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

With no annotations, the description carries the full behavioral burden. It does disclose the core semantics ('how many std deviations from the mean') and scopes the computation to a population, which is real behavioral information. However it says nothing about degenerate cases (zero std deviation), sample-vs-population distinctions, input parsing, or error behavior for a numeric utility.

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 tight sentences, front-loaded with the core definition followed by the input/output contract. The leading 'Zscore:' merely restates the tool name and is slight waste, but the rest is efficient.

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 two-parameter, no-output-schema numeric tool the description covers the essentials: what is computed, what to supply, and what comes back. It still leaves open how the 'values' string is delimited, which std-dev convention is used, and what happens on zero variance, so it is adequate but not fully 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 nominally 100%, but the schema descriptions are vacuous ('Value to process', 'Values to process'). The description compensates by explaining the relationship between the two parameters: 'values' is the population array and 'value' is the element being scored. That is meaningful semantics the schema does not provide, though it does not reconcile the odd string typing of both fields.

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 states a specific verb and resource ('Calculate the z-score (standard score) of a value within a population') and even parenthesizes the synonym, so the operation is unambiguous. It does not name the obvious sibling x402-zscore-array or x402-standardize to disambiguate single-value vs whole-array behavior, but the phrase 'Provide values array and value' implies the single-element scope.

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?

There is no explicit when-to-use guidance, no prerequisites, and no mention of an alternative sibling (x402-zscore-array, x402-standardize, x402-normalize-array) that an agent must choose between. Usage is only inferable from the described inputs.

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