binomial_cdf

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

No annotations are provided, so the description must fully disclose behavioral traits. It only states what the tool calculates without mentioning input constraints (e.g., valid ranges for k, n, p), error handling, performance characteristics, or output format. This is insufficient for a tool with three parameters and no output schema.

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 description is extremely concise and front-loaded, consisting of a single sentence that directly states the tool's purpose. There is no wasted verbiage or unnecessary information, making it efficient for quick understanding.

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 the complexity of a statistical calculation with three parameters, no annotations, and no output schema, the description is incomplete. It lacks essential details such as parameter meanings, constraints, example usage, and what the output represents. This makes it inadequate for effective tool 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?

The input schema has 0% description coverage, and the description does not add any parameter semantics. It fails to explain what k, n, and p represent (e.g., k = number of successes, n = trials, p = probability of success) or their valid ranges. With three undocumented parameters, this is a critical gap.

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 clearly states the tool's purpose: 'Calculate the cumulative distribution function (CDF) of the binomial distribution.' It specifies the verb ('calculate'), resource ('CDF'), and domain ('probability, Category: general'). However, it does not explicitly differentiate from sibling tools like 'binomial_pmf' or 'binomial_sample,' which would be needed for a perfect score.

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?

The description provides no guidance on when to use this tool versus alternatives. It mentions the domain and category but does not specify use cases, prerequisites, or comparisons to related tools such as 'binomial_pmf' or 'normal_cdf.' This leaves the agent without clear usage instructions.

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