MCP Math Server

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

No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool performs a statistical test but does not describe key behaviors such as output format (e.g., p-value, test statistic), assumptions (e.g., large sample sizes), or error handling. This is a significant gap for a tool with no annotation coverage, limiting the agent's ability to predict its behavior.

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 concise and front-loaded, consisting of a single sentence that directly states the tool's purpose, followed by domain/category in parentheses. There is no wasted text, and it efficiently communicates the core function. However, it could be slightly more structured by separating usage notes, but this is minor.

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 test with 5 parameters, no annotations, and no output schema, the description is incomplete. It does not explain the tool's behavior, output, or parameter meanings, leaving critical gaps for the agent. While conciseness is good, the lack of contextual details makes it inadequate for effective tool use.

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 description coverage is 0%, meaning none of the parameters (successes1, n1, successes2, n2, alpha) are documented in the schema. The description does not add any parameter semantics—it does not explain what these inputs represent (e.g., counts and sample sizes for two groups, significance level) or their constraints. With low coverage and no compensation in the description, the agent lacks necessary context for correct invocation.

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: 'Perform two-proportion z-test to test whether two population proportions differ significantly.' It specifies the verb ('perform'), resource ('two-proportion z-test'), and domain/category. However, it does not explicitly differentiate from sibling tools like 'z_test' or 'fishers_exact_test', which might handle similar statistical tests, so it falls short of 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 minimal usage guidance. It mentions the domain ('statistics') and category ('inference'), which implies context, but does not specify when to use this tool versus alternatives (e.g., 'z_test' for one-sample tests or 'fishers_exact_test' for small samples). No explicit when/when-not instructions or prerequisites are given, leaving the agent with insufficient guidance.

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