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

Annotations already declare readOnlyHint, idempotentHint, and destructiveHint=false, so the safety profile is covered. The description adds that mean & variance are returned (useful since there is no output schema) and how params map per distribution, but says nothing about pagination, error behavior, or return structure beyond that.

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?

Two dense sentences, zero waste, front-loaded with the verb and resource before the per-distribution parameter mapping. Every clause earns its place.

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 4-param tool with a nested object, no output schema, and safety annotations, the description covers families, operations, combinability, and param keys. It could note that only 'dist' is required and clarify the return shape beyond mean & variance, but is otherwise complete.

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?

With only 50% schema coverage, the description carries the key gap: it fully documents the otherwise-bare nested 'params' object, giving per-distribution keys (normal {mean,sd}, t {df}, chi2 {df}, binomial {n,p}, poisson {lambda}). The 'at' and 'p' meanings are already in the schema, so this adds strong but not exhaustive value.

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?

States a specific verb ('Evaluate') and resource ('probability distribution'), then enumerates the supported families and the exact operations (pdf/pmf, cdf, quantile). An agent can immediately distinguish this statistical-evaluation tool from siblings like bayes_update or hypothesis_test.

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?

Provides clear context for when the tool applies by spelling out the operations ('pdf/pmf and cdf at a value, and/or the quantile at a probability'), and the 'and/or' signals these can be combined. It does not name alternatives or state when another tool (e.g., hypothesis_test) is preferred, so it stops short of explicit routing.

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