calculate_probability_binomial

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

Without annotations, description carries full burden. It states it returns exact_probability, cumulative_probability, and std_deviation, adding some value. However, it does not mention constraints like k must be ≤ n or error scenarios, which the schema partially covers.

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 sentences: first defines core function, second lists outputs and directs to related tools. No redundant information, efficiently front-loaded.

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?

The description mentions outputs and bundles, but lacks usage context such as when to choose binomial over other distributions. However, given the output schema exists and parameters are well-defined, it is mostly 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?

Schema coverage is 100% with adequate descriptions. The description adds no additional meaning for parameters beyond the schema, hence a baseline score of 3.

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?

Description clearly states it calculates binomial probability P(X=k) and cumulative P(X<=k), with specific output fields. It distinguishes from sibling calculators by referencing the 'education' bundle, making its purpose unambiguous.

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?

No explicit guidance on when to use this tool vs alternative probability calculators. The pointer to list_bundles for related calculators is vague and does not help an agent decide between binomial and other distributions.

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