destructive, and the description adds genuinely new behavioral context: a paid x402 call at $0.001 USDC per successful invocation and an equivalent HTTPS endpoint. It also discloses validation rules (digit in the k! place must be 0..k, at most 20 digits) that determine when a call fails, though it doesn't say what an invalid input returns.

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?

Four short sentences plus a pricing line, front-loaded with the core definition and examples before constraints and payment details. No filler; every clause (format, examples, validity bounds, cost) contributes information an agent needs.

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?

With one required parameter, no output schema, and thin annotations, the description covers the return value ('the integer value'), input format, validity limits, and payment model. The only gap is error/failure behavior for non-canonical digits, which matters given the paid per-successful-call model.

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 0%, so the description must carry the semantics, and it largely does: the array is most-significant-first with the last entry as the 0! place, each position has a per-place bound, and two worked examples ground the encoding. What it doesn't add is behavior on out-of-range or over-long input, but the format itself is well covered.

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?

It states the operation and resource clearly: it converts factorial-base (factoradic) digits to their integer value, with worked examples ([2,1,0]=5, [3,2,1,0]=23) that remove any ambiguity about direction. It does not explicitly distinguish itself from the sibling factoradic/factoradic_digit/factoradic_length tools, so an agent must infer that this is the decode direction while 'factoradic' is the encode direction.

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 direction of conversion is implied by the input/output framing and the examples, but the description never says when to use this versus the sibling encode tool or the digit/length helpers. No exclusions or prerequisites are given; usage must be inferred from the tool name.

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