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

Annotations already declare readOnly, idempotent, non-destructive and closed-world, so the safety profile is covered. The description still adds real value beyond them: concrete API ceilings (hypergeometric draws 200, shapes/df 1000, Poisson mean 1000) that are tighter than the browser, the decimal-probability convention, the no-fitting/no-guarantee caveats, and a prompt to inspect the returned source URL.

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?

The first sentence is well front-loaded and the limits are concrete, but the tail becomes a string of terse imperatives ('Put tool fields inside inputs', 'Do not pass the REST calculator field inside MCP arguments') that are cryptic out of context and partly redundant with 'Follow its required fields and exact choices'.

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 tool this complex — 20+ oneOf branches, nested objects, deep-conditioned required fields — the description covers scope, numeric caps, assumption caveats and nesting conventions, and an output schema exists so return values need not be explained. The remaining gap is a mapping from real-world question to the correct mode/query combination, which the agent must reconstruct from enum names.

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?

Reported schema coverage is 0%, but the mode-specific branches do carry per-field descriptions (e.g. rate as 'average event COUNT', shape as 'supplied or separately fitted'), so the schema does much of the work. The description contributes structural guidance — wrap fields in 'inputs', pass units/modelVersion only when listed, do not pass the REST calculator field — but never explains what mode, query, x or target mean, leaving a real gap for a 26-mode tool.

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 opening sentence gives a specific verb plus an enumerated set of resources: probabilities, tails, percentiles, event relationships, Bayes updates, counts, expected values, and Wilson/exact proportion intervals, and '26 explicit methods' matches the 26 mode enum values in the schema. The scope exclusions ('No distribution fitting, random simulation or real-world guarantee') further separate it from adjacent calculators, though no sibling is named explicitly.

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?

Negative scope ('no distribution fitting, random simulation or real-world guarantee') functions as when-not guidance, and 'inspect assumptions and returned source URL' hints at workflow. However, there is no routing guidance telling the agent when to prefer this over sibling calculators, and most of the remaining text addresses serialization rather than tool selection.

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