probability.poisson_pmf

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

Annotations already declare readOnly/idempotent/closed-world, so safety is covered. The description adds meaningful behavioral detail: computation via scipy float64 and a return value rounded to 10 significant figures as a string, which the agent would otherwise not know.

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?

Three sentences, front-loaded with the formula, then numeric-precision behavior, then the parameter caveat. Efficient and every sentence carries information.

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?

An output schema exists so return structure needn't be re-explained, yet the description still flags the rounded string return. Both parameters and the key computation semantics are covered; little is missing for a two-parameter math tool.

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 0%, so the description carries the full burden. It specifies k is a non-negative integer, lam is a positive decimal string, and gives the important semantic constraint that lam must match the observation interval length — compensating well for the empty 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 states a specific verb and resource: compute the Poisson probability mass P(X=k; λ). It is clearly distinguishable from poisson_cdf (cumulative) and other probability siblings by naming the exact function computed.

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?

It provides a valuable usage caveat that lam must be the interval-matched mean, not a per-unit-time rate. However, it never explicitly routes between this and siblings like poisson_cdf, so when-to-use versus alternatives is only implied.

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