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

No annotations are provided, so the description carries the full behavioral burden, and it discloses nothing: not whether the tool returns a probability, a log-probability, or a distribution array, not whether k must be a non-negative integer, and not that lambda must be positive. For a computational tool with zero annotation coverage this is a complete 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?

Brevity here comes from under-specification, not conciseness: the entire body is a duplicated token with zero informational content. There is nothing to front-load because nothing was said.

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?

No annotations, no output schema, and no domain constraints mean the agent cannot know the return type or valid input ranges for a two-parameter math function. The 100% schema coverage keeps this from being a total failure, but the definition is far from sufficient for correct invocation.

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 even though the description itself adds no parameter meaning. It is worth noting the schema's own text ('K to process', 'Lambda to process') is vacuous and conveys neither that k is the event count nor that lambda is the rate parameter, but the structured field does technically document both parameters.

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 'Poisson Pmf: Poisson Pmf' merely restates the tool name/title with no verb, no statement of what is computed or returned, and no differentiation from siblings such as x402-binomial-pmf, x402-geometric-pmf, or x402-normal-pdf. It is a tautology rather than a purpose statement.

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?

There is no when-to-use guidance, no mention of alternatives, and no indication of when a Poisson PMF is the right model versus other probability-mass tools in the sibling list. The agent is given nothing to route on beyond the name.

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