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

No annotations are provided, so the description carries the full burden of behavioral disclosure, yet it provides nothing. It does not state whether this returns a probability value, a distribution object, or a sample; whether it is a pure computation; or what the output format is. With zero annotation coverage, this is a critical gap.

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?

While brief, the content is pure redundancy—the same phrase repeated. Being short is not a virtue when it conveys no information; this is under-specification, not conciseness.

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 this is a probability-distribution calculation tool with no annotations and no output schema, the description should explain the formula or expected inputs/outputs. It supplies none of this, leaving the agent completely unable to invoke it correctly without external knowledge.

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 coverage is 100% but both parameters are typed as strings with generic descriptions ('K to process', 'P to process'). The description adds nothing about what k and p represent mathematically (number of trials, success probability), their domains, or valid ranges. For a math tool, this is inadequate despite the schema nominally existing.

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 'Geometric Pmf: Geometric Pmf' merely restates the tool name twice without specifying what it computes or returns. It does not distinguish this from numerous sibling probability tools like x402-binomial-pmf, x402-poisson-pmf, or x402-multinomial, leaving an agent guessing what a 'geometric PMF' calculation entails or which distribution parameters it uses.

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?

No guidance on when to use this tool versus alternatives. With hundreds of sibling statistics/probability tools, an agent has no basis for selecting this one over x402-binomial-pmf or x402-poisson-pmf, nor any indication of the mathematical use case this serves.

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